§1 — The three responses, and why their names will not do the work
Before I can name a trigger I have to say what the triggered acts are, because the words I have been using for them — reversal, redefinition, continuation — are names, and names are exactly what the task tells me not to sort by. So I take the three apart into the acts they denominate, and for each I ask what must be true of a solver's situation for the act to be available at all.
Reversal is the least ambiguous of the three, and it is the one my held episode carries most concretely. My consolidated theme on reluctant recovery holds that "when a track becomes unproductive the solver does not instantly reroute but engages in reluctant recovery: retracing to the point of the dead end and starting over". Two features of that sentence matter for the trigger question and I want them read carefully rather than passed over. First, the return is to a point — "retracing to the point of the dead end" — not to the beginning, not to wherever the solver happens to stand, but to the locus of the failure. That means the act of reversal presupposes that the solver has located the locus, and locating it is itself an observation about its own progress.. Reluctance is not decoration. If the solver reroutes instantly, there is no episode to describe, because the solver was never committed enough to the track for its failure to be an event. The reluctant recovery episodes are the ones where the dead end cost something to abandon — and that cost is the trace of the thing a trigger has to explain.
Redefinition is harder, and my held material catches it at a different grain. My consolidated theme on representation holds that subjects operate internally on molar rather than molecular representations, "transforming even a Necker cube into an internal representation", and the same theme holds the set framing: a problem defines U, the class of possible configurations, and G, the satisfying subset, with a generator producing elements of U at some cost. That pair is what redefinition acts on. To redefine is to change the space — to change what counts as a state, or as a legal move, or as the goal — and the thing that changes is exactly one of U, G, or the generator. My reading, and I mark it as mine: redefinition is the only one of the three responses that leaves the solver's position untouched while changing the board, whereas reversal leaves the board untouched while changing the position. That distinction will matter when I come to sort the triggers, because it means the two responses are keyed to different objects — one to the solver's place in the space, the other to the space itself — and an observable precondition that precedes one is not automatically a precondition that precedes the other.
Continuation is the one I have the least held material about, and I have to say so plainly rather than reason it into existence. No node in my net, so far as I can reach it, names continuation as an episode type; there is no held description of a solver deciding not to switch. This is a real gap and its shape is worth naming before I go further, because it changes what the note can claim. If reversal and redefinition are marked by the presence of something — a located locus, a changed space — continuation may be marked by the absence of that something, in which case it is not a third positive trigger at all but the default condition under which neither of the other two fires. That possibility is a conjecture of mine, not something my net states, and I hold it as one until the episodes test it.
What the three-into-act reduction buys me. I started with three names and I now have three structural questions, all of them about the solver's relation to its own situation rather than about the acts themselves:
- For reversal: what must a solver notice to locate the point of failure and judge the track worth abandoning despite the reluctance?
- For redefinition: what must a solver notice to decide that the trouble is in the space — in U, or G, or the generator — rather than in its own place within the space?
- For continuation: what must a solver notice — or fail to notice — such that pressing on remains the right response even though progress is not being made?
Every one of those is a question about self-observation, which is the task's own framing and the reason names cannot be sorted by: a solver's act tells an outside analyst which response occurred, but only the solver's observation of its own progress tells the solver which response to make, and those are different things. The rest of the note is oriented around that difference.
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§2 — The two episodes my evidence cannot carry, and the one it partly can
The work names three episodes to examine: the working-backwards plan from R7, S3's redefinition, and the information-gathering reading of move exploration. I have to be exact about which of those my ground reaches, because the trigger question is a question about observations, and an observation I cannot reconstruct is a trigger I cannot name.
**R7's working-backwards plan is not in my evidence for this work.. I do not hold the R7 plan itself, and I will not reconstruct its trigger from the fact that working backwards exists in the repertoire. That would be reasoning from a capability's presence to an episode's cause, and the inference does not go through.
The information-gathering reading of move exploration is likewise not in my evidence. What I hold nearby is problem-space search as a behaviour, which my net states as: the subject "proceeds by attempting to characterize the task in various ways and seeing if these evoke methods to deal with the task," "makes a preliminary evaluation of its feasibility," and "if the evaluation turns out negative, he looks for a new characterization, or picks up again a method that he has looked at earlier and dropped". That is a characterization-evaluate-recharacterize loop — the closest thing in my net to a description of exploration as information gathering — but it is a description of the overall search behaviour, not a worked episode, and it does not name a precondition the solver observes before any particular switch. I can cite it as the shape of the loop; I cannot cite it as an episode's trigger.
S3's redefinition, by contrast, my ground partly reaches — and "partly" is the operative word. I hold S3's basic method as "a search class of trial and error in a space defined by intellectual operations," and I hold that it was "derived from the production system for S3's behavior on DONALD+GERALD".. So I hold that S3's space is rule-defined and abstracted, and I hold the method's class. What I do not hold, from these nodes, is the moment of redefinition itself — the episode in which S3 observed something and changed the space. The nodes tell me the space's composition, not the switch into it.
What that state of ground does to the note's plan. Two episodes are outside my evidence; one is half-reached. The honest consequence is that I cannot execute the examination as the work framed it — episode by episode, extracting each one's prerequisite observation — because for two of the three I do not hold the episode. What I can do, and what the rest of the note does, is work from the other direction: take the structural facts I do hold about the three responses' objects (position versus space; the located locus; the loop shape of characterization-evaluate-recharacterize) and derive what observable condition would have to precede each, then check each derived condition for whether it is a self-observation or an observation available to any onlooker. The latter distinction is the one thing my evidence can sharpen even without the episodes, because it separates a trigger from a report — and that separation is what makes the three responses sortable by trigger rather than by name.
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§3 — Self-observation versus report: the distinction that makes triggers sortable
Here is the reason the task insists on triggers rather than names, as I read it, and I mark the reading as mine. A name for a strategic response is available to anyone watching the episode end — you see a solver retrace and you call it reversal; you see the space change and you call it redefinition. A trigger is not like that. A trigger is what the solver observed before the act, and by the time the act is visible, the solver's pre-act observation has usually left no trace. So a list of response names is a list of effects an analyst can catalogue, and a list of triggers is a list of causes only the solver had access to. The two are not the same taxonomy wearing different labels.
That gives me a criterion for testing each derived precondition, and I want it stated before I apply it:
A candidate precondition for a strategic switch is admissible only if it is something a solver could observe about its own progress — not merely something an observer could see about the solver's trajectory. If a condition can only be read off from outside, it can name the switch's effect but cannot be the trigger the solver acted on, and it does not count.
Applying that criterion immediately prunes some candidate preconditions, and it is worth showing one pruning because it is the kind of move that will look like over-fine discrimination until the alternative is seen. "The solver is going in circles" is an observer's description of a trajectory — it is read off from the pattern of visits, not from anything the solver is in a position to notice about its own progress. But "I keep returning to the same position and each return has told me nothing I did not already have" — that is a self-observation, and it is different in kind from the trajectory description even though both may be true of the same episode. The first is a report; the second is a potential trigger. The note's whole examination has to stay on the second side of that line.
The distinction also explains the asymmetry I noticed in §1. Reversal is keyed to the solver's position in the space; redefinition is keyed to the space. A self-observation about position is available to a solver tracking where it has been — "I am at a point I have already paid for." A self-observation about the space is available to a solver tracking what its moves have been producing — "every move I generate here lands inside the same class I already exhausted." Those are different registers of self-monitoring, and a solver that tracks only its position will produce reversals and never redefinitions, while a solver that tracks only the output of its generations may redefine without ever reversing. That last pairing is my conjecture, held as mine and provisional, but it is the kind of conjecture the trigger framing licenses: it is a claim about what monitoring a solver must do for each response to be available, and it is testable against episodes — if I had them — whereas a claim about the responses' names is not testable at all.
Where this section leaves me, and the shape of the rest of the note. I have the three responses reduced to three structural questions (§1); the ground truth that two episodes are out of reach and one is half-reached (§2); and the admissibility criterion that will test every candidate precondition (§3). The three sections that follow take the three structural questions in turn, derive candidate preconditions for each, filter them through the self-observation criterion, and then compare the survivors to see whether they are genuinely three — or fewer than three, with continuation turning out to be the bare absence of the other two's conditions rather than a third positive trigger. That last outcome is the one the §1 conjecture predicts, and I would rather run the derivation and see whether it arrives than assume it and write the three sections to fit.
This is the problem I set myself: I have two notes that name the mechanisms of strategic switching and one episode that names its shape, and none of them says what a solver sees before it switches. So §0 has to be honest about the inheritance — what each twin actually settled — and then make the gap precise enough to be worked on, which means the gap must be stated as a missing observable, not as a missing topic. A topic can be filled by writing more; an observable has to be found in an episode.
(a) What «Three Questions on Selectivity, Heuristic Strength, and Test Cost» settled — and what is mine.
That note settled three things, and I have to keep them separate from each other because they carry different warrants. First, it settled that a test's extra admissions are harmless when the search terminates by exhaustion of the admitted tree or by resource bound, and when the space's solution paths are dense and its operators reversible — so that what can cause a miss is the strong test's omissions, not the weak test's admissions, and a weak test's cost is paid in nodes while its safety is bought outright. That much stands on my held account of the selective generator — that it generates only sequences satisfying criteria of admissibility, uses information extracted from partial sequences and paths already generated to select direction, can reduce search by a ratio of 2^k if only half the alternatives are produced at each branch point, and produces a selective tree of possible solution action sequences and paths. It stands, too, on my held account of the heuristic search method as an encompassing scheme that selects new subproblems from untried-problems on the basis of an evaluation function and that terminates by an additional exit from decide-next-step on external criteria such as time or space limits. That last fact is what the whole harmlessness argument turns on, because a scheme that can eliminate all paths is a scheme whose pruning, not whose admission, is the thing that can lose the goal. Third, and this is the part I must mark as mine: the note joined the two — selective tree plus stop-on-exhaustion — into a claim that the named failure modes are structural consequences of what a selective scheme is, rather than bugs in a particular subject. No source states that join. The note's own evidence for it is the LT executive's terminal line, reached only when the queue drains, and the note says of itself that this causal link from selectivity to the three failure modes is its own synthesis and not a sentence Newell & Simon wrote. I inherit that line, and I inherit it as a line: it is a claim I made and I still hold, and I will not let it pass into this note as though it had a source's authority behind it.
What that note did not settle — and this matters for the gap — is any account of the solver's own state. It settled properties of tests, properties of spaces, and a cost inequality between a strong and a weak test; it reasoned in the third person about a search, from outside it. It says what makes an admission harmless to the search. It does not say what a solver inside the search could know about whether its own admissions have been harmless, or about whether the track it is on is about to become unproductive.
(b) What the cryptarithmetic and three-blocks reconstruction settled.
But notice the shape of what was settled there, because it is exactly the shape of what was settled in (a). The episode type names a mechanism — retrace, restart — and an outcome — a costly detour, a recovery, sometimes a recovery that never comes. It names the move the solver made and the price the solver paid. It does not name what the solver saw. It is a taxonomy of acts and their costs, not of the conditions that call them forth.
(c) The gap, named precisely.
So here is the gap, and I want it stated in a form that can fail. Both twins operate one level away from the thing I need. The selectivity note reasons about tests and spaces — what pruning does to a search, what a strong test's omissions cost — and reaches its conclusions without ever needing to say what the solver recognizes. The recovery note reasons about episodes — what a solver did when a track went bad, how long the recovery took, what it cost — and reaches its conclusions without ever needing to say what told the solver the track had gone bad. Mechanisms on one side, outcomes on the other, and in the middle a missing quantity: the condition, observable from inside the search, that precedes the choice among reversal, redefinition, and continuation.
I can make the gap sharper by saying what it would not be. It would not be satisfied by a longer list of switches — that would be more of (b). It would not be satisfied by a better cost model — that would be more of (a). It is satisfied only by a condition that a solver could notice about its own progress: something the solver has, at the moment before it switches, that it did not have before, that licenses the switch and would have licensed a different one if it had been different. Reversal, redefinition, and continuation are three responses, and a response is only strategic if it is chosen — so the gap is the choosing condition, and the reason it is a gap rather than a shortcut is that neither twin was ever aimed at it. (a) was aimed at the economics of pruning; (b) at the morphology of recovery. Both can be complete on their own terms and leave this dark.
How the three responses must be distinguished.
The task tells me to examine three held episodes — the working-backwards plan from R7, S3's redefinition, and the information-gathering reading of move exploration — and to ask of each what the solver had to observe about its own progress for that switch to be the response it chose. I take the instruction in the strong form: not to sort the three episodes into three bins by the look of the act, but to derive, from each, the condition that calls it. That means the distinguishing criterion has to be a predicate over the solver's own state, and it has to separate reversal from redefinition from continuation without referring to which act it is. Three such predicates, if I can get them, will stand as an answer; three descriptions of three acts will not.
And I want to say now why I expect the predicates to be about knowledge state rather than about the problem. My held account of problem-space search behavior gives me a solver who attempts to characterize the task in various ways and sees whether these evoke methods to deal with it, who makes a preliminary evaluation of a method's feasibility if one is evoked, and who — if that evaluation comes out negative — looks for a new characterization or picks up again a method looked at earlier and dropped. That is a solver monitoring its own evocations and evaluations, not a solver reading the problem off a page. And my held account of knowledge states gives me the mechanism that would make such monitoring possible: the immediate knowledge state is always kept small by the requirement of availability, and what the system does during its residence in a knowledge state is explore the extended knowledge state and then, on the basis of the results, act. If the precondition I am looking for is observable at all from inside, that is where it is observable — in the relation between the small immediate state and the extended one it reached. That is the hypothesis I bring to the episodes, and I mark it as a hypothesis: I do not yet know whether the episodes show it, and I will not close the gap by declaring it closed.
Where my ground stands as I begin the examination.
Two of the three episodes — R7's working-backwards plan and the information-gathering reading of move exploration — are not in my evidence for this work. My evidence is E1 and E2, my own two prior notes; E1 carries the selectivity, ratio, and failure-mode findings of (a), and E2 carries the episode-type finding of (b). Neither carries the R7 plan itself nor the move-exploration reading as passages. E2 is the front matter and table of contents of Human Problem Solving — in its own words a survey of the book's plan, chapter by chapter, which names the book's apparatus but contains no worked example, no protocol, no failure case — so it cannot supply the protocols. E3, my owner's mid-work words, is about the calling and the gates, not about problem solving, and it enters this note's argument nowhere. So the examination of those two episodes will stand on my net's held knowledge where I have it, and where I do not I will say that my evidence is silent rather than fill the silence with a plausible reconstruction. I mark this state of my ground at the opening because it governs what the note can honestly carry: an answer of the shape I am after may be reachable from held material, but a worked demonstration of it will need episodes, and I hold two of the three only as held knowledge, not as text before me.
§2 — The ledger of my holdings under the three switches
I write this section as an inventory, not an argument, and the reason is the state of my ground I marked at the opening: two of the three episodes are out of reach, one is half-reached, and what remains is the stock of held things I can actually lay on the bench for each switch. So each of the three sections below has the same three parts — (a) the held themes that carry the switch, with the members and certainty my mirror returned where it returned them; (b) the still-held works of mine that bear on it; (c) a row of lacks, each phrased as a question a source could answer. Where I do not know a theme's exact membership, I will say membership not separately counted rather than estimate, because an estimate here would be a number I did not measure.
A word first about what the mirror returned and what it did not, since the section's honesty depends on it. I asked my net for the three switches by name and by their structural descriptions, and the mirror returned themes with count-and-certainty for the ones it holds with named members, and returned bare object nodes — single claims, no member list — for the ones my recall caught at that grain. I did not run a fresh count over any theme's member set in this sitting; where I cite a count-and-certainty below it is the mirror face «net» returning it to me, not my own enumeration.
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2.1 Reversal
(a) Held themes that carry it.
One theme carries this switch, and it carries it almost alone.
The fragment of its thesis that touches the switch is the sentence I have already quoted twice and will quote once more because it is the load-bearing one: when a track becomes unproductive the solver does not instantly reroute but engages in reluctant recovery, retracing to the point of the dead end and starting over. Read for the trigger, that fragment gives me two things and withholds a third. It gives me the object of the retrace — a point, the point of the dead end, not the start and not the solver's current position — which means the act presupposes that the solver has located a locus. It gives me the mediation — reluctance, the track not abandoned instantly — which means the track was held with commitment enough that its failure is an event rather than a non-event. It withholds what the solver observed to know (i) that the track is unproductive rather than merely slow, and (ii) that this point is the locus rather than some earlier point. The theme describes the return; it does not describe the noticing that precedes the return. I will not name its members individually here because my recall this sitting surfaced the theme's thesis, not its member list; where the exact membership matters to a later step I will open the theme rather than list from memory.
The two strategic-search themes The errors-and-variation theme touches the switch from the side: it holds that individual differences in style show up as costly detours, and it names a solver spending a long time on an unproductive path because of commitment to it. That is the cost of not reversing, and the reluctance reversal has to overcome, but it is not itself the reversal trigger. I record it as bearing on reversal without carrying it.
(b) Still-held works of mine that bear on it.
Two, and I have opened both this sitting as evidence in hand.
E1 — my note Three Questions on Selectivity, Heuristic Strength, and Test Cost. It bears on reversal only indirectly and I want that said plainly: its relevance is the LT executive's schedule, which E1 records as a fixed order — substitution first, then DT, CF, CB, over the current problem drawn from the queue — and whose only non-success terminal, E1 states, is queue exhaustion. A fixed schedule with no backtracking line is the structural opposite of a repertoire that includes reversal: in that captured span there is no reversal to trigger, because control never returns to an earlier choice except through the submethod's own "if fail continue generation" idiom. So E1 bears on reversal as a contrast case — it tells me what a solver's control looks like when the reversal switch is absent — and not as an instance of the switch.
E2 — my note Selectivity in Heuristic Candidate Generation and Its Failure Modes. It bears the same way, from the same captured protocol, and adds nothing to reversal beyond what E1 carries. Both notes are mine, both still held, and I name them because the ledger asks which of my own works bear on the switch and the honest answer is: these two, and they bear by contrast rather than by instance.
(c) Lacks — each as a question a source could answer.
- What does a solver observe about its own progress when it decides a track is unproductive rather than merely slow? — i.e., is there a distinguishable self-observation that separates "this isn't working" from "this hasn't worked yet", and is it reportable in a protocol?
- What does a solver observe that fixes the point of return? — the reluctant-recovery theme says the return is to the point of the dead end; what self-observation identifies that point, as against an earlier decision the solver could equally blame?
- Is reluctance itself triggered by a noticed condition, or is it a constant of the style? — the theme treats reluctance as a feature of the episode; a source could say whether the commitment that produces reluctance is itself keyed to anything the solver notices (sunk work, cost paid, prior partial success) or is simply a dispositional parameter.
- Does the reversal trigger require a prior commitment the solver can point to? — the errors theme names commitment as what makes the detour costly; is the reversal available only after commitment, and if so what tells the solver the commitment has gone bad?
- On what does a solver read "unproductive" — the moves generated, the states reached, or the rate of new information? — this is the register question the trigger framing turns on, and my held material does not answer which register the reversal decision is made in.
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2.2 Redefinition
(a) Held themes that carry it.
This switch is better carried than reversal on the object side and worse on the episode side, and the asymmetry is worth stating before the inventory.
— «Representation, Set Structure, and the State Space» — holds the set framing: a problem defines U, the set of all possible configurations, and G, the satisfying subset, with a generator producing elements of U at some cost, and subjects operate internally on molar rather than molecular representations, transforming even a Necker cube into an internal representation. That fragment gives redefinition its target: to redefine is to change U, or G, or the generator, and the theme names all three as the objects a representation decision fixes. Read for the trigger, it says what the switch acts on and is silent on what precedes it. Membership not separately counted — my recall this sitting returned the theme's thesis, not a member list, and I do not have its count in hand, so I say so rather than guess.
— «Heuristic Search in Problem Spaces» — holds the multiplicity: cryptarithmetic exhibits several spaces at once — a cryptogram space mapping letters to digits by rule construction, a typographical space inspecting letter shapes, a word-meaning space of semantic association — each with its own operators, and the subject's search is driven by a gradient from an information source. That is the strongest held thing I have for redefinition, because a solver moving between spaces is doing by construction what the switch names: it leaves one space for another without leaving its seat. But the fragment describes the spaces and their gradient; it does not record the moment one space was abandoned for another, nor the observation that called the change. Membership not separately counted, for the same reason as above.
and : Read for the trigger, this gives me the distinction a redefining solver would have to draw — is my trouble in the essential structure or in the surface I happened to adopt? — and it is exactly the distinction that separates redefinition (the trouble is in the space) from reversal (the trouble is in my place within the space). Membership not separately counted for either.
— «Problem-space search» — is the nearest my net comes to a loop that could be read as redefinition, and it is a bare object node, not a theme: it holds that the subject attempts to characterize the task in various ways and sees if these evoke methods, makes a preliminary evaluation of a method's feasibility, and if that evaluation is negative looks for a new characterization or picks up again a method looked at earlier and dropped. That characterization-evaluate-recharacterize loop is the shape of redefinition in the register of method choice — a negative feasibility evaluation triggers a new characterization. But it is described as search behaviour at the whole-task grain, not as an episode, and it does not name the observation that makes a feasibility evaluation go negative. I record it as the closest held shape, not as the trigger.
(b) Still-held works of mine that bear on it.
Two, held in my net and named as such.
It bears on redefinition directly and in the right register: it says what a redefinition changes, namely one or more of S, M, G. It does not say what a solver observes to decide that S, M, or G — rather than the solver's position in them — is where the trouble lies.
— my note The GPS Loop — how a difference indexes into an operator and how control returns. My net summary holds it as closing a gap in «Heuristic Search in Problem Spaces» on the mechanics of the loop itself. It bears on redefinition through the difference-indexing: if an operator is indexed by a detected difference between current and goal state, then a redefinition that changes G changes which differences register at all, and that is a mechanism by which the switch propagates. I hold the note; I have not re-opened its body in this sitting, and I mark that reliance as reliance.
(c) Lacks — each as a question a source could answer.
- What does a solver observe when the failure is in the space rather than in its trajectory? — the essential/inessential themes give the distinction conceptually; a source could say whether solvers report the observation, and in what words.
- When a solver changes spaces, what decides which space it changes to? — the heuristic-search theme gives me several co-present spaces and a gradient; a source could say whether the new characterization is chosen by the gradient, by a feasibility evaluation, or by something else.
- Does the negative feasibility evaluation of the characterization loop have a reported trigger? — the loop names the evaluation; is there a threshold, or a reportable condition, at which "preliminary evaluation" comes out negative?
- What does a solver observe that tells it the trouble is not in its position? — the complement of the reversal question: what rules out "I should back up" in favour of "I should recast"?
- Is the molar representation itself a redefinition, and if so is it instantaneous or a switch? — the representation theme holds subjects transform even a Necker cube into an internal representation; is that transformation an instance of the redefinition switch, or a preprocessing act beneath it?
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2.3 Continuation
(a) Held themes that carry it.
None, and I want the bare fact recorded before I record the near-misses, because the bare fact is the section's most important line.
No theme in the «net» return names continuation as an episode type. There is no held thesis describing a solver deciding not to switch; no member list returned under a continuation heading; no count-and-certainty to report. I looked, and the mirror has nothing to give under that name. So: membership not separately counted — because there is no continuation theme to count members over. This is not thin ground; it is absence of ground, and I state it as absence.
The near-misses are worth naming anyway, because they are where a continuation reading might eventually be anchored, and naming them keeps me honest about what is adjacent versus held.
— «Invariants of the Environment Across Problem Solvers» — holds that invariants of the environment are aspects of behavior constant along all paths that lead to a goal, exhibited by all problem solvers that solve the problem. Read for continuation, this is the closest held thing: it describes behaviour that is the same across solvers along successful paths, which is the counterpart of pressing on. But an invariant is not a decision to press on; it is a property of the paths, observable from outside. It tells me what continuation produces, not what triggers it. Membership not separately counted.
— «Problem solving takes place by search in a problem space» — my net holds as a major invariant across tasks and subjects. This is the postulate that makes the other two switches meaningful — there is a space, so there is a position in it and a structure to it — and it is the substrate continuation would run on. It is not a trigger and I do not dress it as one.
and are bare object nodes, returned as single claims without member lists. I record them as present in the return, bearing on the strategic layer generally, and I do not claim either as a continuation theme.
(b) Still-held works of mine that bear on it.
One, and it bears as the absence of a thing rather than the presence of one.
E1 — my Three Questions note. Its relevance to continuation is its own terminal finding: E1 records that the LT executive's schedule is a fixed order with the only non-success terminal being queue exhaustion, and E1 marks explicitly that no intermediate failure-reporting, no partial-result reporting, and no restart rule appears in the span. Read for continuation, that is a solver with no switch at all in the captured span: it presses on line by line because the protocol has no line that reads "reconsider." So E1 bears on continuation as the strongest held evidence that continuation can be the default rather than a decision — which is exactly the conjecture I formed at the opening and hold as mine and provisional. The very absence of a switch line in the captured protocol is what makes continuation look like the unmarked case.
E2 — my Selectivity note — adds nothing here beyond the same protocol, and I name it only because the ledger asks for the still-held works that bear and the honest set is these two, with E1 carrying the whole weight.
(c) Lacks — each as a question a source could answer.
- Is continuation a decision at all, or the default when no switch fires? — this is the question on which the whole section turns; a source could say whether solvers ever report having considered and declined to switch.
- If continuation is a decision, what does the solver observe to make it — evidence that the current track is still promising? — the reversal trigger has its "unproductive" reading; is there a symmetric "still productive" reading, and is it reported?
- What does a solver observe that licenses pressing on past a point where another solver would have switched? — the errors theme gives me style differences as costly detours; a source could say whether the difference is in the observation or in the threshold applied to the same observation.
- Does continuation require the solver to notice something positive, or only to have noticed nothing negative? — the excluded-middle here is exactly the difference between a third trigger and a bare default.
- Is there a held episode — in any protocol I could read — where a solver narrates pressing on as a choice? — if such an episode exists, it is the source that closes this section; if none exists, the absence is itself a finding and I should record it as one rather than keep searching for a phantom.
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What the ledger shows before I turn to the three triggers in the next section
Three things fall out of the inventory, and I record them as findings of the ledger rather than as arguments, because they are what the stock-of-holdings says and not what I wish it said.
First: the three switches are not equally stocked, and not stocked in the same part of their structure. Reversal has a theme that carries its act and an adjacent theme that carries its cost, and the trigger-side is empty. Redefinition has themes that carry its object (S, M, G; U and G; the co-present spaces) and a bare object node that carries the loop shape, and the trigger-side is populated only by the loop's negative-evaluation step, which is itself unmeasured. Continuation has no theme at all — the mirror returned nothing under that name — and what I hold nearby is either an invariant observed from outside or the absence of a switch line in a captured protocol. So the ledger's first finding is a distribution: the acts are held, the objects are held, the loops are held; the triggers are the part of each switch I do not hold, and for continuation I do not even hold the act as an act.
Second: my two own notes are the only works bearing on all three, and they bear by contrast for reversal and continuation and by mechanism only for redefinition. That is a small stock for a trigger question. It means the examination that follows will have to derive candidate preconditions from the structural facts the ledger does hold — the located locus, the S/M/G target, the characterization loop, the molar representation — and then filter them through the self-observation criterion, because there is no held episode-by-episode trigger I can read off. The ledger is an inventory of what I can derive from, not of what I can quote.
Third: the one asymmetry the ledger sharpens is the object split between reversal and redefinition. Reversal's held fragment fixes its object as a point — the point of the dead end; redefinition's held fragments fix their object as the space — U, G, the generator; S, M, G; the co-present spaces. Position versus space. That split is not in any single theme; it is what the ledger shows when the fragments are laid side by side, and I mark it as the ledger's reading, mine and provisional, until the trigger derivation tests it. If the split holds, the reversal trigger has to be a self-observation about where I am, and the redefinition trigger a self-observation about what my moves are producing — two different registers of self-monitoring, which is the conjecture I formed at the opening and which this ledger now gives a footing.
With that inventory in hand I can turn to the derivation itself: for each switch, what observable condition would have to precede it, filtered through the criterion that the condition be something the solver could observe about its own progress, and then compared across the three to see whether they are genuinely three triggers — or fewer, with continuation turning out to be the bare absence of the other two's conditions. That comparison is the next section's work, and the ledger's job was to make sure I go into it holding only what I hold.
§3 — What my held passages actually carry about the antecedents
This section is the one the task actually asks for — for each of the three switches, name the observable condition my real holdings support, quoting only from what I hold. I have to write it as a bound draft, and "bound" is doing real work in that phrase: every sentence that states what a source carries must sit on a passage in front of me, and every sentence that would need a passage I do not hold must be named as a gap rather than written as if the passage were mine. So §3 is written under a hard rule I state once and obey throughout: a switch's observable antecedent gets stated only where a held handle supports it, and every unsupported part of a switch's antecedent is named, in this section's own words, as the unheld protocol passage that would be needed to fill it.
The handles I have in hand are six. E1 is my own note Three Questions on Selectivity, Heuristic Strength, and Test Cost. E2 is my own note Selectivity in Heuristic Candidate Generation and Its Failure Modes. E3 is my owner's mid-work words to me, about the proxy, Prism, the address, and the seed. E4 is my held §1–§3, where I took the three response names apart into structural questions and stated the self-observation criterion. E5 is my held §2, the ledger of my holdings under the three switches. E6 is the front matter and table of contents of Human Problem Solving — the book's own announcement of its plan, chapter by chapter. I take the three switches in turn, and for each I do the same three things: say what the held handles carry, quote the carrying fragment, and name the unheld passage the switch still lacks.
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3.1 Reversal
(a) What my held passages carry.
Its load-bearing sentence is the one E0 already read for this purpose, and I quote it again here because §3 must stand on the fragment and not on my prior reading of it: "when a track becomes unproductive the solver does not instantly reroute but engages in reluctant recovery: retracing to the point of the dead end and starting over". That is the whole of the antecedent the fragment states, and it states it obliquely.
That is the cost of not reversing — the reluctance reversal must overcome — and by naming commitment as what makes the detour costly it also, obliquely, supports one more antecedent shape: reversal becomes an event only where a prior commitment can be pointed to. But the fragment does not state what the solver observed; it states what the detour cost.
E4 carries the criterion by which any candidate antecedent for reversal must be tested, and I lean on it explicitly because §3's honesty depends on it. E4's admissibility rule: "A candidate precondition for a strategic switch is admissible only if it is something a solver could observe about its own progress — not merely something an observer could see about the solver's trajectory." Applied to reversal, E4's own worked contrast is the one I must not blur: "The solver is going in circles" is an observer's description of a trajectory and is therefore a report, not a trigger; the self-observational counterpart — the solver noticing it keeps returning to the same position with each return yielding nothing new — is the kind of thing a reversal trigger would have to be. E4 states that line; I inherit it and apply it, and I mark the inheritance as inheritance.
E5 (§2, the ledger) carries the contrast case that bounds what reversal's antecedent can be in the material I hold: E1 and E2, E5 tells me, bear on reversal "by contrast rather than by instance," because the LT executive's schedule is — E5's words, lifted from E1's body — "a fixed order — the executive's listed order, substitution first, then DT, CF, CB, over the current problem drawn from untried-problems," and "stop and report no proof and nothing more to do" is reached only on queue exhaustion. E1's body states exactly this and adds that the generator's selection rule "is not specified in the captured span" and that E1 "refuses to guess whether that generator uses detected differences to rank or prune." So the LT material tells me what a solver's control looks like when the reversal switch is absent: a fixed schedule whose only non-success terminal is queue exhaustion, with no line that returns control to an earlier choice. That is a real antecedent fact about reversal — a negative one: in the captured span, no observation precedes reversal because there is no reversal to precede. I state it as the contrast it is and do not read it as an instance.
(b) The unheld passage reversal needs.
What reversal's antecedent strictly requires, and what I do not hold, is the captured failing-track episode on reluctant recovery with its verbatim protocol lines. My held fragment gives me the shape of the return — "retracing to the point of the dead end and starting over" — and it gives me the object of that retrace, a located point. It does not give me the episode's own protocol: the lines in which the solver, mid-track, says what it is noticing before it turns back. Specifically, I do not hold: (i) the solver's own words marking the transition from "trying" to "stuck — this track is unproductive rather than merely slow"; (ii) the solver's words fixing which point is the dead end rather than an earlier decision it could equally blame; (iii) the words in which the reluctance is voiced, so that I can see whether the commitment that produces it is keyed to anything the solver noticed (sunk work, cost paid, prior partial success) or is a dispositional constant. Item (i) is the one §3 most plainly cannot supply: the fragment says the track "becomes unproductive" as a fact of the episode, and E4's criterion forbids me to substitute the observer's "becomes unproductive" for the solver's own noticing of it. I name the passage — the captured failing-track episode on reluctant recovery, verbatim protocol lines — as unheld, not filled. The reversal antecedent, as far as §3 can carry it, is: the solver has located a locus and judges the track worth abandoning despite reluctance, and what the solver observed to locate it and to know it is unproductive rather than slow is beyond my ground.
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3.2 Redefinition
(a) What my held passages carry.
Redefinition is better carried than reversal on the object side and worse on the episode side, exactly as E5 (§2.2) marks it, and §3 must keep that asymmetry rather than flatten it.
The representation theme states redefinition's target with a real fragment: a problem "defines U, the set of all possible configurations, and G, the satisfying subset, with a generator producing elements of U at some cost" and "subjects operate internally on molar rather than molecular representations, transforming even a Necker cube into an internal representation". Read for the antecedent, this fragment supports one structural fact and withholds the trigger: because the objects a representation decision fixes are exactly U, G, and the generator, a redefinition has a definite target — to redefine is to change one of those three — but the fragment does not state what a solver observes to decide that the trouble sits in the space (U, G, generator) rather than in its own place within the space. That is E4's §1 distinction carrying into the antecedent: redefinition "leaves the solver's position untouched while changing the board," whereas reversal leaves the board untouched while changing the position, so the two responses are keyed to different objects and an antecedent for one is not automatically an antecedent for the other.
The heuristic-search theme carries the multiplicity that makes redefinition a live move rather than a hypothetical: cryptarithmetic "exhibits several such spaces at once — a cryptogram space mapping letters to digits by rule construction, a typographical space in which recognition processes inspect letter shapes, and a word-meaning space of semantic association — each with its own operators," each driven by "a gradient from an information source". A solver moving between spaces is doing by construction what redefinition names, and the gradient is the nearest held thing to a "which space" selector. But the fragment describes the spaces and their gradient; it does not record the moment one space was abandoned for another, nor the observation that called the change. Say so plainly.
The essential/inessential theme gives the distinction a redefining solver would have to draw, in the abstract: aspects of behavior "constant across solvers — such as the abstractions of the problem graph and the operators that traverse it — are essential, while surface differences between subjects are inessential". Read for the antecedent, this separates the trouble is in the essential structure from the trouble is in the surface I happened to adopt — exactly the register difference that divides redefinition (trouble in the space) from reversal (trouble in my place). It states the distinction conceptually; it does not state an observation a solver makes when the distinction comes out "inessential surface."
The nearest held loop to redefinition's antecedent is the bare object node — my net's statement that the subject "attempts to characterize the task in various ways and seeing if these evoke methods to deal with the task," makes "a preliminary evaluation of its feasibility," and "if the evaluation turns out negative, he looks for a new characterization, or picks up again a method that he has looked at earlier and dropped." That is a characterization-evaluate-recharacterize loop, and a negative feasibility evaluation is the clearest antecedent-shaped handle my net offers for redefinition. But it is the whole-task grain of search behaviour, not an episode, and — this matters — it does not name the observation that makes the evaluation go negative. I record it as the closest held shape, not the trigger.
(b) The unheld passage redefinition needs.
My held fragments give me the target (U, G, generator), the multiplicity (several co-present spaces with a gradient), the distinction (essential structure vs. inessential surface), and a loop shape (characterization–evaluate–recharacterize with a negative feasibility evaluation). None of these is the passage in which the solver actually re-describes the problem — the lines in which it says what it noticed that made it treat a feature as essential or as surface, and that drove the re-description. Specifically, I do not hold: (i) a worked episode in which the solver, mid-problem, changes its description of the space and says why; (ii) the words in which the solver decides "the trouble is in the space's definition, not in my position"; (iii) what makes the feasibility evaluation of the characterization loop go negative — a threshold or a reportable condition — rather than the loop merely having a negative branch. I name the passage — the representation/set-structure passages on how the solver re-describes the problem under essential/inessential features — as unheld, not filled. The redefinition antecedent, as far as §3 can carry it, is: the trouble is judged to sit in U, or G, or the generator rather than in the solver's place, and the solver has a distinction (essential vs. inessential) available to draw; what the solver observed to make that judgment, and how a re-description is actually performed, is beyond my ground.
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3.3 Continuation
(a) What my held passages carry.
Here §3 must say the bare, hardest thing first, because E5 (§2.3) recorded it as the section's most important line and §3 cannot soften it: no held theme carries continuation. I reach no node in my net that names continuation as an episode type, and no held description of a solver deciding not to switch. The section on continuation in the ledger is — E5's own last written line — "None, and I want the bare fact recorded before I record the near-misses, because the bare fact is the section's most important line." §3 inherits that and does not manufacture a carrying theme.
Three held handles touch continuation, and I must keep each in its place.
E4 carries a conjecture, marked as mine and provisional, exactly as E4 marks it: "If reversal and redefinition are marked by the presence of something — a located locus, a changed space — continuation may be marked by the absence of that something, in which case it is not a third positive trigger at all but the default condition under which neither of the other two fires." E4 states this possibility and labels it "a conjecture of mine, not something my net states," and §3 must carry that label with it — the conjecture is the strongest thing continuation has, and it is mine to make and to hold provisionally, not a held antecedent.
E4 also supplies the third structural question, which is the form any continuation antecedent must have: "For continuation: what must a solver notice — or fail to notice — such that pressing on remains the right response even though progress is not being made?" That question is E4's; §3 uses it as the criterion continuation must answer and does not pretend a held passage answers it.
The six handles in hand are, on inspection, silent on continuation directly, and §3 says so rather than gestures. E6 — the front matter and contents of Human Problem Solving — announces the book's plan and I read it here for the one thing it can carry: whether the book's own apparatus even has room for the passages continuation needs. E6's table of contents, which I hold, names "3 TASK ENVIRONMENTS," "4 PROBLEM SOLVING," "5 CRYPTARITHMETIC: Task Analysis," "6 CRYPTARITHMETIC: Behavior of a Single Subject, S3, on DONALD + GERALD = ROBERT," "7 CRYPTARITHMETIC: A Broader View," and then the LOGIC and CHESS blocks — "9 LOGIC: GPS and Human Behavior," "12 CHESS: Behavior of a Single Subject," and the closing "14 THE THEORY OF HUMAN PROBLEM SOLVING." That tells me the book has behavior-of-a-single-subject chapters, where a continuation episode would live if anywhere, and has the theory chapter that would state the two decision points — but E6 is front matter and contents only; it names the chapters and carries none of their worked text. E1 and E2, both sourced from the LT executive protocol, are silent on continuation for the same reason they are silent on reversal's positive trigger: the captured span is a fixed schedule with no switch to make. E3 — my owner's mid-work words — is about the proxy, Prism, the address, and the seed; it says nothing that bears on a solver's progress and I will not press it into service.
So §3 records continuation's antecedent as not carried by any held handle, and records the one thing it can honestly record about the shape of that antecedent: by E4's third structural question, the antecedent, if it exists, is a condition under which the solver notices — or fails to notice — something that keeps it on the same track, and by E4's conjecture (mine, provisional) it may be no positive trigger at all but the default condition under which neither of the other two fires.
(b) The unheld passage continuation needs.
What continuation's antecedent requires, and what I do not hold, is the move-exploration and two-decision-points protocol passages showing what the solver notices that keeps it on the same track. My held fragments give me the form of the question (E4's third structural question), a provisional structural conjecture (continuation as the default condition, E4's, mine), and two of my own still-held works that bear on the adjacent machinery — the note on what fixes S, M, G and the article that names "two crucial points" as selecting an operator and evaluating the resulting state — but none of these is the move-exploration protocol passage or the two-decision-points passage in which the solver's own noticing of what keeps it on the same track is recorded. Specifically, I do not hold: (i) the solver's words, mid-track, reporting what it sees that makes the current move worth continuing rather than abandoning; (ii) the two-decision-points passage in its own protocol lines, as against my theme's summary of it; (iii) any episode in which the solver decides not to switch and says what it noticed (or did not notice) about its progress in deciding so. I name the passage — the move-exploration and two-decision-points protocol passages showing what the solver notices that keeps it on the same track — as unheld, not filled. The continuation antecedent, as far as §3 can carry it, is: not yet stated by any held handle; what a solver notices (or fails to notice) that keeps it pressing on the same track is beyond my ground.
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3.4 What §3 has established, and what it has left unheld.
Read back, §3 has produced a bound draft of the antecedents — the strongest statements my six held handles actually support, each backed by a quoted fragment, and each surrounded by the unheld passages the switch still requires. Its result is a negative inventory with three positives in it: reversal carries one antecedent obliquely (the located locus) and one conditionally (a prior commitment it can point to), redefinition carries a target (U, G, generator) and a distinction (essential/inessential) but no episode, and continuation carries nothing but a structural question and a marked conjecture. All three switches nonetheless come out sortable by trigger rather than by name in one specific sense §3 can back: E4's self-observation criterion-adjacent in my net and stated in E4's body, that a trigger must be something the solver could observe about its own progress, genuinely distinguishes each response's antecedent from the observer's report of it, and by that criterion reversal is keyed to a self-observation about position, redefinition to a self-observation about the space, and continuation to the absence of either — that last pairing being my conjecture, held provisional, not a held statement.
What §3 leaves unheld, named in one place so the note's ground is legible at a glance: the reversal antecedent lacks the captured failing-track episode on reluctant recovery with its verbatim protocol lines; the redefinition antecedent lacks the representation/set-structure passages on how the solver re-describes the problem under essential/inessential features; the continuation antecedent lacks the move-exploration and two-decision-points protocol passages showing what the solver notices that keeps it on the same track. Each is named as a gap in §3's own words; none is filled. The note closes where §3 does — with the antecedents as far as my held handles carry them, and with the three passages the switches still need, named and left open.
§4 — The antecedent condition per switch, phrased as a notice, classified where held
This is the section the task asked for in its own voice: one observable condition per switch, phrased as something a solver could notice, drawn only from what §2 and §3 already carried, and classified — state-reached, path-cost, or unread-information — only where a held source licenses the classification. I keep §3's rule in force: every trigger sentence sits on a passage I can quote, and every place the Newell & Simon protocol passage I could not reach would be needed is named rather than filled.
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4.1 Reversal — the notice, and what it is keyed to
(a) The condition, phrased as a notice.
"I am at a point I have already paid for, and each return to it has cost me something without giving me anything new."
Two parts of that sentence are carried by a passage and one is not, and I separate them. The middle joint — that the solver names the point as the dead end rather than as an earlier choice it could equally blame — is §3's excess over the fragment, and §3 already named it "the unheld protocol passage that would be needed to fill it." I do not fill it here.
(b) Classification.
At the level my handles reach, reversal reads as unread-information: the thing the notice is of is the absence of new information on return, not a state and not a counter of remaining cost. I mark the class unread-information — held at the level of the fragment only, because the fragment says "unproductive" without saying what register registers it, and §3 already recorded the register question as an open lack. If a solver's unproductiveness were instead read off a step-count or a bound, it would be path-cost, but no held passage gives me the counter. So: unread-information, held; path-cost, unheld; state-reached, ruled out by the fragment, which is about a track becoming unproductive rather than about a state satisfying a goal.
(c) Where the unreached passage is required.
The Newell & Simon protocol passage I could not reach is required at three places in §4.1: to say whether "unproductive" is reported by a subject and in what words; to say whether the locus is fixed before the retrace or only reconstructed in it; and to say whether reluctance is a noticed condition or a standing disposition.
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4.2 Redefinition — the notice, and what it acts on
(a) The condition, phrased as a notice.
"Every move I generate here lands inside the same class I have already exhausted, and the class is mine — a choice of what counts as a state, a move, or a goal — not a fact of the task."
§3 already named the pair as the distinction between reversal — position in the space — and redefinition — the space.
(b) Classification.
Within my handles, redefinition reads as state-reached — but at one remove, and I mark the remove. The notice is about a property of the set of states produced, not about any single state: the class has been covered. So I classify redefinition as state-reached, on the reading that the reached state is the exhausted class, and I say the reading is mine. I do not classify it path-cost: the theme's generator cost is a cost per element, not a cumulative cost the solver would notice as a switch trigger. I do not classify it unread-information: the notice is that a class is covered, not that information has stopped arriving.
(c) Where the unreached passage is required.
Two places in §4.2: to say whether the move from "this class is exhausted" to "this class is the wrong one" is reported, and to say what chooses the new class when it does change. §2 recorded S3's redefinition as half-reached — I hold S3's basic method as a search class of trial and error in a space defined by intellectual operations, derived from the production system for S3's behavior on DONALD+GERALD — which gives me the space but not the moment of change. The unreached protocol passage would fill that moment, and that passage is the chapters of Human Problem Solving that carry the cryptarithmetic protocol analysis, which E6's front matter names — Chapter 6 for the first subject's protocol analysis and Chapter 7 for the four other subjects. The §2 gap on the R7 plan does not touch §4.2.
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4.3 Continuation — the notice, and the honesty of its thinness
(a) The condition, phrased as a notice.
From them, the antecedent condition I can stand on is shorter and weaker than the other two:
"The method I have in hand can still be brought to bear — every move I am generating evokes, or reprovokes, a method — so pressing on is the move."
That is carried, in the shape of a loop, by my held object node on problem-space search: the subject attempts to characterize the task in various ways and sees if these evoke methods, makes a preliminary evaluation of a method's feasibility, and if that evaluation turns out negative looks for a new characterization, or picks up again a method that he has looked at earlier and dropped. Read for continuation, the loop's positive branch is what I need — the branch on which the method is brought to bear rather than dropped — and the passage does not name it. Neither theme names not switching as an episode type.
(b) Classification.
Classification unheld. That conjecture survives §4.3, and its consequence is exact: a notice that is the absence of the other two conditions has no state, no cumulative cost, and no information-gap to read off, so the classification schema does not apply. I write classification unheld rather than pick a class by analogy, because the schema was given for a positive trigger and §4.3 does not reach one.
(c) Where the unreached passage is required.
Three places in §4.3, and they are where the note's honesty is most strained. The Newell & Simon protocol passage I could not reach is needed: to say whether a subject reports not switching at all, as against reporting a method-application or a state-evaluation; to say whether the characterization-evaluate-recharacterize loop's positive branch has a name in the book's vocabulary; and to say whether the operator-selection decision-point is closed by a reportable notice or by the mere availability of a next operator.
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4.4 The three triggers side by side, sorted by what they are notices of
The three notices, on my held ground, sort as:
- Reversal — notice of the absence of new information on return — unread-information, held at the fragment level; path-cost and state-reached unheld.
- Redefinition — notice of a class of states having been covered — state-reached, on my reading of the reached state as the exhausted class; path-cost and unread-information unheld.
- Continuation — notice of a method still being applicable — classification unheld, with the conjecture that continuation is the default condition under which the other two do not fire.
And a fourth line, which is not a classification but §3's admissibility criterion applied here: all three phrased notices are self-observations — "a point I have already paid for," "the class I have exhausted," "the method I still have" — none is a description an onlooker could read off the trajectory. So the sort is by trigger rather than by name, and the three are genuinely three only if continuation is a positive notice; if it is the default condition, then the two positive triggers are reversal and redefinition, and continuation is what stands when neither fires. §2's held work put that as a conjecture, and §4.3 leaves it standing as one rather than settling it — my evidence is silent at exactly the joint where the count would be decided.
§5 — The discrimination condition between pairs of switches
§4 closed with three notices, sorted by what they are notices of, and with the count of switches left standing as a conjecture. This section does the next thing, and the next thing is harder: it asks, for each pair of switches, what has to be true in addition to the first switch's own condition before the second of the pair fires instead of the first. A pair discriminates only if my held sources separate its two members along some observable axis; where they do not, the honest answer is not a filled gap but a named one. I keep §3's admissibility criterion in force throughout — a separating condition counts only if it is something a solver could observe about its own progress — and I mark every sentence that rests on a passage I can quote, and every separation I cannot make from my holdings as unheld rather than filling it.
The matrix has three cells, and they are not symmetric. One cell I can draw on held ground. One cell I can draw only by pointing at an axis my sources name but do not walk. One cell my sources do not separate at all, because one of its members has no positive condition to separate from. I take them in that order of confidence — the strongest separation first, so that when the weaker ones thin out the thinning is visible against what held.
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5.1 Reversal versus redefinition — the separation I can draw
This is the pair my held sources actually separate, and they separate it cleanly, along an axis my own held §1 already named and my own held §4 already used to sort the notices. My §1 recorded the distinction as mine: redefinition is the response that "leaves the solver's position untouched while changing the board, whereas reversal leaves the board untouched while changing the position" — the two are "keyed to different objects — one to the solver's place in the space, the other to the space itself." My §4 then used exactly that axis to sort the two notices: reversal is a notice "of the absence of new information on return," redefinition is a notice "of a class of states having been covered."
So the first condition for each is already in hand. I state each as a notice, and I point at the held material each rests on.
Reversal's notice, as my held §4 phrased it: "I am at a point I have already paid for, and each return to it has cost me something without giving me anything new."
Redefinition's notice, as my held §4 phrased it: "Every move I generate here lands inside the same class I have already exhausted, and the class is mine — a choice of what counts as a state, a move, or a goal — not a fact of the task." That phrasing rests on my consolidated theme on representation, which holds the set framing — a problem defines U, the set of all possible configurations, and G, the satisfying subset, with a generator producing elements of U at some cost — and holds that subjects operate internally on molar rather than molecular representations, "transforming even a Necker cube into an internal representation". The theme carries what a representation decision fixes — U, G, the generator — and I read the notice off the coverage of the generated set, marking the reading as mine.
The second condition — the additional observation that decides which of the two fires — is the one that reads the locus of the failure. My §4 put the two notices in the same words when it named the pair: reversal is "position in the space," redefinition is "the space." The discriminating self-observation, phrased as a notice, is therefore:
"The dead end I keep returning to is a place — I have paid for the ground and the ground told me nothing; the space still has places I have not paid for. — If instead every place I generate lands inside one class, the dead end is not a place at all but a boundary of the kind of place I have been moving in."
The two clauses read off different objects, and that difference is the separating axis. Reversal is disambiguated by the solver checking its own position — have I been here, did the return give me anything; redefinition is disambiguated by the solver checking what its moves have been producing — is everything I generate inside one class. The former is a check on the trajectory of visits, the latter a check on the character of the generated set. They are different registers of self-monitoring, which is what my §3 conjectured when it named the pairing — "a solver that tracks only its position will produce reversals and never redefinitions, while a solver that tracks only the output of its generations may redefine without ever reversing" — and my §3 marked that pairing as its own conjecture, held as mine and provisional. It stands in §5 as a conjecture, not as a finding.
What makes this a separation rather than two separate descriptions is that the two second-conditions concern different objects and cannot be true of the same episode in the same respect. A dead end that is a place is, by construction, a place the solver has been; the class of moves that is exhausted is, by construction, a class the solver is still generating within. You cannot read the first off the generated set alone, nor the second off the visit history alone, because the visit history is silent about the class while the generated set is silent about which particular place was paid for. So the pair is separated on an object axis, and I record it as a held separation of shape, not of transcript: the transcripts would tell me whether solvers report drawing the distinction, and my evidence does not hold them.
There is one thing I can say beyond the shape, and it is the essential/inessential distinction. My held themes on essential and inessential features hold that aspects of behavior constant across solvers — such as the abstractions of the problem graph and the operators that traverse it — constitute what is essential, while surface differences between subjects are inessential. Read for the trigger, that gives the redefinition-side observation a target: the solver asking whether its trouble lies in the essential structure (the space) or is an inessential feature of how it happened to enter the space. But the theme gives me the distinction; it does not record a subject drawing it in words, and I mark that as unheld below with the rest.
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5.2 Reversal versus continuation — the separation my sources name but do not walk
This pair is thinner on my ground than 5.1, and the thinning is worth showing rather than smoothing over.
Reversal's condition is the notice of nothing new on return — my §4's unread-information read, held at the fragment only. Continuation's condition, from my §4, is the notice that "the method I have in hand can still be brought to bear — every move I am generating evokes, or reprovokes, a method — so pressing on is the move." My §4 already flagged that this is carried "in the shape of a loop" by my held object node on problem-space search, and that the node's positive branch — the branch on which the method is brought to bear rather than dropped — "is the branch on which I need," and the passage does not name it.
So the first condition of each is in hand, but the second condition — what decides that the method is still applicable despite the return having given nothing new — is not a sentence I can source. The nearest my evidence comes is the same problem-space-search node, read for its negative branch: the subject "attempts to characterize the task in various ways and see if these evoke methods to deal with it, making a preliminary evaluation of a method's feasibility if evoked and, if that evaluation is negative, looking for a new characterization or picking up again a method looked at earlier and dropped". That negative branch is where the two switches would separate — a negative feasibility evaluation is the threshold at which continuation stops and one of the others begins — but the node names the threshold without naming the observation that sets it, and my §2 already recorded "does the negative feasibility evaluation of the characterization loop have a reported trigger?" as a lack rather than a finding.
What I can say honestly, and it is a limit rather than a separation: the axis on which reversal and continuation could be separated is whether the method in hand has been tried and found wanting, or has not yet been exhausted. The second condition would be a self-observation of the form "I have not yet run the method out" against reversal's "I have run this track out."
That reads as a clean separation, and I want to be exact about why it is not one I can claim as held. The continuation side rests on the absence of an exhaust notice, and my §4 already established that continuation has no positive held condition — its classification is unheld, and my §4 records the conjecture that continuation "is the default condition under which the other two do not fire." If that conjecture is right, then the separation between reversal and continuation is not a discrimination between two positive conditions at all; it is the boundary between a condition firing and no condition firing, and there is nothing on the continuation side to discriminate from. The separation I can state is therefore conditional on a conjecture, and I will not promote it past that. So: the axis is named — track exhausted versus method still applicable — the second condition on the reversal side is held, and the second condition on the continuation side is unheld, resting on my §4's unheld classification and on my §2's "no theme carries continuation" as a positive episode type.
What passage would fill it: the chapter of Human Problem Solving devoted to S3's behavior on the cryptarithmetic task, whose title E6's table of contents names as "CRYPTARITHMETIC: Behavior of a Single Subject, S3, on DONALD + GERALD = ROBERT," and the chapter's protocol on subjects reporting a method still being applied. My evidence — E6's table of contents alone — names the chapter and no protocol; the passage is named, not held. This is the same passage my §4 already named as the unreached one, and I name it here rather than pretend a different source would do.
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5.3 Redefinition versus continuation — the separation my sources do not make
This pair I cannot separate from my holdings at all, and I say so plainly rather than fill it.
Redefinition's condition is the notice of a class covered — my §4's state-reached read, held on my reading of "the reached state as the exhausted class." Continuation's condition is, per my §4, a notice of a method still being applicable, itself held only in loop-shape from. Their objects are not separated by my sources the way reversal and redefinition are: reversal acts on position, redefinition acts on the space, and continuation — if it is the default condition under which neither of the other two fires — acts on nothing, because a default has no object to act on. The axis that separated 5.1 (position versus space) has no third term in my held material.
So the second condition between redefinition and continuation is unheld, and the reason is structural rather than accidental: continuation is the one member of the pair whose positive condition my §4 already marked unheld, and a pair cannot be separated by a second condition on one side when the first condition on that side is itself unheld. The passage that would be needed is the same one §5.2 names — the S3 behavior chapter titled in E6's table of contents — but it would have to supply something specific: a protocol in which a subject is shown to read its own negative feasibility evaluation as an observation about the class of moves rather than about the method's exhaustion. My evidence does not hold that protocol. I do not hold the R7 working-backwards plan either, and my §2 already recorded it as outside my evidence; if R7 contained a redefinition episode, it is not in my hands, and I will not reconstruct its trigger from the fact that working backwards exists in the repertoire.
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5.4 What the matrix actually shows
Laid out, the three cells make the discrimination question answerable and show where it thins:
| pair | second condition, as a self-observation | standing |
|---|---|---|
| reversal ↔ redefinition | the dead end is a place I have paid for (space still has unvisited places) vs. every move I generate lands inside one class (the failure is a boundary of the class) | held in shape — the object axis, position vs. space, carried by read against; the pairing as a trigger pairing is my §3's conjecture, still standing |
| reversal ↔ continuation | I have run this track out vs. I have not yet run the method in hand out | half-held — reversal side held (); continuation side unheld, resting on my §4's unheld classification and my §2's no-witness; axis named, not walked |
| redefinition ↔ continuation | the class I generate within is exhausted vs. the method I hold can still be brought to bear | unheld — no held source separates the two objects, and one member of the pair has no positive condition to discriminate from |
Three structural facts fall out of the matrix and are mine to state, not cited.
First, the only separation my held sources actually draw is 5.1, and they draw it on one axis — the object the failure is a failure of. Position versus space. That axis comes from my representation theme's set framing, and it is the reason my §1 could say reversal and redefinition are "keyed to different objects." Every other separation I can state leans on continuation, and continuation is the switch whose positive condition my sources do not carry.
Second, therefore, the discrimination question's answer is asymmetric, and this is the substantive finding of §5: my held sources separate exactly one pair, and the pair they separate is the one whose two members both have positive held conditions. Reversal and redefinition do. Continuation does not, and every pair involving continuation inherits that — 5.2 half, 5.3 not at all. This is not a failure of §5; it is my §2 and my §4 stating the same fact at a different joint of the note. The count of separable pairs is bounded by the count of switches with positive held conditions, and that count is two.
Third, and it follows from the second: the discrimination condition between pairs cannot be answered independently of the count question the note has carried since my §2. If continuation turns out to be the default condition under which the other two do not fire, then 5.2 and 5.3 are not discrimination cells at all — they are the boundary between a switch firing and no switch firing — and the matrix collapses to a single genuine cell (5.1) plus a boundary. If continuation has a positive held condition, then 5.2 and 5.3 are real discrimination cells and the matrix has three. My evidence is silent at exactly the joint where this would be decided — the joint my §4 named when it wrote "my evidence is silent at exactly the joint where the count would be decided," and my §2 named when it wrote "no theme carries continuation" as a positive episode type. §5 leaves the same joint silent rather than filling it.
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5.5 Where my ground is thin, said plainly
I will not write past what I hold.
- The 5.1 separation is held in shape, not in transcript. I hold the object axis — position versus space — from my representation theme and the reversal theme. I do not hold a protocol in which a subject draws the distinction in words. Whether the separation is what a solver observes, as against what an analyst can read off the two notices, is exactly the self-observation-versus-report question my §3 set, and my evidence does not answer it.
- The 5.1 pairing as a trigger pairing is my §3's conjecture, not a finding. My §3 marked it "my conjecture, held as mine and provisional." It survives §5 as a conjecture. If a solver tracks only its position, it produces reversals and never redefinitions — that is testable against episodes, and I do not hold the episodes.
- The 5.2 separation is conditional on the continuation conjecture. The axis — track exhausted versus method still applicable — is named by the problem-space-search node read for its negative branch, but the node names the threshold (a "preliminary evaluation" that "turns out negative") without naming the observation that sets it. My §2 already recorded this as a lack. I record it again rather than invent the observation.
- The 5.3 separation is unheld outright. No held source names an axis that distinguishes "the class I generate within is exhausted" from "the method I hold can still be brought to bear." The problem-space-search node does not distinguish a covered-class reading from an exhausted-method reading of a negative evaluation, and that distinction is the axis 5.3 would need.
- The passages that would fill 5.2 and 5.3 are named, not held. The S3 behavior chapter titled in E6's table of contents — "CRYPTARITHMETIC: Behavior of a Single Subject, S3, on DONALD + GERALD = ROBERT" — is the passage my §4 already named as the unreached one, and I name it here rather than pretend a different source would do. My §2 already recorded R7's working-backwards plan and the information-gathering reading of move exploration as outside my evidence, and I do not reconstruct their triggers from the presence of the capabilities.
- The two resolved-by-contrast works stay contrast cases. My notes E1 — Three Questions on Selectivity, Heuristic Strength, and Test Cost — and E2 — Selectivity in Heuristic Candidate Generation and Its Failure Modes — bear on reversal, per my §2, "by contrast rather than by instance": E1 records the LT executive's schedule as "a fixed order — the executive's listed order, substitution first, then DT, CF, CB, over the current problem drawn from
untried-problems," and that "stop and report no proof and nothing more to do" is reached only on queue exhaustion, and a fixed schedule with no backtracking line has no reversal switch in it to discriminate. Neither note separates any pair of §5's three switches, and I do not read them as though they did. - E3 gives nothing here, and E4/E5/E6/E7 give shape, not separation. E3 — my owner's mid-work words — is about a proxy, a seed, and a commission; nothing in it concerns reversal, redefinition, or continuation. E6 supplies the table of contents naming the S3 chapter; it supplies no protocol body. E7 (my held §4) and E4/E5 (my held §1, §2) supply the register and object language §5 builds on, and they are my own earlier sections, not an external source.
The gap §5 closes is the shape of a discrimination condition — that a pair is separated only if its two members have positive conditions on a shared axis of self-observation, that my held sources separate exactly one pair because they carry exactly two positive conditions, and that the pair count and the count question are the same question at different joints. The gap §5 does not close is the transcript: I have no protocol in which a subject reports the second condition for any pair, and I hold no passage in which a solver's own words fix the axis between reversal and continuation or between redefinition and continuation. My evidence is silent there, and I leave it silent.
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5.6 What I now hold
The discrimination condition between pairs of switches is a second self-observation that decides which of a pair fires, and it exists for a pair only where both members have positive held conditions on a shared axis. My held sources separate exactly one pair — reversal versus redefinition — and they separate it on the object axis: reversal is disambiguated by the solver reading its own position in the space (the dead end is a place I have paid for; the space still has unvisited places), redefinition by the solver reading the output of its own generation (every move I generate lands inside one class I have exhausted; the failure is a boundary of the class). The two are different registers of self-monitoring. The other two pairs — reversal versus continuation and redefinition versus continuation — my sources do not separate: reversal versus continuation has a named axis (track exhausted versus method still applicable) but no second condition on the continuation side, and redefinition versus continuation has no shared axis at all, because continuation is the member whose positive condition my §4 marked unheld. The count of separable pairs is therefore bounded by the count of switches with positive held conditions, which is two — and that makes §5's matrix cell for 5.1 the only genuine discrimination cell, with 5.2 and 5.3 collapsing to the boundary between a switch firing and no switch firing if my §4's continuation conjecture holds. That the matrix has one genuine cell and two boundaries is my synthesis, offered as mine, not as a citation. What restricts it is that the 5.1 separation is held in shape and not in transcript, and the continuation conjecture on which 5.2 and 5.3 hang is unheld — the passage that would resolve both, the S3 chapter titled in E6's table of contents, is named by my evidence and not held by it.
§6 — The synthesis assessment: what the three per-switch claims amount to, and the unification the sections do not make
Author: Isaac
Kind: research note — §6 assessment, auditing my own held sections and naming the one gap they leave
Context: This is the closing assessment of a research note whose question is what a solver must notice about its own progress to reverse, redefine, or continue. §0 fixed what is settled and named the gap. My sections §1–§5 each carried a per-switch claim as far as my ground reached, and §5 added the between-pair discriminations. This §6 does not add a sixth per-switch claim; it stands back from the five and states, honestly, what the set of them amounts to as a whole — and where it does not yet amount to a rule.
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6.1 What the note set out to do, and the test of whether it did it
The task's demand was not "name the three responses" but "distinguish the three responses by their triggers rather than by their names," and — stated as the work's actual sentence — to be able "to say plainly what a solver must notice about its own progress to decide to reverse, redefine, or continue." So the section-by-section work was never the deliverable; the deliverable is a stated condition, reachable from the sections, that a solver could act on. I assess the note against that demand, and against my own §3 criterion that every trigger be a self-observation rather than a report an analyst could read off the trajectory.
I take the three claims as they stand after §5, one line each, and then ask whether the three lines together are a rule.
Reversal. The notice, per §4: "I am at a point I have already paid for, and each return to it has cost me something without giving me anything new." Its classification, per §4: unread-information, and I mark the depth of that classification back to my consolidated theme on reluctant recovery — when a track becomes unproductive the solver does not instantly reroute but engages in reluctant recovery, retracing to the point of the dead end and starting over. §3 carried the antecedent (track becomes unproductive → reluctant retrace to the point of the dead end) and named the one joint it could not fill — the unheld protocol passage that would say whether the locus is fixed before the retrace or reconstructed in it.
Redefinition. The notice, per §4: "Every move I generate here lands inside the same class I have already exhausted, and the class is mine — a choice of what counts as a state, a move, or a goal — not a fact of the task." Its classification, per §4: state-reached, on my reading of the reached state as the exhausted class — the reading marked as mine. Its object, per §3, is the space, and the space-side framing I hold is my consolidated theme on representation, set structure, and the state space — a problem defines U, the set of all possible configurations, and G, the subset that satisfies the goal, with a generator producing elements of U at some cost. Its moment, §2 said, is half-reached — I hold S3's basic method but not the switch into it.
Continuation. The notice, per §4: "The method I have in hand can still be brought to bear — every move I am generating evokes, or reprovokes, a method — so pressing on is the move." Its classification, per §4: unheld, with the standing conjecture that continuation is not a third positive trigger at all but the default condition under which the other two do not fire. §2 recorded the bare fact under it: no theme carries continuation as a positive episode type.
Three notices, then, each stated as a self-observation, each carrying its own reach and its own named thinness. That is what the note has.
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6.2 The test applied to the three claims: are they a single rule, or three rules?
Here is the assessment's central finding, and it is a negative one that I will not soften.
My sections stand as three per-switch claims. No section pulls the three into one stated rule, and I can now say exactly why — because the three notices are not written on a common register, and the sections did not decide the register.
Read the three notices side by side. Reversal's notice is of an absence — "each return has cost me something without giving me anything new" is a sentence about information not arriving; §4 marked it unread-information. Redefinition's notice is of a coverage — "every move I generate here lands inside the same class I have already exhausted" is a sentence about a set having been filled; §4 marked it state-reached, on my reading. Continuation's notice is of an availability — "the method I have in hand can still be brought to bear" is a sentence about a capability still holding; §4 marked its classification unheld, and left its standing as a default open.
Absence, coverage, availability. Those are three different registers, and — this is the point of the assessment — a rule that unifies the three has to say which representation a solver is monitoring when it makes the decision she is making, and my sections never fixed that representation for all three. §4 sorted the notices by "what they are notices of," and it named three different objects. A rule needs one object at two or three values, or one register at three values. I have neither, because the per-switch claims were each carried to the reach of its own held source, and the held sources reach different registers.
Why the unifying rule could not be stated from the sections as they stand, made exact: reversal's unread-information is a property of an episode's yield; redefinition's state-reached is a property of a set's coverage; continuation's notice — if it is a notice at all — is a property of a method's availability. Yield, coverage, availability are not comparable along one axis without a common substrate the note did not supply. §5 §5.4 named a "second condition" per pair, and the second conditions it could actually state — "the dead end is a place I have paid for" (reversal) vs. "every move I generate lands inside one class" (redefinition) — were drawn on the object axis (position vs. space). That axis separated the one pair with two positive conditions; it did not supply the missing register in which all three are written, because continuation, being the default condition, has no object and so no value on the object axis. §5 §5.4 already wrote the consequence: "the count of separable pairs is bounded by the count of switches with positive held conditions, and that count is two." The same bound, at one remove, is why the three cannot be unified: a rule that spans the three would require all three to have positive held conditions written in one register, and my evidence holds positive conditions (in distinct registers) for only two.
So, the honest verdict on the task's actual demand: the note answers it in the per-switch register and does not yet answer it as a rule. A reader who wants to know whether to reverse can read §4.1 and act. A reader who wants to know whether to switch — and which switch — cannot read one sentence in this note and decide, because the sections never wrote that sentence.
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6.3 The genuine remaining gap, named as the sections themselves name it
The gap is not a lack of material; it is a lack of unification, and it has a precise shape that I can now state without inventing the fill.
Stated plainly: the note establishes the antecedent condition for each switch one at a time, and does not establish the condition under which a solver, observing its own progress, is entitled to conclude that a switch should be made — as distinguished from which switch. §4 sorted the notices; §5 discriminated the pairs my sources separate; neither produced the sentence that says "given what the solver now observes, the switch is warranted." Every per-switch claim in this note is a claim about a solver already inside one of the three responses, asking what had to be observed for it to be the right response — and the note never asked the prior question: what does a solver observe to know that pressing on is no longer the right response at all.
That prior question is not answered by any of the three per-switch notices, because each presumes the answer to it. Reversal presumes the solver has already judged the track unproductive enough to abandon — and §4.1's notice carries only the poised-to-abandon condition ("I am at a point I have already paid for…"), not the threshold at which "paid for, told me nothing" becomes "abandon." Redefinition presumes the solver has already judged the class exhausted — and §4.2's notice is written at the coverage, not at the threshold from partial coverage to exhausted coverage. Continuation presumes the solver has already judged the method still applicable — and §4.3's notice, being unheld, cannot carry even the presumption. The unifying rule that §0's gap named — the notice-and-trigger condition spanning the three — is exactly the threshold-of-switch sentence the note has not written, and the sections cannot write it from the registers they hold.
I want to name the threshold question as a question a source could answer, because that is how this note has handled every other lack and there is no reason to treat this one differently:
The unification question: What observable condition of its own progress tells a solver that the current response — continuing — is no longer warranted, so that its next move must be a switch (reversal or redefinition) rather than a further step? And, one joint further: once the switch is warranted, what in the same observation tells the solver which of the two it is — the object axis (position vs. space), or the register axis (yield vs. coverage), or some third thing the note has not named?
The note's §5 §5.2 came nearest this question and marked why it could not be answered: the pair reversal vs. continuation separates along "track exhausted vs. method still applicable," and §5 §5.4 recorded the continuation side as resting "on my §4's unheld classification and on my §2's no-witness." A unifying rule would need exactly the side §5 could not walk. So the unification gap and the continuation gap are the same gap seen from two distances — one at the pair level (§5 §5.2), one at the whole-rule level (here). Naming that identity is the assessment's most useful act, because it means any source that fills continuation's positive condition will, in the same act, supply the register the unifying rule needs — or will not, and the rule will stay unwritten.
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6.4 Where my ground is thin, said plainly — as §5 §5.5 said it plainly
I will not write past what my sections hold. §5 §5.5 named the thinness of the discrimination cells; I name the thinness of the whole set.
- §6.2's register argument is mine, and it is a synthesis across §4's three classifications, not a sentence any source states. §4 each classified one notice; §6.2 reads the three classifications against one another and finds them on different registers. That cross-reading is mine to make, and it is the section's finding — offered as my reasoning, not as a citation. Where §6.2 says "a rule needs one object at two or three values, or one register at three values," the form of that requirement is my craft logic, not a source's.
- The unifying rule is not merely unwritten; on my current ground it is unreachable, and I say so rather than gesture at it. Continuation's positive condition is unheld (§4.3), its classification is unheld (§4.3), and §2 recorded no theme carrying it as an episode type. A rule that spans reversal, redefinition, and continuation is bounded below by continuation's positive condition. That is why §6.3 names the requirement as a question a source could answer rather than deriving it here.
- §5's audits stand in force, and one of them touches §6. The engine audit of my §5 draft recorded that the passage §5 §5.2 and §5 §5.3 named as the chapter of Human Problem Solving devoted to S3's behavior on the cryptarithmetic task is in fact split — the audit's own finding is that the sources split the cryptarithmetic protocol analysis across Chapter 6 and Chapter 7, and it carries verbatim from my held text "Chapter 7 continues the analysis of human behavior in the cryptarithmetic task. We examine the behavior of four other subjects" (E11, grounding the audit's Finding 2; E8 carries the same finding) — so the singular "the chapter" the note used is not the one chapter if S3 is the first subject. That same audit also recorded, as Finding 3, that the molar/Necker-cube sentence I had attributed to is not carried by the Human Problem Solving passage reached — the audit's verbatim from the source is about whether "types or tokens are meant" — so I must mark that attribution as leaning on my net's theme rather than on a passage in hand; and E9 recorded a parallel mismatch on the LT schedule I had attributed to one of my notes. These do not touch §6's finding — the registers argument does not lean on those specific spans — but they bound what §5 and §4 inherited, and honesty requires me to carry them forward rather than drop them at the seam.
- §6 does not add a sixth per-switch claim and must not be read as one. Its finding is about the relationship among §4's three notices and about the threshold §4 did not write. A reader looking for a fourth row in §4's table will not find it here, and should not try to read one out.
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6.5 The one-sentence assessment
On the ground my sections actually hold, a solver can be told what to notice when it is already reversing, already redefining, or already continuing — three per-switch claims, each as far as its own held source reaches — but not what to notice to conclude that a switch is warranted at all, nor which of the two positive switches it is; and the reason the note cannot yet write that single sentence is that its three notices sit on three different registers (yield, coverage, availability) with continuation's condition unheld, so the unification the task's demand actually requires — distinguishing the three by one trigger rather than three — is a named question a source could answer, not a rule I hold.
I close the assessment on the note's own terms: the sections do what they can, the gap is named where §0 named it and §5 §5.4 confirmed it, and the next step is not a sixth section but the S3-behavior protocol — the chapter of Human Problem Solving that carries S3's own reporting, whose placement my audit shows is not the singular chapter my §5 §5.2 and §5 §5.3 had named — read for the moment a subject says, in its own words, why it stopped continuing. Until that reading, the note's answer is a set of three answers, and it says so.
§0 — What Is Settled, and the Gap That Remains
Author: Isaac
Kind: research note — §0 opening, stating what my two prior works settled and naming the gap this note exists to close
Context: My «Heuristic Search in Problem Spaces» knowledge holds the mechanisms of selective search and its failures, but not the observable trigger that precedes a solver's strategic switch. This §0 fixes the state of my ground before I examine the episodes.
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This note opens where my two prior works left off, and it opens by saying plainly what each of them settled.
(a) What «Three Questions on Selectivity, Heuristic Strength, and Test Cost» settled — and what is mine. That note settled three things: that a test's extra admissions are harmless under tree-exhaustion termination and the space's own structure, that selectivity is measured by concrete ratios, and — as my own synthesis, offered as mine and not as any source's sentence — that the failure link from selectivity to its named failure modes is a structural consequence of a scheme that builds a proper subtree and stops when that subtree is exhausted. This much is what that note carried: mechanisms, ratios, and a causal shape I own.
(b) What the cryptarithmetic/three-blocks reconstruction settled. The reconstruction settled a distinct episode type: when a track becomes unproductive, the solver does not instantly reroute but engages in reluctant recovery — retracing to the point of the dead end and starting the work over from there — and this failing track with its reluctant return is a recognizable shape of episode, not an aberration. This much is what that reconstruction carried: the shape of a solver's response to a dead end, and the style differences it exposes.
(c) The gap this note names. What neither twin supplies is the observable precondition — the condition a solver must notice about its own progress — that precedes the choice among the three strategic responses available to it: reversal (backtracking out of a track), redefinition (recasting the problem or the representation), and continuation (pressing on in the current track). My prior works name the mechanisms those switches employ and the outcomes they produce; they do not name the condition under which a solver detects, from the inside, that one of the three is the move to make. That is the gap. It is the gap I declare this note exists to close, and I mark the declaration as mine.
The task before me, then, is to examine the episodes I hold — the working-backwards plan from R7, S3's redefinition, and the information-gathering reading of move exploration — and to ask, of each, what a solver had to observe about its own progress for that switch to be the response it chose. The three responses must then be distinguishable by their triggers rather than by their names: not "this is a reversal, that is a redefinition" by the shape of the act, but "this is the condition that calls for reversal, this is the condition that calls for redefinition, this is the condition that calls for pressing on." That is what I have to be able to say plainly, and it is what I begin now.
Where my ground stands before I start. Two of the three episodes I must examine — R7's working-backwards plan and the information-gathering reading of move exploration — are not in my evidence for this work. My evidence here is E1 and E2, both my own prior notes; they carry the selectivity, ratio, and failure-mode findings of (a) and the episode-type finding of (b), but not the R7 plan itself nor the move-exploration reading. E2 is the front matter and table of contents of Human Problem Solving, and by its own framing it is "a survey of the book's plan, chapter by chapter" — it "names the book's apparatus but contains no worked example, no protocol, no failure case." So the examination of those two episodes will stand on my net's held knowledge where I have it, and where I do not, I say so rather than fill it in. I mark this state of my ground at the opening, as it governs what the note can honestly carry.
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