Theories

Registered falsifiable claims from research/theories/. Each theory names its mechanism and the criteria that would refute it; experiments and results link back to these claims. Historical theories that predate the machine-readable registry live in the experiment ledger and on their approach pages.

not-supported-as-testedassessedpilotpublic-policyTH-20260820-distributional-afterstate-ranker-7aba7fb3

Successor-closed distributional afterstate values rank siblings as well as fair D4

Claim

A single action-free public-afterstate evaluator, trained only on successor-closed labels (every legal sibling at each root, aligned chance scenarios, a fixed public continuation policy), ranks the legal root actions of disjoint whole-origin games at least as accurately as fair D4, and therefore can serve as the value core of a direct 1-ply chance-averaged policy with exact D4 fallback.

Mechanism

Prior learned policies in this repository failed for a diagnosed reason: they were trained on the action the behavior policy played (or a sparse sibling sample), so deployment required ranking actions whose successors were never labeled; low value error on visited states coexisted with poor sibling ranking. Making the evaluator action-free (its input is the fully resolved public afterstate: board, next visible disc, moves-until-rise) and the corpus successor-closed (every legal sibling's afterstates receive labels under common event-keyed chance scenarios) removes both the action-identity shortcut and the coverage gap by construction: every candidate action at deployment is scored by the same function on in-support states. Distributional (quantile) targets plus a within-root ranking loss train the relative ordering the policy actually needs rather than only absolute calibration, and the multi-move continuation labels supply the long-horizon signal that a one-ply heuristic lacks.

Falsification criteria

On preregistered held-out whole origins, the model's scenario-mean action ranking underperforms exact fair D4's ranking of the same roots in top-1 accuracy against the H40 long-outcome target by more than the frozen margin.
Within-root pairwise accuracy or normalized regret fails the frozen thresholds on any held-out origin fold.
Action stability between independent scenario halves is below the frozen threshold, showing the labels themselves are too noisy to learn the ranking.
The corpus cannot be built successor-closed (any legal sibling missing a label) at the pilot scale within the frozen compute budget.

Evidence: EX-20260820-afterstate-pilot-h40-29b8588a (completed)EX-20260820-afterstate-pilot-h40-k256-65a05477 (completed)EX-20260820-afterstate-pilot-h40-k64-d7a9faf5 (completed)EX-20260820-d4-toptwo-override-gate-0bdb39a1 (completed)EX-20260821-afterstate-d2-teacher-58772f17 (completed)EX-20260821-afterstate-full-train-override-ec7f28f4 (completed)result: inconclusiveresult: inconclusiveresult: failresult: failresult: failresult: fail

mixedassessedpublic-developmentpublic-policyTH-20260821-depth-gradient-beyond-fair-d4-034314fc

The fair search's depth gradient continues past the fourth ply once the chance estimator is exact

Claim

With seven chance strata (one stratum per disc value, so every individual chance marginal is exact), adding a fifth ply of look-ahead to the fair expectimax search raises mean score on the shared 64-game development cohort by a paired margin whose one-sided 95% whole-game bootstrap lower bound is above zero, as the third-to-fourth ply does (+86,172 with a lower bound of +26,468, finding-05). With five strata, where the third-to-fourth ply gradient is absent (-7,723, not significant), no fourth-to-fifth ply gradient is expected either. Depth and chance-estimator exactness are therefore complements, and the fourth ply is not a special stopping point.

Mechanism

finding-05 measured a depth gradient that exists only at the higher stratum count: at five strata the search's chance estimate is biased enough that a deeper horizon compounds the bias faster than it adds information, while at seven strata the estimate's marginals are exact and the extra ply pays. If that is the whole mechanism, the same exchange should continue at the fifth ply, which is also the first depth that always contains a row rise (a rise happens every five placed discs), so a five-ply search is the shallowest one that can never be surprised by the rise schedule. The competing account is that the fair search's terminal utility has no death-depth shaping - bestFutureValue returns the same -1,000,000 whether the game ends at ply 1 or ply 5 - so a deeper horizon finds more within-horizon deaths, flattens the sibling value surface, and hands the decision to column-order tie-breaking. The two accounts differ in sign at the fifth ply, which is what makes this worth the compute.

Falsification criteria

At seven strata, the paired depth-5 minus depth-4 score delta over the complete 64-game cohort has a one-sided 95% whole-game bootstrap lower bound at or below zero.
At five strata, the paired depth-5 minus depth-4 score delta over the complete 64-game cohort has a one-sided 95% whole-game bootstrap lower bound at or below zero.
Numbered clears per move, covered reveals per move and mean occupancy do not all move toward the survival requirement (2.400 clears and 1.400 reveals per move) from depth 4 to depth 5 at the same stratum count.
A depth-5 arm cannot complete its declared depth within its work bound (any decision below the requested depth voids the arm rather than falsifying the theory).

Evidence: EX-20260821-depth5-chance-exactness-factorial-a6a604fd (running)result: failresult: inconclusive

not-supported-as-testedassessedpublic-developmentpublic-policyTH-20260821-factored-chance-depth-compounding-aca01725

Chance-node decorrelation and search depth compound rather than substitute

Claim

Factoring the fair search's chance node into independent next-disc and reveal draws pays at every depth, so applying it on top of the fourth ply raises mean score over the same four-ply search with a single reveal sample by a paired margin whose one-sided 95% whole-game bootstrap lower bound is above zero. The depth-3 gain finding-09 measured (+64,116 with a lower bound of +7,475 from one to six reveal samples) is therefore an increment that adds to depth rather than an alternative way of buying the same thing.

Mechanism

finding-09 diagnosed a specific defect: the reference search indexed the next-disc draw and the covered-disc reveal with the same counter, so with seven samples it saw seven of the 49 joint outcomes and those seven were perfectly correlated. A move whose value depends on the combination could not be evaluated. That defect is a property of the chance node, not of the horizon, and the frozen four-ply search contains exactly the same defective node. If the defect is what the extra reveal samples repair, repairing it inside a deeper search should be worth at least as much as repairing it inside a shallower one, and the two axes should add. The competing account is that depth and chance-estimator quality are exchangeable ways of spending one budget - both ultimately buy a less biased estimate of the same expectation - in which case paying for both at once buys little beyond paying for either.

Falsification criteria

The paired depth-4 (N=7, M=2) minus depth-4 (N=7, M=1) score delta over the complete 64-game cohort has a one-sided 95% whole-game bootstrap lower bound at or below zero.
The depth-3 reveal ladder stops ordering with joint chance coverage: taking reveal samples from six to twelve (85.7% to 100% joint coverage) does not raise the paired mean over the six-sample arm.
Any arm completes a decision below its requested depth, which voids that arm.
The joint-coverage attribution fails: an arm with higher joint (disc, reveal) coverage scores below one with lower coverage at the same depth and the same work bound.

Evidence: EX-20260821-reveal-sampling-unfinished-arms-470677b5 (running)result: failresult: fail

untesteddraftproposalpublic-policyTH-20260821-search-guided-self-play-at-scale-299ed02f

Search-guided self-play with every-sibling labels converts compute into long-horizon strength

Claim

A search-guided self-play loop — actors that run a fair public-information search at every visited position, record the value of every legal sibling column under aligned chance scenarios, and train a public board evaluator on those successor-closed labels, which then becomes the leaf of the next iteration's search — produces a frozen public student whose mean whole-game score on fresh paired development cohorts rises with the compute spent per iteration, and at sufficient scale exceeds fair D4's mean by a preregistered margin.

Mechanism

Most learned evaluators in the ledger failed at ranking siblings because training data labelled only the move that was played (status.md §4-§7; sibling extrapolation). The distributional-afterstate pilot (TH-20260820-distributional-afterstate-ranker-7aba7fb3) removed that defect — it labelled every legal sibling under chance scenarios shared across siblings — and its four recorded pilot experiments relocate the bottleneck rather than resolving it: label stability required raising aligned scenarios from 8 to 256, and the resulting model still lost to fair D4 on ranking, with its own result record naming an undertrained checkpoint (11 of 20 epochs) and a weak D1-continuation teacher as the likely causes. This theory claims the missing element is the loop: using a search to produce the labels makes them stronger than the evaluator that guided the search (policy improvement), and feeding the trained evaluator back as that search's leaf and repeating is approximate policy iteration. Each iteration's labels then come from a strictly stronger searcher, which is the mechanism by which additional compute - more actors, more aligned scenarios per label, deeper or wider search per label, more iterations, longer training - turns into longer-horizon play rather than into a more confident copy of the same bias. It is the AlphaZero pattern adapted to a single-player stochastic game with a hard information boundary. No iteration of that loop has been run in this repository.

Falsification criteria

Pilot scale (this workstation): after a preregistered number of iterations, the evaluator's held-out sibling ranking on a locked every-sibling panel (top-1 and pairwise agreement with the fair-D4 gold standard, as in the 477-root panel) does not improve across iterations, or never reaches fair D4's own agreement.
Compute response: doubling actor compute between two consecutive iterations, with the data pipeline and learner held fixed, produces no paired SCREEN-tier (32-game) mean-score improvement beyond the whole-game bootstrap interval.
Deployment: the frozen public student of any iteration, evaluated through the public interface on a fresh paired 64-game development cohort, does not exceed fair D4's mean with a one-sided 95% whole-game bootstrap lower bound on the paired difference above zero.
Information boundary: any student that reads seed, hidden values, future discs, score, level, or move number is disqualified regardless of score.

Evidence: EX-20260821-afterstate-d4q-stage1-40136e9e (completed)result: fail