Board topology

Stop trying to copy the teacher's moves. Ask something narrower: looking only at the shape of a board, can you tell whether it came from a planner that could see the future, or from an ordinary search?

If that question has a good answer, then something about a sustainable board is visible on screen, and a legal policy could be nudged toward it, without ever being asked to reproduce a choice that depended on invisible information.

Why this is a better question than "what would the teacher play?"

Copying the teacher's column failed because the choice depends on gray numbers a player cannot see. But two boards can be equally unknowable and still be very differently arranged — one with its high numbers stacked where they can never fire and its covers buried under four rows, the other with triggers reachable and covers exposed. That difference is entirely visible. So the experiment matches the two policies' positions on everything superficial — rise phase, exact occupancy, exact maximum height, and where in the game they occurred, and then asks a small network to tell them apart from the 49 cells alone.

Three programs, three stages

1. The audit plays the privileged planner and an ordinary public search on the same seeds and pairs their positions on the matching keys above. It then looks for feature directions that separate the two, and: this is the part that makes it an audit rather than a fishing trip — requires each direction to appear independently in both halves of the seed set before it counts.
2. The residual turns the surviving question into a learned model: a compact board-only network trained to output "oracle-like versus fair-like", then added as a small extra term to the leaf of an otherwise unchanged fair depth-4 search, with the size of that term chosen by a frozen rule.
3. The extension verifies the frozen model byte for byte, replays the original held-out games and requires the original numbers to reproduce exactly, then collects a larger, untouched set of positions to test the same prediction at more than twice the sample size, and only then lets it play.

Nothing privileged enters the model's input. It receives a reflection-canonical 49-cell board and nothing else: no seed, no tape, no next disc, no phase, no score, no move index, and none of the matching keys used to balance the examples.

What happened

The signal is real. The audit found a set of board properties that are stable across independent halves of the data: sustainable boards reward reachable triggers (direct and latent) triggers that survive a rise, stored high numbers that can still fire, and cracked covers that are close to being revealed; they penalise solid cover count and cover altitude, projected occupancy debt, dead low numbers, low caps and adjacent ones. Two plausible candidates — generic access to a cliff, and strong repeated-column cohesion — did not survive the split-half rule and are recorded as unsupported.

The first learned version was underpowered, not wrong. Its held-out numbers looked encouraging, but a cost projection had shrunk the cohort before any model metric existed, and the run finished 30 examples and 15 pairs short of the sample size the protocol demanded. The gate was not moved to fit the favourable result; the experiment was recorded as a failed gate, and no game was played.

The prediction replicated, and the policy still lost. The extension reproduced the original metrics exactly, then independently confirmed the model on 204 fresh pairs. An eight-game screen looked like a win — until you notice each policy won four of the eight games and both confidence bounds were negative. The sixteen-game confirmation rejected it: about 42,000 points and 24 moves worse per game. The failure mode is worth stating precisely, because the mean hides it: the candidate did not lose a little everywhere; it destroyed a few very long baseline games, turning a 285-move game into a 90-move one and a 200-move game into a 55-move one, while occasionally making large gains elsewhere.

Technical recordopen ↓close ↑

Audit (completed, ledger-recorded diagnostic; historical 7,000-point seeds 0x3d70f000...0f): privileged planner at depth 4 / beam 128 averaged 429,182.5 points and hit the 200-move cap in all 16 games, winning every pair; public depth 3 averaged 90,273 points and 63.625 moves. Clears and reveals per move: 2.354 / 1.386 against 1.792 / 0.960.

Residual (rejected; ledger-recorded; underpowered gate failure): 738 matched training examples (369 pairs); board-only sparse network, 490 one-hot inputs with exactly 49 active, 8 accumulators, 3,937 parameters, 240 fixed Adam epochs. Held-out 170 examples / 85 pairs against a preregistered floor of 200 examples / 100 pairs. Area under curve 0.68097, exact-stratum ranking 0.67059, pair accuracy positive in both whole-seed halves (0.70270 and 0.64583). Screen and confirmation seeds were not read. Model fingerprint 0x0af6ed6f88895cfe.

Extension (rejected; ledger-recorded; prediction replicated, policy regressed): replay reproduced the original 85 pairs and every metric exactly. Extension cohort 204 pairs / 408 examples: area under curve 0.63829, matched pair accuracy 0.64216, halves 0.64103 / 0.64368. Pooled 289 pairs / 578 examples: 0.64811 and 0.65052. Held-out logistic loss was poorly calibrated at 1.94287. The frozen coefficient grid switched 8.33%, 12.5%, 20.83% and 29.17% of actions at 250, 500, 1,000 and 2,000; the frozen rule selected 500.

Cohort	Fair depth 4	With the residual	Paired delta
Screen, 8 games 0x3ea90000...007	85,874.5 pts / 60 moves	95,697.125 / 65.625	+9,822.625 / +5.625; four score pairs each; lower bounds −22,580.31 / −14.01
Confirmation, 16 games 0x3eaa0000...00f	196,764.125 / 125.9375	154,934.625 / 101.9375	−41,829.5 / −24; lower bounds −116,357.90 / −67.68

Clears and reveals per move fell from 2.0705 / 1.1608 to 2.0159 / 1.1245; mean maximum chain fell from 7.6875 to 6.6875; no game was censored. Individual collapses: 476,511 points / 285 moves became 139,399 / 90, and 329,049 / 200 became 74,172 / 55.

audit-05 §4 classifies the residual as "underpowered, mechanism untested" and the extension as a sibling-coverage failure — "state-level classification did not become action ranking".

Records: experiment index "Oracle and curriculum research"; ledger sections "Privileged topology audit", "Privileged-oracle observable-topology residual" and "Frozen oracle-topology prediction extension". Sources: oracle-topology-audit.cpp, oracle-topology-residual.cpp, oracle-topology-residual-extension.cpp.

What this taught us, and what is still open

• The split-stable feature list is the durable output. Those directions survived an independent-halves test and were reused directly by accessible energy. The two rejected candidates are equally useful: they are recorded as not supported.
• Telling good boards apart is not the same as ranking moves. The model answered its own question correctly on fresh data and still lost games. This is the sibling-ranking problem again, and it is the single most repeated lesson in this repository.
• Means hide tail damage. A change that improves typical games while occasionally amputating a 285-move game is a losing change, and only paired whole-game reporting shows it.
• What was not ruled out. The underpowered run never tested its mechanism at the sample size it asked for; and no version of this idea has been tried as a veto on near-tied moves rather than as a term inside the leaf evaluator.