---
title: Board topology
family: oracle-curriculum
summary: Ask whether a player can recognise, from board shape alone, the positions a future-reading planner creates.
status: rejected
evidence: ledger-recorded
reads: teacher
---

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?

<EvidenceLabel status="rejected" evidence="ledger-recorded" reads="teacher" />

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](/approaches/oracle-curriculum/oracle-distillation)
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.

<TechnicalDetails>

**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`](/docs/exploratory/audit-05-optimistic-curriculum) §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](/docs/research/experiment-index) "Oracle and
curriculum research"; [ledger](/docs/research/history) 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`.

</TechnicalDetails>

## 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](/approaches/oracle-curriculum/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](/learn/concepts/ranking-siblings) 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.