---
title: "Stage D0: the fair value of oracle-visited boards"
family: oracle-curriculum
summary: Measures whether the boards a clairvoyant oracle chooses to stand on are still good boards when the future is replaced by ordinary public randomness, by re-valuing them and matched fair-search boards under the same 32 independent public futures.
status: completed
evidence: ledger-recorded
reads: teacher
---

Measures whether the boards a clairvoyant oracle chooses to stand on are
still good boards when the future is replaced by ordinary public randomness,
by re-valuing them and matched fair-search boards under the same 32
independent public futures.

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

## The intuition

The [oracle](/learn/glossary) sees the whole future: every hidden gray-disc
value and every disc it will be dealt. Its games last far longer than any
fair policy's. The open question of the oracle-curriculum family (stated as
"the single missing measurement" in `docs/exploratory/audit-05-optimistic-curriculum.md`
§5.4) is *why*: does the oracle survive because it builds genuinely better
boards, or because it knows the tape and threads a needle no public player
could see?

The two explanations dictate opposite research programs. If the boards are
genuinely better, a student can be trained on them with honest labels — the
H-pool idea. If the advantage is the tape, those boards teach nothing
transferable and the program should close.

Stage D0 separates the two by a controlled measurement, with no model and no
training:

1. Take boards the oracle actually stood on (pool **O**).
2. Take boards a [fair depth-4 search](/learn/concepts/expectimax) stood on,
   matched to pool O on rise phase, occupancy and maximum height (pool **F**),
   so the comparison is between boards of the same coarse shape.
3. Strip both to public information only, then re-value every board the same
   way: play 25 further moves with a fixed public depth-1 fair policy under
   32 independent futures derived (through domain-separated hash streams)
   from the board itself — never from the game's seed. The mean number of
   moves survived is the board's **fair value**, `R_fair`.

If oracle boards are better boards, `R_fair(O)` should exceed `R_fair(F)` by
a sizable fraction of the realised-lifetime gap the oracle actually enjoyed.
That fraction is the transferable fraction

> τ = (R_fair(O) − R_fair(F)) / (R_tape(O) − R_real(F)),

where `R_tape`/`R_real` are the remaining moves each board actually had on
its own trajectory, both capped at the same 25-move horizon.

## How it works

The implementation reuses the repository's frozen machinery rather than
rewriting it; `d0.cpp` builds into two binaries so that the privilege
boundary is enforced by the linker, not by discipline.

1. **`d0-generate`** (privileged, teacher-side) plays 64 oracle games
   (depth 4, beam 128, 500-move cap — the constants of
   `approaches/oracle-curriculum/state-curriculum/oracle-curriculum.cpp`) on
   the leased training seeds `0xa52e0000–0xa52e003f`, and samples up to 31
   public states per game from move 50 onward — one from each of 31 equal
   stretches of the game, with a seed-keyed offset inside each stretch so the
   sample cannot alias with the five-move rise cadence. Each state is
   exported as the public tuple (board, next disc, moves until rise) plus
   labels: the oracle's column, fair D4's column at the same root (a public
   computation), and the realised remaining moves.
2. The same binary then plays fair-D4 reference games
   (`approaches/fair-expectimax/reference/fair-only-depth4.cpp`: depth 4,
   five strata) on `0xa52e0100–0xa52e01ff`, lazily in fixed batches of 16
   seeds, and matches their post-move-50 states 1:1 to pool O on the exact
   bucket (rise phase, occupancy ÷ 4, maximum height ÷ 2) — the binning of
   `approaches/oracle-curriculum/topology/oracle-topology-audit.cpp` — at
   most two per bucket per game, stopping when every O state is matched or
   the 256 seeds run out. Unmatched O states are dropped and counted.
3. **`d0-relabel`** (public-only; its symbol table is checked to contain no
   oracle planner and no headless-tape accessor) reads back only the public
   tuple of each record and computes `R_fair`: 32 independent restarts at
   horizon 25 under fair depth-1 continuation, with reveal and visible-disc
   streams drawn from the domain-separated `"CRRV"`/`"CRVS"` streams of
   `oracle-curriculum.cpp`, seeded from the canonical public-state hash. It
   also values **every legal first column** of every O root under the same 32
   futures (common random numbers), which gives the fair-top-1 comparison:
   how often the oracle's column is fair-best at its own roots versus how
   often fair D4's column is.
4. **`analyze.py`** computes τ, the four R numbers, origin-game halves, the
   `kBlocked` flow-band fraction, the top-1 rates, and a 10,000-resample
   cluster bootstrap over origin games (seed `0xb0071eaf`).

Two deliberate differences from the original curriculum relabeller, both
visible in `d0.cpp`'s header comment: K = 32 scenarios instead of 7, and the
restart is played in the canonical mirror orientation at every step, which
makes `R_fair` of a board and of its mirror image equal exactly rather than
approximately.

The CHECK gates (`gate.sh`) run before any leased seed is read, on the
already-opened probe range `0xa5278000–0xa52784ff` only: the symbol-table
privilege check, byte-identical generation at 4 and 16 threads,
byte-identical relabelling across two runs and thread counts, exact mirror
invariance, metadata independence (score, level and move counter cannot
change any restart), domain separation of the streams, and label blindness
(editing every label field in the input changes no relabel output byte).

## What happened

The measurement came back against the idea, and the H-pool program closed.
On the same 32 public futures, the boards the oracle stood on were only about
a quarter of a move better than matched fair-search boards over a 25-move
lookahead — and the oracle's own choice of column at those boards was fair-best
*less* often than the fair search's choice at the very same boards. Boards the
oracle reaches are fine boards; its moves from them are tape-reading, not
transferable judgement.

All numbers below are from the result record
`RS-20260823T205143Z-ead14c9d` (run `RUN-20260823T195750Z-1cb2f9de`).

- Pool O: 1,984 states from 64 oracle games (63 of 64 reached the 500-move
  cap). Pool F: 1,271 matched states from all 256 fair-D4 games (match rate
  0.641; 713 O states from buckets fair D4 rarely visits were dropped, as
  preregistered).
- `R_fair(O)` = 24.783 vs `R_fair(F)` = 24.520: a fair-value advantage of
  +0.263 moves (cluster bootstrap 95% [+0.156, +0.367]), the same positive
  sign in both origin-game halves — real, but small, and compressed by the
  25-move ceiling (92–96% of futures survive the horizon).
- `R_tape(O)` = 24.338 vs `R_real(F)` = 24.611: with almost every oracle game
  censored at the 500-move cap, 94–95% of both realised remainders sat at the
  25-move cap, so the realised-lifetime gap the preregistered τ divides by
  came out at −0.274 moves instead of the large positive gap the definition
  assumed. τ = −0.959 (95% [−3.069, −0.390]) — a **fail** against the
  preregistered τ ≥ 0.25 gate, though a fail driven by a degenerate
  denominator rather than by a negative fair-value difference; the result
  record states this limitation explicitly.
- The action-quality criterion failed on its own, unaffected by the ceiling:
  the oracle's column was fair-top-1 at its own roots 76.6% of the time
  against fair D4's 81.4% at the same roots (difference −0.049,
  95% [−0.069, −0.029]; on the 194 roots with a unique best column, 26.8%
  vs 38.7%).
- Under fair randomness almost no oracle board is a trap: 0.5% of matched O
  states fall in the `blocked` flow band (F: 2.6%).

<TechnicalDetails title="Run record">

Preregistration `EX-20260823-hpool-stage-d0-e0ad1c65` (CHECK tier,
diagnostic), theory `TH-20260823-hpool-optimistic-states-fair-labels-bb707bc9`,
lease `SL-20260823T200000Z-a52e0000` (training role, 0xa52e0000–0xa52e01ff,
opened once). Gates passed before the lease was opened
(`runs/RUN-20260823T191900Z-b9f8f80d/d0/gates.log`); main run 3,132 wall-
seconds on 16 threads, peak RSS 152 MB, artifacts under
`runs/RUN-20260823T191900Z-b9f8f80d/d0/`. Outcome: run valid, scientific
outcome fail, theory assessed not-supported-as-tested at pilot tier. Two of
the three preregistered refusal conditions triggered (τ < 0.25; oracle column
fair-top-1 less often than D4's); the sign-agreement condition passed.

</TechnicalDetails>

<TechnicalDetails title="Preregistered gate">

Stage D0 refuses the H-pool theory
(`TH-20260823-hpool-optimistic-states-fair-labels-bb707bc9`) if any of:

- τ < 0.25 pooled;
- the two origin-game halves of pool O disagree in the sign of
  `R_fair(O) − R_fair(F)`;
- the oracle's column is fair-top-1 at O roots less often than fair D4's
  column at the same roots.

A refusal closes the optimistic-teacher program; a pass licenses exactly one
follow-on (the fair / optimistic / mixed pool-comparison experiment), and is
itself a diagnostic — never a policy claim.

</TechnicalDetails>

## What this taught us / what is still open

The measurement audit-05 called "the single missing measurement" now exists,
and it says the oracle's advantage lives overwhelmingly in what it does with
the tape, not in the boards it builds: the fair value of its boards is only
marginally above matched fair boards, and its actions are worse than fair
D4's under honest randomness even on its own boards. Per the preregistration,
no student is trained on the optimistic state pool and the E1 ordering
ablation is not run.

Still open, and not answered by this experiment: whether the small but real
+0.26-move board-quality edge would grow at a longer relabelling horizon or a
deeper continuation policy (the 25-move horizon capped both sides of the
comparison), and whether the 713 unmatched O states — boards whose shapes
fair D4 never reaches — are better or worse than the matched ones. Both
questions would need a new preregistration; neither revives the H-pool
teacher on this evidence.