Public regenerative B0

Spend the measurement budget where it matters: eliminate weak columns cheaply, test the survivors hard against the reference, and override the reference only on proof.

The intuition

The family's earlier programs gave every column the same expensive treatment. That is wasteful: at most positions, four or five of the seven columns are obviously poor, and the entire question is which of the remaining two or three is best. So run the comparison as a tournament instead of a survey — a short look at everything, a longer look at the survivors, and a final independent test between the winner and the reference's own move.

The word "regenerative" refers to the cycle structure of the game. The board rises every five moves, and a policy is really trying to arrive at each rise in a state it can recover from. The staged horizons here — 25 moves, then 50, then 75 — are five, ten and fifteen of those cycles.

There is one more piece of discipline, and it is the reason this experiment is worth reading even though it failed. Each stage uses independent chance scenarios for the decision it is making. Reusing the same imagined futures to first choose a winner and then confirm it would let a column that got lucky in the first round keep that luck in the second; independent panels make the confirmation an honest test.

How it works, step by step

1. At a stored public position, evaluate every legal column under seven shared 25-move continuations.
2. Keep the three best challengers, plus whatever the exact four-move reference would play, and re-evaluate all of them under 21 nested 50-move continuations.
3. Put the survivor through an independent 21-scenario, 75-move panel. It may be admitted only if it beats the reference on all three of a paired return lower bound, the number of discs cleared, and the number of covered discs revealed.
4. Compare the admitted column with the reference on one final, independent 35-scenario, 75-move panel.
5. Every continuation is played by a completed, full-width public two-move-ahead search; the exact four-move reference remains the fallback whenever no challenger is admitted.

The policy is handed only the board, the visible next disc and the rise phase. Origin, score, history, scenario identity and any future disc or reveal are excluded from it; origin identity is used only by the coordinator, to split the positions into eight whole-game folds.

What happened, in plain English

It came out very nearly identical to simply keeping the reference — and the "very nearly" is the result.

Out of 477 positions, the whole apparatus changed the reference's mind eleven times. Of those eleven changes, six helped. Score and survival ended up about a tenth of a percent above the reference, which sounds like a tie and, once the confidence bounds are computed, is worse than a tie: the lower bounds on both the score advantage and the lifetime advantage were negative, meaning the data cannot rule out that the overrides made things worse. Its clear and reveal rates were a hair below the reference's. When its own scenario halves were compared, it agreed with itself about half the time. Five of eight origin games did not regress, where six were required.

Every frozen gate except the ordered-halves check failed, and the experiment was recorded as a valid negative. The ledger's own reading is worth repeating because it resists the comfortable explanation: the missing signal is score, survival and flow — not merely commitment stability. In other words, the problem is not that the method was too timid about overriding. It is that when it did override, it had not actually found anything better.

Two limits belong with this. This is an offline root-panel proxy: only the root action was improved and every subsequent action reverted to the two-move-ahead policy, so it is not a complete-game result. And the 477-position panel had already been read by earlier work, so it is diagnosis rather than fresh model-selection evidence.

The technical record

Rejected, ledger-recorded. It opened only the locked, already-consumed corpus of 477 public roots from eight whole-game origins; the stored H200 outcomes were not used for selection, no origin game was replayed, and zero gameplay, protected or final seeds were opened.

The frozen gate required at least 70% split stability, 5% override coverage, 75% beneficial-override precision, 1.10× D4's raw score, 1.05× its restricted mean survival, positive one-sided 95% whole-origin lower bounds for utility and moves, non-regressing clear and reveal flow, at least six of eight non-regressing origins, and non-regression in both ordered halves.

Measure	Candidate	Gate or comparator
Overrides	11 of 477 (2.3061%)	≥ 5% coverage
Beneficial overrides	6 (54.5455%)	≥ 75%
Score ratio vs D4	1.000718	≥ 1.10
Restricted mean survival ratio	1.000621	≥ 1.05
Mean utility delta	+695.637 (lower-95 −169.897)	lower bound > 0
Mean move delta	+0.02660 (lower-95 −0.01365)	lower bound > 0
Clears / reveals per move	1.966311 / 1.053280	D4: 1.966329 / 1.053383
A1/A2 split stability	49.6855%	≥ 70%
Non-regressing origins	5 of 8	≥ 6 of 8
Ordered halves	both passed	pass

Cost: 2,509,342 synthetic transitions, 2,436,507 D2 calls, 4,625,296,860 D2 work units and 572,887,018 D4 work units, in 1,867.000 effective four-thread root seconds at 35,831,808 bytes peak RSS. Source, result, checkpoint and preflight SHA-256 values are all recorded. The ledger adds a requirement for any successor: bind a combined transitive-source hash rather than only the top-level source hash, before a passing result can be trusted.

Source: "Public regenerative policy-iteration B0 (rejected)" in the experiment history; the terminal-policy-iteration table in the experiment index.

What this taught us, and what is still open

• "Statistically indistinguishable from the reference" is a real result. A staged, careful, well-instrumented comparison could not find eleven reliable improvements in 477 positions. That constrains how much easy headroom sits next to the reference's choices.
• Coverage and effect size have to be reported together. An override rule firing at 2.3% of positions cannot move a mean even if every firing were right — and only 55% of them were.
• The staging machinery is reusable. Cheap elimination followed by independent confirmation panels is a sound design; what it was given to measure, a two-move-ahead continuation over 75 moves, is the part that did not carry enough signal.
• Still open: the same architecture with a stronger continuation policy, on fresh successor-closed data rather than a panel that has already been read.