A one-entry leaf memo across chance strata is a semantics-preserving speedup of the fast fair-D4 search
web/content/research/TH-20260822-leaf-memo-semantics-preserving-3bb0ac6b.mdx and it will appear here. The registered record is shown below.The registered record
Claim
Memoising the fast fair leaf's eighteen board-only features across consecutive leaf calls with the same (board, moves_remaining), recomputing only next_disc_vertical_options, produces bit-identical leaf values, identical actions, logical work, nodes, cache hits and completed depth, and reduces the wall time of a depth-4 decision by at least 1.5x at five and seven chance strata.
Mechanism
Within one chance node the strata share the post-move board whenever the cascade consumed no reveal draw; only the sampled next disc differs, and fast-leaf.hpp reads next_disc in exactly one term. Identical inputs give identical doubles; the dot product is re-run in the frozen order; the memo sits below the search's work increment so no recorded observable changes (audit-06 and its adversarial review).
What would prove it wrong
- Any leaf-value bit mismatch, any action/work/node/cache-hit/completed-depth mismatch against FastSearch, or any thread-count-dependent result on the probe games: not semantics-preserving.
- Interleaved timing ratio below 1.5x on real roots at either strata setting: the speedup claim is not supported as tested.
Experiments that test it
- CHECK gates for the one-entry leaf memo: bit identity, search parity, determinism, interleaved timing on real probe seedsfast-engine-memo MemoSearch vs fair-d4 · CHECK · completed
Results recorded against it
One-entry leaf memo (fast-engine-memo/MemoSearch) on real probe seeds: leaf bits 0/4,260 (d4s5) and 0/2,500 (d4s7) mismatches in the search's feeding order; parity with FastSearch 0 action/work/node/cache-hit/completed-depth mismatches over 160 (d4s5, 117,732,775 leaf calls) and 50 (d4s7, 119,607,901 leaf calls) moves; determinism 0 mismatches at 1 vs 4 threads; memo hit rate 61.74% (d4s5) and 68.47% (d4s7); interleaved timing plain/memo 1.581x (d4s5, 12 real roots x 3 reps) and 1.634x (d4s7, 6 roots x 2 reps) under load ~31, indicative. Engineering result: semantics-preserving; no strength claim.
- ✓0 leaf bit mismatches at d4s5 and d4s7 — observed: 0/4,260 and 0/2,500
- ✓0 parity mismatches vs FastSearch — observed: 0 over 160 and 50 moves
- ✓0 determinism mismatches — observed: 0 over 4 games
- ✓timing ratio >= 1.5 at both strata (indicative) — observed: 1.581 and 1.634 under load
Recorded metrics
- d4s5
- boards
- 4,260
- mismatches
- 0
- hitRateFeedOrder
- 0.5655
- d4s7
- boards
- 2,500
- mismatches
- 0
- hitRateFeedOrder
- 0.6392
- d4s5
- moves
- 160
- mismatches
- 0
- leafCalls
- 117,732,775
- hitRate
- 0.6174
- d4s7
- moves
- 50
- mismatches
- 0
- leafCalls
- 119,607,901
- hitRate
- 0.6847
- games
- 4
- threads
- 1
- 4
- mismatches
- 0
- d4s5
- roots
- 12
- reps
- 3
- plainSeconds
- 7.1319
- memoSeconds
- 4.5098
- ratio
- 1.5814
- d4s7
- roots
- 6
- reps
- 2
- plainSeconds
- 12.5726
- memoSeconds
- 7.6951
- ratio
- 1.6338
- Timing ratios were measured on a host at load ~31 and are indicative; an idle-host, three-repeat measurement is owed before any throughput claim.
- Probe cohorts are small (210 parity moves); the bit-identity argument is structural and the gates are confirmation, not the proof.
- Not adopted by any cohort runner yet.