Section 5.4, paragraph 1Restatement of the single-frame barrier as the motivation for rollouts
Informal interpretation Motivation, interpretation or scope; not a formal claim.
1 Paper text
Theorem 5.2 shows that no circuit can evaluate the nim-sum in a single forward pass. A natural follow-up is whether planning—testing candidate moves and simulating play, as in Monte-Carlo Tree Search (MCTS)—can compensate.
Generated from paper_jmlr.tex, lines 627–628.
2 Explain this
The single-frame barrier rules out computing the needed invariant in one shallow pass. The natural next question is whether planning (simulating play) can make up for it. This subsection studies a deliberately simple planning interface to answer that question precisely.
3 How this is formalised
A restatement of Theorem 5.2 (barrier), whose precise content is winning-move selection on the encoded family; the paper's phrase "evaluate the nim-sum" is the informal reading of that result.
| Paper anchor | sec:search-gap-p1 (website anchor; the manuscript has no label here) |
|---|---|
| Displayed as | Section 5.4, paragraph 1 |
| Claim | Restatement of the single-frame barrier as the motivation for rollouts |
| Coverage category | Informal interpretation |
| Statement source | paper_jmlr.tex lines 627–628; SHA-256 of the normalised block source a5063fd156793c21… |
| Depends on | Theorem 5.2 (barrier) |
| Explanations | explain/c-search-intro, formal/c-search-intro |
| Build evidence | fresh isolated rebuild, audit report |
4 Lean statement and source
No Lean statement corresponds to this claim. This is interpretation or motivation, not a formal mathematical claim.
Build evidence: fresh isolated rebuild of all 38 bundled modules with Lean (version 4.26.0, started 2026-10-10T15:21:56Z, finished 2026-10-10T15:27:00Z: 38/38 modules compiled, 1588 axiom reports, no errors. See Build for the commands and the independent audit of 2026-10-10 (dated evidence).