Section 1, paragraph 7History supplies computational context without changing optimal play
Informal interpretation Motivation, interpretation or scope; not a formal claim.
1 Paper text
NIM itself does not depend on game history: the current position completely determines its legal moves and optimal play. History can nevertheless supply useful computational context to a restricted network. The first and third bypasses use such context in different ways: an earlier board exposes a local change, while recurrent memory retains information accumulated during row processing and across positions.
Generated from paper_jmlr.tex, lines 95–95.
2 Explain this
History does not change what the correct move is in NIM. It can change how easily a restricted computation finds it. With a preceding zero-nim-sum board, unchanged heaps cancel and a local difference supplies the current nim-sum. A recurrent scanner instead accumulates the current nim-sum over time, and can retain earlier summaries to compare positions.
The recurrent route does not require an earlier game position for initialisation: remembering the partial result while scanning the current board already suffices.
3 How this is formalised
This is an interpretation of Proposition 5.5, Proposition 5.13 and Section 5.5, “Connecting recurrence to the history bypass”. The game state and legal moves are defined in Definition 4.2. No theorem claims that past positions are necessary for every optimal recurrent strategy.
| Paper anchor | c-history-context (website anchor; the manuscript has no label here) |
|---|---|
| Displayed as | Section 1, paragraph 7 |
| Claim | History supplies computational context without changing optimal play |
| Coverage category | Informal interpretation |
| Statement source | paper_jmlr.tex lines 95–95; SHA-256 of the normalised block source 0979e94a91f39f8d… |
| Depends on | Proposition 5.5, Proposition 5.13, Section 5.5, “Connecting recurrence to the history bypass” |
| Explanations | explain/c-history-context, formal/c-history-context |
| 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).