Section 8.5, paragraph 1Representability removes one obstacle; it does not determine whether training finds the computation
Informal interpretation Motivation, interpretation or scope; not a formal claim.
1 Paper text
The constructions establish that the required computations can be expressed using the stated resources: a shallow restoration rule, structured rollout policies, or a shallow recurrent update iterated over the board. This removes one obstacle before training begins. It does not determine whether gradient descent will find those computations, whether sparse game rewards provide enough guidance, or whether the resulting behaviour generalises.
Generated from paper_jmlr.tex, lines 1257–1257.
2 Explain this
The constructions show that the needed computations can be expressed with the stated resources. That removes one obstacle before training starts. It does not decide whether gradient descent finds them, whether sparse game rewards give enough signal, or whether the resulting behaviour generalises.
3 How this is formalised
A statement about the scope of the results; not formalised.
| Paper anchor | sec:opt-gap-p1 (website anchor; the manuscript has no label here) |
|---|---|
| Displayed as | Section 8.5, paragraph 1 |
| Claim | Representability removes one obstacle; it does not determine whether training finds the computation |
| Coverage category | Informal interpretation |
| Statement source | paper_jmlr.tex lines 1257–1257; SHA-256 of the normalised block source c782d009bceb3860… |
| Explanations | explain/c-opt-gap, formal/c-opt-gap |
| 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).