Section 8, paragraph 1The three bypasses supply different resources for a global invariant
Informal interpretation Motivation, interpretation or scope; not a formal claim.
1 Paper text
The three bypasses identify different resources for handling a global invariant: multi-frame inputs expose local transition information, multiple rollout heads provide complementary channels, and persistent recurrence accumulates the invariant through sequential updates. In the recurrent route, memory connects successive positions while the growing processing horizon supplies the depth needed for parity. The common design principle is to match the information and computation available to the agent to the invariant it must maintain. We briefly discuss directions beyond the specific NIM setting.
Generated from paper_jmlr.tex, lines 1223–1223.
2 Explain this
The common design principle behind the three bypasses: match the information and computation available to the agent to the invariant it must maintain. Two frames expose local transition information; several rollout heads provide complementary channels; persistent recurrence accumulates the invariant, with memory connecting positions and a growing processing horizon supplying the depth that parity needs.
3 How this is formalised
A summary; the formal content is Proposition 5.14.
| Paper anchor | sec:discussion-p1 (website anchor; the manuscript has no label here) |
|---|---|
| Displayed as | Section 8, paragraph 1 |
| Claim | The three bypasses supply different resources for a global invariant |
| Coverage category | Informal interpretation |
| Statement source | paper_jmlr.tex lines 1223–1223; SHA-256 of the normalised block source 893b4b62c9dff25a… |
| Depends on | Proposition 5.14 |
| Explanations | explain/c-discussion, formal/c-discussion |
| 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).