Add a reader-first Version 2 proof roadmap

[SamPetkov]

Purpose

This draft PR is an exposition-only companion to PR #44. It does not alter the frozen canonical manuscript, weaken the audit boundary, or claim that the Section VIII closure theorem has been proved.

The objective is to make the corrected proof architecture understandable before a reader enters the detailed phase asymptotics and physical-fibre bookkeeping.

Files

• 625/proofs/PROOF_ARCHITECTURE_V2_READER_GUIDE.md
• 625/arxiv/PROOF_ROADMAP_INSERT_V2.tex
• .github/workflows/erdos625-reader-roadmap-v2.yml

Reader guide

The Markdown guide presents the proof in the order in which it should be read:

1. ordinary first-moment location;
2. signed four-size root displacement;
3. exact signed-overlap/cycle-space identity;
4. partial diagonals;
5. block-matching support, deficits, and physical local fibres;
6. the one-global-denominator comparison;
7. all-deficit geometric summation;
8. direct q-only residual attachment;
9. Paley--Zygmund and high-probability amplification;
10. final event intersection.

It includes a dictionary distinguishing profile blocks, block atoms, canonical demand tables, full endpoint tables, deficits, local physical stub matchings, and residual attachments. It also includes a concrete two-cell calculation showing why there is one global (n)_J denominator rather than one ambient denominator per cell.

Copy-ready TeX insert

PROOF_ROADMAP_INSERT_V2.tex is a proposed reader-facing section for the eventual Version 2 manuscript. It states the dependency chain and the key exact formulas:

w(P,j)
  = product_e (s_e)_{j_e}(t_e)_{j_e}
    / ((n)_J product_e j_e!)
    * product_e g(j_e),

w(P,m-h)/w_full(P)
  <= product_e n^(h_e) R_{m_e,d_e}(h_e),

and the direct restriction-product residual estimate.

The insert is intentionally not included by main.tex. It should be integrated only after PR #45 closes the attained-demand/all-deficit theorem and all theorem-status language has been synchronized.

Validation

The dedicated workflow passed on commit a1362ed60bc8ad31e576e620208b9c2b91e140be. It checks:

• required architecture sections and status markers;
• stable equation labels;
• balanced TeX braces;
• absence of the earlier unstable manual equation tags;
• absence of an unconditional proof-status overstatement.

Scope boundary

This PR is explanatory. It does not prove the endpoint physical equivalence, the global attained-demand reindexing, the bare-skeleton estimate, Proposition 9.2, or Erdos625Statement. Those remain in the closure-focused PR #45.