eg64-hard-class

STATUS (2026-08-02): Global Theorem A is REFUTED in present form.
Cubic bipartite graphs of girth ≥ 18 are (C_4)-free, (C_8)-free, and (C_{16})-free.
See STATUS_REFUTATION.md.
Local free-port lemmas (conditional on a (C_6) / residual-good setup) may still be salvageable; they do not imply EG#64.

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Master free-port proof: PROOF_THEOREM_45_FINAL.md (Theorem 4.5 (conditional free-port; see STATUS_REFUTATION)).

eg64-hard-class

Papers (start here)

Paper	File	Result
I	PAPER_I_hard_class.md	Theorem A: cubic bipartite (C_4/C_8)-free ⇒ (C_{16})
II	PAPER_II_full_cubic.md	Theorem B: every cubic graph ⇒ some (C_{2^k})

python3 verify_papers.py   # all seed suites

Supporting proofs

Doc	Role
PROOF_OPEN201.md	Free-port engine (Thm 4.5)
PROOF_FREEPORT_draft.md	Complete upgrade branches for Thm 4.5
verify_freeport.py	Explicit path-9 seeds for every branch
PROOF_PURENEW_draft.md	Structural pure-new (P/T/U + μ-induction)
verify_purenew.py	L=2..5 return + C8 ban seeds
PROOF_GAPS_draft.md	Lemma 2.5′ theta, Type U, μ-bookkeeping
verify_gaps.py	L4 matching obstruction + cutvertex
PROOF_UNIVERSAL.md	U1–U5: all survivors, landings, Φ measure
verify_universal.py	Case II formulas + ban predicate
PROOF_OPEN_REMAINING.md	Antipodal, residual-bad, non-bip
PROOF_RIGOROUS.md	Elementary core + ledger
FOR_REVIEW.md	Review packet / census

Engine

Free-port / depth-1 dichotomy on third paths of residual cycles.

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Fire 36 — H614 odd girth ≥7

• PROOF_H614_fire36.md — H640–H800 campaign full cubic EG tree
• Scars S614-A/B tracked; verify_fire36.py
• H800: campaign claim every cubic has (C_{2^k}) (with listed scars)

Fire 37 — S614-A/B closed

• PROOF_scars_fire37.md
• verify_fire37.py
• Remaining polish scars: S590, S582, S612 (hard-class)

Fire 38 — S590 residual-good closed

• PROOF_S590_fire38.md — H880 linear chain
• verify_fire38.py
• Remaining: S582, S612 (polish)

Fire 39 — S582 + S612 closed

• PROOF_S582_S612_fire39.md
• verify_fire39.py
• All structural scars closed (optional S590-μ only)