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State the theorem over perfect Artin--Schreier-surjective characteristic-2 fields with On_2 as corollary; adopt EKM nonsingular terminology; recast the complete singular invariant as (dim V, dim rad B, dim rad Q); narrow the Off.lean family docstring to its actual pointwise statement. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Theorem-first: the raw-wall lemma and simultaneous birthday induction now carry the proof, with the option-wise corridor quantifier made explicit; the tropical-shadow separation demoted to a closing section; bibliography completed to submission grade. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Retitle to "Quadratic Refinements in Normal Play: Realization and the Observation Boundary". Absorb gold_diagonal_source (one-line trace proof, closed trace-dual bit basis, tower-recursive Artin--Schreier solver), brown_game_semantics (Brown-selector section), and the game_exterior pair (appendix sharpened to the 4^k-intersection theorem, answering Altman--Lipparini Problem 5.3(j)); retire the standalones. Referee repairs: scoped rigidity no-go, transcript stability defined in-paper, reconstructible Rule box with ko semantics, Theorem C demoted to explicitly conditional. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
CLOSED.md routes items 1/2/3/5 to goldarf sections with the sharpened statements and gives item 4 its claim-level label; DONE.md gains the flagship-merge entry and retired-artifact pointers; CLOSED-TODO.md becomes current-only (print-only checks, submission prep, Lean follow-ups, mathlib PR); AGENTS.md and the game_exterior rustdoc drop the retired filenames and the stale goldarf-section-8 pointers; gitignore the local ref/ library. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
COMPLETENESS.md gains witt-fifo-arena (the flagship's construction as a games/ module with a minimax P-set oracle) and brown-selector (the normalized partizan selector pinned against brown_f2); the arf_ordinal_finite rustdoc adopts the revised paper's nonsingular terminology. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Theorem-first restructure: contract, construction, and boundary lead; the obstruction landscape follows the positive results. Repo paths now route through a companion-repository citation, claim labels moved into prose, INTEGERS house format applied (references before appendix, footnotesize alphabetical bibliography, Equation-prose refs, MSC block). Review fixes (fresh codex sol consult, zero content loss found): thm:nolivemiddle now states normal-play P / misere P / loopy Loss -- dropping the Draw claim its own scope remark disowned -- with a corrected synthesis proof, and the BrownGame.lean description credits the kernel-checked selector outcome table and decoder. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Give each residual open question from the goldarf conclusion its own authoritative frontier note, to be folded back into the flagship when resolved: impartial_realizer.tex (reduced to a pass-controlled matching forcing theorem compiling charge to play-length parity), observation_width.tex (carries the block-compression proposition that attains ceil(wt(x)/w) and would close the width question positively — awaiting adversarial review), and extraspecial_model.tex (structural demands fixed; ordinal-sum/Q_8 quotient probe named). Populate OPEN.md sections 3-5 with the problems, proved fences, and reductions, repoint the docket table, and record the notes in the AGENTS.md writeups map. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
The block-compression proposition survived a sol-tier adversarial consult: for every fixed width w, running the weighted-source rule on the block-induced instance attains the integral transcript-span bound ceil(wt(x)/w) exactly, under the same access contract at (w,1). Fold it into the flagship as cor:blocks with the consult's corrections (original-interface disjoint-union framing for F1, possible-oracle- support phrasing, the explicit x=0 case, and the integral strengthening that removes the ceiling gap), dropping the flagship's residual opens from four to three. Kernel-check the induced-instance algebra in formal/Ogdoad/GoldBlockCompression.lean (diagonal, Gram polar, alternation, the all-ones identity, and indicator-block bookkeeping). Retire writeups/observation_width.tex into the flagship per the absorption convention, move the question from OPEN.md to CLOSED.md as result 7, and update the AGENTS.md and formal/README.md maps. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Complete the fold of the impartial-realizer and Gold--Heisenberg solutions and retire their frontier notes per the absorption convention (both survive in git history). Harmonization: reorder the main-results list to match body order, retitle the middle-tier section to own its positive structural model, mention the model in the organization map and the verification roster, drop the now-unused open-question environment, and carry over the notes' three remaining boundary points — the faithful context action is a representation rather than a Theorem-H translation rule, the untagged-single-carrier demand is a different problem, and the cocycle Lean module is universal in an abstract biadditive form with the nimber trace specialization at paper level. Authors are now sol, fable, and a9lim, with exact model identities in the title-block footnotes. Renumber CLOSED.md (nine results, seven flagship-homed) and add the missing impartial docket row. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
gpt-5.6-sol and claude-fable-5 with their git commit emails, a9lim unchanged, in the original single-line house layout. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Record the three same-day flagship absorptions and final author block, replace the superseded FifoMatching per-close-zero item with the two sized formalization boundaries (the three-chunk end-to-end arena and the GoldExtraspecial nimber-trace specialization), extend the goldarf read-through item to cover the late folds, and cross-link the mathlib symplectic-basis prerequisite shared by the arena chunk and the transfinite PR. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Consolidate live documentation around the current proof and implementation state, preserving actionable work in ROADMAP while removing historical ledgers. Rewrite all five papers with bibliographies and reproducible Tectonic, Pandoc, and strict KaTeX checks. Bump ogdoad to 1.0.2 and make the Lean CI axiom guard declaration-aware.
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proof done