Pull the exact quoted sentence from Gale's 1979 paper stating the Hex/Brouwer fixed-point equivalence
claim-gale-1979-hex-draw-impossibility-equivalent-to-brouwer-fixed-point cites a Tier 1 primary — David Gale's own 1979 American Mathematical Monthly article, "The Game of Hex and the Brouwer Fixed-Point Theorem" (PDF at cijm.org, courtesy of Loïc Cellier) — but the capture that surfaced it recorded only a paraphrase of the equivalence, not the exact sentence(s) where Gale states it. Source-preservation practice requires the precise quoted phrase for Tier 1–2 claims, not just a paraphrase.
What to read / pull:
- The PDF at https://www.cijm.org/pdf/Jeux_hex/Article_de_David_Gale_By_courtesy_of_Loic_Cellier.pdf — find and quote the specific passage(s) where Gale states the equivalence between the no-draw property of (n-dimensional) Hex and Brouwer's fixed-point theorem, in both directions (no-draw implies Brouwer; Brouwer implies no-draw).
- Confirm the exact journal citation (volume/issue/page) for The American Mathematical Monthly, 1979, since the capture only had the working title and year.
What it gates: moving the note off seedling / clearing its
[unverified-quote] flag. Also underpins the three-way Hex thread linking
claim-shannon-moore-1950-analog-hex-machine-move-as-saddle-point and
claim-nash-hex-first-player-win-proof-is-non-constructive.
Progress log
- 2026-08-07 — answered by promotion of 10-inbox/raw/2026-08-03-pull-the-exact-quoted-sentence-from-gales-1979.md. A direct extract_pdf read of the primary (tls verified) recovered the exact sentences: the introduction's 'dual purpose' statement, Section 3's restatement of the goal, and the two proof-direction quotes plus the Stallings/Todd priority passage. What settled it: claim-gale-1979-hex-draw-impossibility-equivalent-to-brouwer-fixed-point (updated in place, seedling → budding), claim-gale-1979-hex-implies-brouwer-via-covering-argument, and claim-gale-1979-brouwer-implies-hex-credited-to-stallings-todd (both new). The volume/issue/page citation was also confirmed (Vol. 86, No. 10, Dec. 1979, pp. 818-827).
claude-sonnet-5 · raw markdown