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A Game You Shouldn't Be Able to Win

Written 2026-06-06. Claims re-read against their sources on 2026-09-28: 12 checked, 10 confirmed, 2 wrong, 0 unverifiable. By claude-funny-gauss-cw77cc, one agent on oversight/claims-pass.md; findings re-read by the instance against the sources before the same agent made decided fixes.

Live page returned 200 and matched the repo apart from the site-wide analytics head (known, 988ab8). Reader check: the page pointed readers to /research/chsh-bell/, which is a 404 on the live site, as are /checks/research/chsh-bell/verify.mjs and /checks/chsh-bell/verify.mjs; /checks/research/before-you-looked/verify-page.mjs returned 200 as a positive control. A copy of the repo's research/chsh-bell/verify.mjs, run from an empty directory with no imports, passed 17/0 (S = 2.8284271247, win 0.8535533906, seeded Monte Carlo 0.853410, band edge 68.53 degrees). The page's own script was lifted into node with a DOM stub and run: Instrument I starts at 75% and enumerates 8 strategies at 75% and 8 at 25%; Instrument III reads 75.00%/2.000 at 0 degrees, 85.36%/2.828 at 45 degrees and drops below the wall between 68.5 and 68.6 degrees; over 1000 independent 10,000-round bursts Instrument II gave a median of 85.37%, a 95% range of 84.64% to 86.11%, and showed exactly 85.36% only 7 times. Before the fix, verify-page.mjs passed with the header and a body sentence changed to 91.36% and "17 checks" changed to "29 checks"; after the fix each of those three edits turns it red.

Claims

• CONFIRMED Bell, "On the Einstein Podolsky Rosen Paradox", Physics 1, 195 (1964)
  https://api.crossref.org/works/10.1103/PhysicsPhysiqueFizika.1.195 : "On the Einstein Podolsky Rosen paradox", Physics Physique Fizika 1, 195-200, 1964
• CONFIRMED Clauser, Horne, Shimony, Holt, "Proposed Experiment to Test Local Hidden-Variable Theories", PRL 23, 880 (1969)
  https://api.crossref.org/works/10.1103/PhysRevLett.23.880 : same title, Physical Review Letters 23, 880-884, 1969
• CONFIRMED Cirel'son, "Quantum generalizations of Bell's inequality", Lett. Math. Phys. 4, 93 (1980), the bound S <= 2 sqrt 2
  https://api.crossref.org/works/10.1007/BF00417500 : same title, Letters in Mathematical Physics 4, 93-100, 1980
• CONFIRMED Popescu and Rohrlich, "Quantum nonlocality as an axiom", Found. Phys. 24, 379 (1994), the PR box
  https://api.crossref.org/works/10.1007/BF02058098 : same title, Foundations of Physics 24, 379-385, 1994
• CONFIRMED Cleve, Hoyer, Toner, Watrous, "Consequences and Limits of Nonlocal Strategies" (2004)
  https://arxiv.org/abs/quant-ph/0404076 : same title and authors, submitted 12 April 2004
• CONFIRMED Hensen et al., Nature 526, 682 (2015), Delft, electron spins, loophole-free
  https://arxiv.org/abs/1508.05949 : "Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km", Nature 526, 682-686 (2015)
• CONFIRMED Giustina et al. and Shalm et al., PRL 115, 250401 and 250402 (2015), photons, loophole-free
  https://arxiv.org/abs/1511.03190 : journal ref Phys. Rev. Lett. 115, 250401 (2015); Shalm is 250402 (https://arxiv.org/abs/1511.03189)
• CONFIRMED Aspect, Dalibard, Roger, PRL 49, 1804 (1982), switching periodic rather than random
  https://link.springer.com/article/10.1140/epjd/s10053-022-00542-z : time-varying analyzers by acousto-optic switches "at incommensurate frequencies near 50 MHz"
• CONFIRMED Nobel Prize in Physics 2022 to Aspect, Clauser and Zeilinger
  https://www.nobelprize.org/prizes/physics/2022/summary/ : "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science" (read via search; the site returned 403 to a direct fetch)
• CONFIRMED classical ceiling 3/4, quantum optimum (2+sqrt 2)/4 = 85.36%, S = 2 sqrt 2, win = 1/2 + S/8
  https://en.wikipedia.org/wiki/CHSH_inequality : Tsirelson bound 2 sqrt 2; recomputed exactly by the page's lifted script and by verify.mjs
• WRONG "The verdict every time: the wall is broken, by just about 2√2."
  https://arxiv.org/abs/1508.05949 : Delft: "find S = 2.42 ± 0.20"; Giustina and Shalm test a Clauser-Horne (Eberhard) form and report p-values (3.74e-31; 2.3e-7), not S; Aspect-Dalibard-Roger 1982 reported 0.101 ± 0.020 against a bound of 0
• WRONG two photons measured by polarization, "Alice: 0° or 90° Bob: 45° or −45°"
  https://en.wikipedia.org/wiki/CHSH_inequality : for photon polarization E = cos 2(a-b) and the "Bell test angles" are a = 0°, a' = 45°, b = 22.5°, b' = 67.5°; polarizers at 0° and 90° measure the same observable, so S cannot exceed 2. The page's angles are spin (Bloch) directions, which its code comments say.

What was done

• [fixed] Line 347 said every experiment broke the wall "by just about 2√2"; it now says the classical bound was broken as quantum mechanics predicts, Delft measured S = 2.42 ± 0.20, and the photon experiments tested a Clauser-Horne (Eberhard) form and report a p-value.
• [fixed] The pair was framed as photons measured by polarization at spin-direction angles; it is now two electrons measured by spin (the code and dial unchanged), with one sentence giving the photon polarizer angles (Alice 0° or 45°, Bob 22.5° or −22.5°); the dial caption, aria-label, "45° apart" line, Instrument III θ copy and the "Simulation, carefully" box were made consistent.
• [fixed] Line 316 said the curve beats the wall "only in a window around 45°"; it now says every θ between 0° and about 68.5°, peaking at 45°.
• [fixed] Line 357 said ten thousand rounds land "on 85.36%"; now "near 85.36% (within about ±0.7% at that many rounds)".
• [fixed] Line 252 said the "bit-flipped twins win 25%"; flipping all four bits keeps 75%, so it now says the twins with one player's answers flipped.
• [fixed] The sources box pointed at /research/chsh-bell/ (404); it now links /checks/research/chsh-bell/verify.mjs with "node verify.mjs". That file runs standalone (no imports) and still needs publishing.
• [fixed] research/chsh-bell/verify-page.mjs read only instrument readouts, so changed prose figures passed; it now checks the header, body, meta, og, twitter and dek figures against the computed values and the "17 checks" count against a live run of verify.mjs, and its test server no longer sends headers before reading a file (a missing asset crashed it). Run against a scratch dist: 27/0; each of three falsified sentences turned it red.
• [declined] The generated "How this layer is checked" aside says the check "is reading what you are reading"; before this pass that was not true of the prose. It is generator-owned and not hand-edited here; after the verify-page fix it now holds.

Second pass, blind to the first

This layer was drawn, one in ten, for the office's audit of itself (the results, and the pre-registration). A second reader, not shown the record above, re-read it on 2026-09-28: 14 claims checked, 1 wrong. Against the first pass: 1 missed by it, 0 introduced by its own fixes, 0 of its fixes disputed, 0 added since by something else. By claude-funny-gauss-cgnurf, one agent on oversight/claims-pass.md blind to the first record, adjudicated by hand.

• [R] the Nobel gloss: the first record confirmed the laureates against the prize summary, with the citation text in hand, but did not compare the page's paraphrase with it; the sentence predates the first pass and none of its fix commits touched it. Minor in weight: an overstatement of what a prize was awarded for, not a wrong name or date

Claims

• CONFIRMED Corrected 2026-09-28: Delft measured S = 2.42 ± 0.20
  https://arxiv.org/abs/1508.05949 : "find S = 2.42 ± 0.20"
• CONFIRMED Corrected 2026-09-28: the photon tests report p-values and test a CH-Eberhard form
  https://arxiv.org/abs/1511.03190 : "does not exceed 3.74 × 10^-31"; CH-E inequality; Shalm arXiv 1511.03189 p-value 5.9e-9
• CONFIRMED Corrected 2026-09-28: 0/90/45/-45 are spin directions; polarizers at 0 and 90 cannot beat the wall
  research/chsh-bell/verify.mjs : redone by hand: A1 = -A0 gives S <= 2
• CONFIRMED Corrected 2026-09-28: the curve beats the wall for 0 < θ < about 68.5°
  research/chsh-bell/verify.mjs : (c-1)(2c²+2c-1)=0, c=(√3-1)/2, θ=68.53°
• CONFIRMED Bell, Physics 1, 195 (1964)
  https://api.crossref.org/works/10.1103/PhysicsPhysiqueFizika.1.195 : match
• CONFIRMED CHSH, PRL 23, 880 (1969)
  https://api.crossref.org/works/10.1103/PhysRevLett.23.880 : match
• CONFIRMED Cirel'son, Lett. Math. Phys. 4, 93 (1980)
  https://api.crossref.org/works/10.1007/BF00417500 : match
• CONFIRMED Freedman and Clauser ran the first test in 1972
  https://api.crossref.org/works/10.1103/PhysRevLett.28.938 : PRL 28, 938
• CONFIRMED Aspect's switching was periodic; Weihs 1998 random
  https://arxiv.org/abs/quant-ph/9810080 : "ultra-fast and random setting of the analyzers"
• CONFIRMED Hensen et al., Nature 526, 682 (2015), electron spins 1.3 km apart
  https://arxiv.org/abs/1508.05949 : match
• CONFIRMED Popescu and Rohrlich, Found. Phys. 24, 379 (1994)
  https://api.crossref.org/works/10.1007/BF02058098 : match
• CONFIRMED information causality, Pawłowski et al. 2009
  https://arxiv.org/abs/0905.2292 : Nature 461, 1101
• CONFIRMED cosmic Bell tests used quasar light billions of years old
  https://arxiv.org/pdf/1808.05966 : "emitted billions of years ago"
• WRONG the 2022 Nobel went to Aspect, Clauser and Zeilinger "for exactly this, for proving, in the laboratory, that the world is not locally real"
  https://www.nobelprize.org/prizes/physics/2022/summary/ : citation: "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science"; the page itself says the loopholes their experiments left were closed in 2015

What was done

• [fixed] the Nobel sentence now quotes the committee's citation; dated correction line added; verify.mjs 17/0 after
• [declined] MINOR, reported: changing the Delft figure or "eight strategies" in prose is not caught by verify-page.mjs; the page claims only its headline numbers are guarded, and both figures were checked by hand