{
 "what": "The registry's C71 > 6.521845710923046575 (Fourier entropy–influence), decided a second time from the cited n = 18 truth table by tools/verify_fei.js (JavaScript BigInt; H in closed form, A - sum B_p log2 p, the logarithms from the atanh series with outward rounding), which shares no code with instruments/fei/fei.py or the claimant; fei.py run beside it through tools/fei-second-harness.py; an Arb reference from fei.py's own spectrum; 12 planted claims of known truth decided by both, fei.py's own verdict recorded beside its three-word reading and required to equal it; what the planted claims found in fei.py at 470fe0b2 and the fix the same day, in findingsAtPin and findings.",
 "generated": "2026-10-19T23:04:09Z",
 "seconds": 21.3,
 "node": "v24.14.1",
 "python": "3.9.6",
 "deciders": {
  "tools/verify_fei.js": "17b77c44cae2e1fbfd0b2a40547bc9babdae36a224e62594fe3ced885ace9766",
  "tools/fei-second-harness.py": "751f421172585bcffdbe32e7ad8ce6e7e5dedd7eae8004361887de674312e5f8",
  "instruments/fei/fei.py": "271e0f4def7ccffb5113a3d166fe73d1ec0de5942035631c5a7d9c672e11d6de",
  "instruments/verdict.js": "b791f9d813a2d8208a9d9afb86a07ea79f8368293cfa6c00ca7d6aeb0ed07e18"
 },
 "inputs": {
  "pins": "corpus/optimization-constants/num2026/meta.json",
  "files": {
   "fei_c71_n18_artifact.json": "57f5a1ad2bf5bcdee873413e796bc868ccc6131521af799c5eb48d5ae13267ba",
   "README.md": "05c75604203c43961af274396c3c24ea14e965205279e4d9d7737467450ba475",
   "71a.md": "f9868e1e466feb76d51566aa6dc7d8dd9d5e182c0f661beb78924cea7056728b"
  },
  "registryCommit": "2c1968cd520b60f1cf3cf50749f7285e800e4e15",
  "threshold": "6.521845710923046575",
  "thresholdFrom": "71a.md, the [Num2026] row",
  "previousUpperEndpoint": "6.514326913930565372650625175957",
  "previousUpperEndpointFrom": "README.md",
  "ledger": "certs/fei-ledger.json",
  "ledgerCode": {
   "instruments/fei/fei.py": "271e0f4def7ccffb5113a3d166fe73d1ec0de5942035631c5a7d9c672e11d6de"
  }
 },
 "js": {
  "verdict": "CERTIFIED",
  "bits": 512,
  "n": 18,
  "nonzero": 2770,
  "distinct": 10,
  "I": "261/128",
  "Iedge": "261/128",
  "spectrumSha256": "9864bbd020585062de1b81785c0d8fa667a493ce1e4ce03f42433cb18b89e82e",
  "histogram": [
   {
    "k": 1024,
    "count": 2413
   },
   {
    "k": 2048,
    "count": 84
   },
   {
    "k": 3072,
    "count": 18
   },
   {
    "k": 4096,
    "count": 18
   },
   {
    "k": 5120,
    "count": 36
   },
   {
    "k": 8192,
    "count": 72
   },
   {
    "k": 9216,
    "count": 72
   },
   {
    "k": 19456,
    "count": 12
   },
   {
    "k": 22528,
    "count": 36
   },
   {
    "k": 58368,
    "count": 9
   }
  ],
  "closedForm": {
   "A": "15379/1024",
   "B": {
    "3": "41067/32768",
    "5": "225/8192",
    "11": "1089/2048",
    "19": "33573/32768"
   },
   "text": "H = 15379/1024 - (41067/32768) log2 3 - (225/8192) log2 5 - (1089/2048) log2 11 - (33573/32768) log2 19"
  },
  "log2": {
   "3": [
    "1.584962500721156181453738943947816508759814407692481060455752",
    "1.584962500721156181453738943947816508759814407692481060455753"
   ],
   "5": [
    "2.321928094887362347870319429489390175864831393024580612054756",
    "2.321928094887362347870319429489390175864831393024580612054757"
   ],
   "11": [
    "3.459431618637297256199363046725792958703231525681768071312801",
    "3.459431618637297256199363046725792958703231525681768071312802"
   ],
   "19": [
    "4.247927513443585493793519422906834422693507569661534014581524",
    "4.247927513443585493793519422906834422693507569661534014581525"
   ]
  },
  "H": [
   "6.77660530900597808251979022189188231478723503802017057474714780625228104636040166",
   "6.77660530900597808251979022189188231478723503802017057474714780625228104636040167"
  ],
  "ratio": [
   "6.52184571092304657565814397294857846836666229222993859825289412932550356341452190",
   "6.52184571092304657565814397294857846836666229222993859825289412932550356341452191"
  ],
  "width": "9.60e-152",
  "ratio128": [
   "6.52184571092304657565814397294857846790079681141418474598021223984903500035602955",
   "6.52184571092304657565814397294857846883079767103785809227376322488179667695136731"
  ],
  "width128": "9.31e-37",
  "checks": [
   {
    "name": "the truth table reads (hexadecimal, no input beyond 2^n)",
    "ok": true
   },
   {
    "name": "the truth table is the one the artifact binds by sha256",
    "ok": true
   },
   {
    "name": "the transform equals the definition at 52 coefficients summed directly",
    "ok": true
   },
   {
    "name": "balanced: a_∅ = 0",
    "ok": true
   },
   {
    "name": "Parseval: sum a_S^2 = 4^n",
    "ok": true
   },
   {
    "name": "I by the spectrum = I by the edge boundary (261/128)",
    "ok": true
   },
   {
    "name": "I = 261/128, the artifact's stated 261/128",
    "ok": true
   },
   {
    "name": "I > 1",
    "ok": true
   },
   {
    "name": "H > 0",
    "ok": true
   },
   {
    "name": "H/(I-1) > 6.521845710923046575",
    "ok": true
   }
  ],
  "ms": 71
 },
 "py": {
  "verdict": "CERTIFIED",
  "why": null,
  "digits": 60,
  "ratio": [
   "6.521845710923046575658143972948578468366662",
   "6.521845710923046575658143972948578468366663"
  ],
  "H": [
   "6.7766053090059780825197902218",
   "6.7766053090059780825197902219"
  ],
  "spectrumSha256": "9864bbd020585062de1b81785c0d8fa667a493ce1e4ce03f42433cb18b89e82e",
  "checks": [
   {
    "name": "the truth table is the one the artifact binds by sha256",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "balanced: fhat(emptyset) = 0",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "Parseval: sum of the weights is 1",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "I = 261/128, the artifact's 261/128",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "I > 1: the amplification rule applies",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "H > 0",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "H/(I-1) > 6.521845710923046575, the registry's bound",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "the artifact's certified floor 6.5218457109230465756581... is inside the enclosure",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "above the record it replaced (6.514326913930565372...)",
    "ok": true,
    "verdict": "CERTIFIED"
   },
   {
    "name": "logic-monotone (the artifact's second claim; the bound then holds among monotone functions too)",
    "ok": true,
    "verdict": "CERTIFIED"
   }
  ],
  "seconds": 1.47
 },
 "arb": {
  "python": "3.12.13",
  "flint": "0.9.0",
  "prec": 1024,
  "I": "261/128",
  "spectrum": {
   "sha256": "9864bbd020585062de1b81785c0d8fa667a493ce1e4ce03f42433cb18b89e82e",
   "a0": 0,
   "histogram": {
    "1024": 2413,
    "2048": 84,
    "3072": 18,
    "4096": 18,
    "5120": 36,
    "8192": 72,
    "9216": 72,
    "19456": 12,
    "22528": 36,
    "58368": 9
   },
   "seconds": 1.09
  },
  "H": [
   [
    "152278210520894621528237887343150872920625132096888059631555337840230327161320346347635508648988586124330163188560797214107202360082383711936041136568770557880651189378771795828904699914081584567256841211573013569639307342220640057389449588054165287276715618361547185899728961859314617629266528125728339727073",
    -1021
   ],
   [
    "152278210520894621528237887343150872920625132096888059631555337840230327161320346347635508648988586124330163188560797214107202360082383711936041136568770557880651189378771795828904699914081584567256841211573013569639307342220640057389449588054165287276715618361547185899728961859314617629266528125728339727103",
    -1021
   ]
  ],
  "ratio": [
   [
    "18319183220558751462043655620228676441578963259776007173720942898072821312640041665880963446494867503678816624187765078388836374145249168353207956278949841549552022782408637092199061643799288368993304205903520429430292612597971736227302206081704094709980826269058308078162882629691984075701236466253033350625",
    -1018
   ],
   [
    "18319183220558751462043655620228676441578963259776007173720942898072821312640041665880963446494867503678816624187765078388836374145249168353207956278949841549552022782408637092199061643799288368993304205903520429430292612597971736227302206081704094709980826269058308078162882629691984075701236466253033350629",
    -1018
   ]
  ],
  "ratioText": "[6.5218457109230465756581439729485784683666622922299385982528941293255035634145219 +/- 4.27e-81]",
  "ms": 1457
 },
 "arbSource": "run now",
 "agreement": [
  {
   "name": "both implementations CERTIFY the registry's bound",
   "ok": true
  },
  {
   "name": "fei.py, run through the harness, re-derives the ledger's row field for field",
   "ok": true
  },
  {
   "name": "the two spectra are identical, coefficient for coefficient with signs (sha256 of the 2^18 comma-joined coefficients)",
   "ok": true,
   "detail": "9864bbd020585062de1b81785c0d8fa667a493ce1e4ce03f42433cb18b89e82e"
  },
  {
   "name": "the histograms of |a_S| agree (10 magnitudes, 2770 nonzero coefficients)",
   "ok": true
  },
  {
   "name": "I = 261/128 by the spectrum, by the edge boundary, in fei.py and as the artifact states it",
   "ok": true
  },
  {
   "name": "the JS enclosure overlaps the ledger's printed interval",
   "ok": true
  },
  {
   "name": "the ledger's printed interval contains the JS enclosure (printed outward: the lower end down, the upper end up)",
   "ok": true
  },
  {
   "name": "fei.py's printed H contains the JS H",
   "ok": true
  },
  {
   "name": "both lower ends are above the registry's 6.521845710923046575",
   "ok": true
  },
  {
   "name": "the Arb ball (1024 bits, from fei.py's spectrum) lies inside the JS enclosure (512 bits)",
   "ok": true
  },
  {
   "name": "the Arb H lies inside the JS H",
   "ok": true
  },
  {
   "name": "the claimant's printed bracket [ratio_lo_dec, ratio_hi_dec] (40 decimals) contains the JS enclosure",
   "ok": true
  }
 ],
 "claims": [
  {
   "id": "registry-bound",
   "claim": "C71 > 6.521845710923046575",
   "what": "the registry's asterisked row, read from the pinned 71a.md (fei.py run as tools/run-fei-ledger.py runs it, with the replaced record)",
   "js": {
    "verdict": "CERTIFIED",
    "why": null,
    "ms": 71
   },
   "js128": {
    "verdict": "CERTIFIED",
    "why": null
   },
   "py": {
    "word": "CERTIFIED",
    "raised": null,
    "reading": "CERTIFIED",
    "why": null,
    "seconds": 1.47
   }
  },
  {
   "id": "strict-improvement",
   "claim": "C71 > 6.514326913930565372650625175957",
   "what": "above the previous record's certified upper endpoint, the bar the pinned README says the claimant used",
   "js": {
    "verdict": "CERTIFIED",
    "why": null,
    "ms": 62
   },
   "js128": {
    "verdict": "CERTIFIED",
    "why": null
   },
   "py": {
    "word": "CERTIFIED",
    "raised": null,
    "reading": "CERTIFIED",
    "why": null,
    "seconds": 1.5
   }
  },
  {
   "id": "logic-monotone",
   "claim": "the n = 18 function is logic-monotone (TRUE = -1)",
   "what": "the artifact's second claim; with it the bound holds among monotone functions too",
   "js": {
    "verdict": "CERTIFIED",
    "why": null,
    "ms": 62
   },
   "js128": {
    "verdict": "CERTIFIED",
    "why": null
   },
   "py": {
    "word": "CERTIFIED",
    "raised": null,
    "reading": "CERTIFIED",
    "why": null,
    "seconds": 1.52
   }
  }
 ],
 "planted": [
  {
   "id": "a-bar-above-the-ledger",
   "claim": "C71 > 6.521845710923046575658143972948578468366664 (from this table)",
   "what": "the bar one unit (10^-42) above the ledger's printed upper end (printed outward since the fix; at the pin it was a truncation read as the string + 10^-42, which gave this same bar): false by the first implementation's record and by Arb; refuted as a statement about this certificate, never about C71. At 128 bits the JS enclosure is wider than the bar's distance (js.width128 in this record), so there it must refuse",
   "js": {
    "verdict": "REFUTED",
    "why": "the ratio is proved at most 6.521845710923046575658143972948578468366664 (a statement about this certificate, not about C71)",
    "ms": 63
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "the enclosure straddles the bar at 128 bits: nothing is proved either way"
   },
   "py": {
    "word": "REFUTED",
    "raised": null,
    "reading": "REFUTED",
    "why": "its upper end, 6.521845710923046575658143972948578468366663, is at or below the bar",
    "seconds": 1.67
   },
   "truth": "FALSE",
   "expected": {
    "js": "REFUTED",
    "js128": "REFUSED",
    "py": "REFUTED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "b-one-bit-flipped",
   "claim": "C71 > 6.521845710923046575 (from this table)",
   "what": "input 131017 of the truth table flipped (the first FALSE input whose every immediate superset is TRUE), the published sha256 kept: the binding fails",
   "js": {
    "verdict": "REFUSED",
    "why": "the sha256 binding fails: the table is not the one the artifact names",
    "ms": 16
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "the sha256 binding fails: the table is not the one the artifact names"
   },
   "py": {
    "word": "REFUSED",
    "raised": null,
    "reading": "REFUSED",
    "why": "fei.py's check failed: the truth table is the one the artifact binds by sha256",
    "seconds": 1.32
   },
   "truth": "MALFORMED",
   "expected": {
    "js": "REFUSED",
    "js128": "REFUSED",
    "py": "REFUSED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "c-unbalanced-binding-bypassed",
   "claim": "C71 > 6.521845710923046575 (from this table)",
   "what": "the same flip with the binding bypassed EXPLICITLY — sha256_table re-signed to the flipped table's own hash and the stated I set to its edge-boundary influence 33409/16384 — so balance is the one defect (the flip keeps the function monotone): fhat(∅) = ±2^-17 and the amplification rule does not apply",
   "js": {
    "verdict": "REFUSED",
    "why": "not balanced: a_∅ = -2, fhat(∅) = -1/131072; the amplification rule needs a balanced g",
    "ms": 68
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "not balanced: a_∅ = -2, fhat(∅) = -1/131072; the amplification rule needs a balanced g"
   },
   "py": {
    "word": "REFUSED",
    "raised": null,
    "reading": "REFUSED",
    "why": "fei.py's check failed: balanced: fhat(emptyset) = 0",
    "seconds": 1.48
   },
   "truth": "MALFORMED",
   "expected": {
    "js": "REFUSED",
    "js128": "REFUSED",
    "py": "REFUSED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "d-bar-below-the-ledger",
   "claim": "C71 > 6.521845710923046575658143972948578468366661 (from this table)",
   "what": "the bar one unit (10^-42) below the ledger's lower end: true by the first implementation's record and by Arb; at 128 bits the JS enclosure is wider than the bar's distance (js.width128), so there it must refuse",
   "js": {
    "verdict": "CERTIFIED",
    "why": null,
    "ms": 62
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "the enclosure straddles the bar at 128 bits: nothing is proved either way"
   },
   "py": {
    "word": "CERTIFIED",
    "raised": null,
    "reading": "CERTIFIED",
    "why": null,
    "seconds": 1.46
   },
   "truth": "TRUE",
   "expected": {
    "js": "CERTIFIED",
    "js128": "REFUSED",
    "py": "CERTIFIED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "e1-stated-influence-moved",
   "claim": "C71 > 6.521845710923046575 (from this table)",
   "what": "the artifact's stated I moved by 1/128 to 131/64, the table untouched: the artifact contradicts its own table",
   "js": {
    "verdict": "REFUSED",
    "why": "the artifact states I = 131/64; its own table gives 261/128",
    "ms": 59
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "the artifact states I = 131/64; its own table gives 261/128"
   },
   "py": {
    "word": "REFUSED",
    "raised": null,
    "reading": "REFUSED",
    "why": "fei.py's check failed: I = 261/128, the artifact's 131/64",
    "seconds": 1.45
   },
   "truth": "MALFORMED",
   "expected": {
    "js": "REFUSED",
    "js128": "REFUSED",
    "py": "REFUSED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "e2-bar-1e-75-below-the-value",
   "claim": "C71 > 6.521845710923046575658143972948578468366662292229938598252894129325503563413 (from this table)",
   "what": "a bar between 10^-75 and 2·10^-75 below the ratio (true by Arb at 1024 bits): inside fei.py's 60-digit enclosure and the JS's 128-bit one, so both must refuse it; decided only at 512 bits",
   "js": {
    "verdict": "CERTIFIED",
    "why": null,
    "ms": 60
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "the enclosure straddles the bar at 128 bits: nothing is proved either way"
   },
   "py": {
    "word": "REFUSED",
    "raised": null,
    "reading": "REFUSED",
    "why": "its enclosure [6.521845710923046575658143972948578468366662, 6.521845710923046575658143972948578468366663] straddles the bar",
    "seconds": 1.44
   },
   "truth": "TRUE",
   "expected": {
    "js": "CERTIFIED",
    "js128": "REFUSED",
    "py": "REFUSED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "e3-bar-1e-75-above-the-value",
   "claim": "C71 > 6.521845710923046575658143972948578468366662292229938598252894129325503563416 (from this table)",
   "what": "a bar between 10^-75 and 2·10^-75 above the ratio (false by Arb at 1024 bits): inside fei.py's 60-digit enclosure and the JS's 128-bit one, so both must refuse it; REFUTED at 512 bits",
   "js": {
    "verdict": "REFUTED",
    "why": "the ratio is proved at most 6.521845710923046575658143972948578468366662292229938598252894129325503563416 (a statement about this certificate, not about C71)",
    "ms": 67
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "the enclosure straddles the bar at 128 bits: nothing is proved either way"
   },
   "py": {
    "word": "REFUSED",
    "raised": null,
    "reading": "REFUSED",
    "why": "its enclosure [6.521845710923046575658143972948578468366662, 6.521845710923046575658143972948578468366663] straddles the bar",
    "seconds": 1.46
   },
   "truth": "FALSE",
   "expected": {
    "js": "REFUTED",
    "js128": "REFUSED",
    "py": "REFUSED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "e4-mask-beyond-2^n",
   "claim": "C71 > 6.521845710923046575 (from this table)",
   "what": "a leading hex digit 1 prepended: the mask sets input 2^18, which does not exist",
   "js": {
    "verdict": "REFUSED",
    "why": "the mask sets input 262144, beyond the 2^18 inputs",
    "ms": 2
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "the mask sets input 262144, beyond the 2^18 inputs"
   },
   "py": {
    "word": "REFUSED",
    "raised": null,
    "reading": "REFUSED",
    "why": "fei.py's check failed: the truth table reads: hexadecimal, no input at or beyond 2^n",
    "seconds": 0
   },
   "truth": "MALFORMED",
   "expected": {
    "js": "REFUSED",
    "js128": "REFUSED",
    "py": "REFUSED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "e5-majority-of-three-below-4",
   "claim": "C71 > 3.999999999999999999999999999999 (from this table)",
   "what": "majority of three (textbook: four weights 1/4, H = 2, I = 3/2, so H/(I-1) = 4 exactly) against 4 - 10^-30",
   "js": {
    "verdict": "CERTIFIED",
    "why": null,
    "ms": 0
   },
   "js128": {
    "verdict": "CERTIFIED",
    "why": null
   },
   "py": {
    "word": "CERTIFIED",
    "raised": null,
    "reading": "CERTIFIED",
    "why": null,
    "seconds": 0
   },
   "truth": "TRUE",
   "expected": {
    "js": "CERTIFIED",
    "js128": "CERTIFIED",
    "py": "CERTIFIED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "e6-majority-of-three-at-4",
   "claim": "C71 > 4 (from this table)",
   "what": "majority of three against 4 itself: the strict inequality fails at equality. Every |a_S| is a power of two, so H is exact in both deciders — the closed form here, fei.py's log2 of a power of two since 2026-10-19 (at the pin its log2 4 was an interval and it could only refuse) — and both refute",
   "js": {
    "verdict": "REFUTED",
    "why": "the ratio is proved at most 4 (a statement about this certificate, not about C71)",
    "ms": 1
   },
   "js128": {
    "verdict": "REFUTED",
    "why": "the ratio is proved at most 4 (a statement about this certificate, not about C71)"
   },
   "py": {
    "word": "REFUTED",
    "raised": null,
    "reading": "REFUTED",
    "why": "its upper end, 4.000000000000000000000000000000000000000000, is at or below the bar",
    "seconds": 0
   },
   "truth": "FALSE",
   "expected": {
    "js": "REFUTED",
    "js128": "REFUTED",
    "py": "REFUTED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "e7-dictator",
   "claim": "C71 > 1 (from this table)",
   "what": "a dictator on two variables: balanced, all weight on one set, I = 1 and H = 0 — the amplification rule needs I > 1, the reason both deciders must give (at the pin fei.py raised \"a weight above 1\" instead)",
   "js": {
    "verdict": "REFUSED",
    "why": "I = 1: the amplification rule needs I > 1",
    "ms": 0
   },
   "js128": {
    "verdict": "REFUSED",
    "why": "I = 1: the amplification rule needs I > 1"
   },
   "py": {
    "word": "REFUSED",
    "raised": null,
    "reading": "REFUSED",
    "why": "fei.py's check failed: I > 1: the amplification rule applies",
    "seconds": 0
   },
   "truth": "MALFORMED",
   "expected": {
    "js": "REFUSED",
    "js128": "REFUSED",
    "py": "REFUSED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  },
  {
   "id": "e8-monotonicity-broken",
   "claim": "the swapped function is logic-monotone",
   "what": "inputs 160 (FALSE) and 161 (TRUE, one coordinate above it) swapped, re-signed: balance kept, logic-monotone false by construction",
   "js": {
    "verdict": "REFUTED",
    "why": "f(160) is TRUE and f(161) is FALSE, the second input above the first in coordinate 0",
    "ms": 124
   },
   "js128": {
    "verdict": "REFUTED",
    "why": "f(160) is TRUE and f(161) is FALSE, the second input above the first in coordinate 0"
   },
   "py": {
    "word": "REFUTED",
    "raised": null,
    "reading": "REFUTED",
    "why": null,
    "seconds": 1.38
   },
   "truth": "FALSE",
   "expected": {
    "js": "REFUTED",
    "js128": "REFUTED",
    "py": "REFUTED"
   },
   "fired": true,
   "pyWordAgreesWithReading": true
  }
 ],
 "plantedSummary": {
  "planted": 12,
  "fired": 12,
  "byTruth": {
   "FALSE": 4,
   "MALFORMED": 5,
   "TRUE": 3
  },
  "falseAccepted": [],
  "trueRefuted": [],
  "pyWordDiffersFromReading": [],
  "pyWordRefutesATrueClaim": []
 },
 "findingsAtPin": {
  "feiPy": "5825dc475292bf4e02e995e276c1a3422de52796bbea89b758149448fcd78141",
  "commit": "470fe0b2",
  "found": "2026-10-19",
  "fixed": "2026-10-19",
  "pyWordDiffersFromReading": [
   "b-one-bit-flipped",
   "c-unbalanced-binding-bypassed",
   "e1-stated-influence-moved",
   "e2-bar-1e-75-below-the-value",
   "e3-bar-1e-75-above-the-value",
   "e6-majority-of-three-at-4"
  ],
  "pyWordRefutesATrueClaim": [
   "e2-bar-1e-75-below-the-value"
  ],
  "ledgerTruncated": true,
  "dictatorReason": "a weight above 1"
 },
 "findings": [
  "FOUND at fei.py 5825dc47… (commit 470fe0b2, 2026-10-19) and FIXED 2026-10-19: certs/fei-ledger.json printed the ratio's two ends as one truncated string (str(...)[:44], H at [:30]), so its printed upper end was below the value. fei.py now prints outward — the lower end down, the upper end up, at the same 43 and 29 significant digits — and the ledger reads [6.521845710923046575658143972948578468366662, 6.521845710923046575658143972948578468366663], which contains the value (the JS enclosure lies inside it).",
  "FOUND at fei.py 5825dc47… (commit 470fe0b2, 2026-10-19) and FIXED 2026-10-19: fei.py had two words, and on 6 of the 12 planted claims (b-one-bit-flipped, c-unbalanced-binding-bypassed, e1-stated-influence-moved, e2-bar-1e-75-below-the-value, e3-bar-1e-75-above-the-value, e6-majority-of-three-at-4) its own word was REFUTED where the three words say REFUSED — on e2-bar-1e-75-below-the-value, a TRUE claim. fei.py now carries the three words check by check and composes them by the method paper's rule (REFUTED if any is refuted, else REFUSED if any is refused, else CERTIFIED); the bound and the record are CERTIFIED iff r_lo > bar, REFUTED iff r_hi <= bar, REFUSED on a straddle; a failed precondition is REFUSED with its reason and the bound is then not decided. Its own word now equals the reading on all 12 planted claims.",
  "FOUND at fei.py 5825dc47… (commit 470fe0b2, 2026-10-19) and FIXED 2026-10-19: log2 of a power of two was an interval, so majority of three at exactly 4 could only be refused. fei.py now writes |a| = 2^v m and takes log2 |a| = v + log2 m with log2 1 = 0 exactly, and refutes it (e6-majority-of-three-at-4).",
  "FOUND at fei.py 5825dc47… (commit 470fe0b2, 2026-10-19) and FIXED 2026-10-19: on the dictator fei.py raised \"a weight above 1\" (the weight is exactly 1) before reaching its I <= 1 test, so instruments/fei/battery.py's red control named for I > 1 fired for that other reason. With log2 4 exact the test is reached: fei.py returns REFUSED, why \"I > 1: the amplification rule applies: I = 1; the rule needs I > 1\", and the battery asserts the reason.",
  "FOUND while fixing (2026-10-19): planted claims b and c flipped input 123457, which also broke monotonicity — claim c stated balance as its one defect, and under the composition rule the refuted monotone check would have decided fei.py's word. The flip is now input 131017, the first FALSE input whose every immediate superset is TRUE, which keeps the function monotone; the claims keep their ids."
 ],
 "timing": {
  "jsMs": 1985,
  "pyMs": 17788,
  "arbMs": 1457
 }
}