--- slug: prime-polynomial passed: 2026-10-18 by: the assay line (research/assay-line/queue-1018/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex checked: 124 confirmed: 119 wrong: 4 unverifiable: 0 observed: 0 stale: 1 --- This pass decided all five queue-1018 triage items before editing prime-polynomial, reread their evidence, and applied the supported repairs using the requested assay date 2026-10-18. The 119 CONFIRMED claims carry forward the source readings in research/assay-line/queue-1018/prime-polynomial/N2-codex.md, pinned at 5333a8e3bd and dated 2026-10-19; their evidence and historical line numbers are attributed to that checker. The layer files matched c52ccf3318 before the fixes. The one WRONG and three MINOR claims count in wrong; the sole STALE claim is the JSON-LD metadata exception. The dated correction appears in the HTML and content Markdown. ## Claims - MINOR | The verifier begins here, before it reads a page value. It checks exactly that | git show 5333a8e3bd:research/prime-polynomial/verify-prime-polynomial.mjs | X1, verifier-anchor-order. Decision fix; reread=true. I read research/prime-polynomial/verify-prime-polynomial.mjs:10-11 and :107-109. The file reads "const html = fs.readFileSync(htmlPath, 'utf8');" before its first assertion, "assert(anchorLeft === SOURCE_O ** 2n,". The anchor is the first assertion, not an operation before reading the page. Keep MINOR and cheaply replace the page wording with "The verifier's first assertion checks exactly that"; no public correction line. - WRONG | The verifier does independently recover 26 variables, fourteen residuals, and degree 25 from a separate transcription. | git show 5333a8e3bd:research/prime-polynomial/verify-prime-polynomial.mjs | X2, independent-variable-census. Decision fix; reread=true. I read research/prime-polynomial/verify-prime-polynomial.mjs:120-121 and :212-244, unchanged from c52ccf3318. The purported census asserts "new Set('abcdefghijklmnopqrstuvwxyz').size === 26" and reports "variable census a through z recovers 26 variables" at :243-244. This counts a supplied alphabet, without inspecting the residual expressions. I also recreated the checker's scratch mutation of the only evaluated "c * u" to "0n * u": it still reported that census and "PASS 1688 checks". The separate residual-length assertion and symbolic degree propagation do check fourteen residuals and degree 25. Keep WRONG. Remove the alphabet-only assertion and narrow the claim in both the HTML and research README to the checks the code performs; retain the correct published variable count of 26. Add one dated Corrected line for this error, mirrored in the content Markdown. - MINOR | Eric Zheng, “A Nonnegative Integer Solution to the Jones-Sato-Wada-Wiens Polynomial,” 20 March 2021. | https://www.ericzheng.org/files/pdf/prime.pdf | X3, zheng-title-article. Decision fix; reread=true. I fetched https://www.ericzheng.org/files/pdf/prime.pdf (HTTP 200, 158636 bytes) and read its first-page title with pdftotext. It says "An Nonnegative Integer Solution to the" followed by "Jones-Sato-Wada-Wiens Polynomial", "Eric Zheng", and "March 20, 2021". The fix is to restore the source's words, changing the quoted title from "A Nonnegative" to "An Nonnegative" in the HTML and the research README. Retain MINOR: author, date, and work identity were correct. No public correction line. - MINOR | Full source checks, independent formulas and known limits are in the verification note. | git show 5333a8e3bd:research/prime-polynomial/README.md | X4, verification-note-access. Decision list; reread=true. I read research/prime-polynomial/README.md, its adjacent verifier, and public/strata/prime-polynomial/index.html:932,945. The README has "## Primary sources" and "## Limits"; the formulas are in the adjacent verifier. The HTML displays "the verification note" and a plain-code verifier path, without links to either artifact. N2 also records HTTP 404 for the literal public research paths, with the article returning 200 as a control. Keep MINOR as a reader-access limitation. A complete public runnable bundle must package the verifier together with its HTML and Markdown inputs and preserve or adapt their paths; that is beyond a few words or a small code change. Under the Tier A rule, list this finding with [declined] and leave the page unchanged for this item. - STALE | "dateModified":"2026-07-30" | git log 5333a8e3bd -- public/strata/prime-polynomial/index.html; git show 2e60bcb5dd1:public/strata/prime-polynomial/index.html | X5, stale-modification-date. Decision fix; reread=true. I read the HTML JSON-LD at public/strata/prime-polynomial/index.html:29 (""dateModified":"2026-07-30"") and git log c52ccf3318 for that file, which records later changes including placards on 2026-08-01 and 2026-09-27 and image-alt text on 2026-10-01. The publication date does not establish last modification. Retain STALE and apply the explicit JSON-LD exception: set dateModified to the requested assay revision date 2026-10-18, with no Updated line. This is the only STALE item, so there are no remaining STALE items to group into a visible Updated line; the WRONG correction dates the revision. - CONFIRMED | An integer object, 1976 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 1, year. JSTOR cover: "Vol. 83, No. 6 (Jun. - Jul., 1976), pp. 449-464". The article, rather than the later witness note, is the 1976 object. - CONFIRMED | Twenty-six nonnegative integers enter a degree-25 polynomial. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 2, degree-domain. Jones p. 449: "a polynomial of degree 25 in 26 variables" and "nonnegative integers". Checked the displayed polynomial in the facsimile. - CONFIRMED | A positive answer can only be prime. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 3, positive-only-prime. Jones Theorem 1: "The set of prime numbers is identical with the set of positive values taken on by the polynomial" on the stated domain. - CONFIRMED | Follow fourteen squared constraints back through Wilson's theorem, then confront why even the witness for 2 cannot be printed in full. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 4, fourteen-and-unprintable. Zheng p. 1 lists equations (1)-(14); p. 2 says "encode the factorial function in Diophantine" equations; p. 5 says directly computing c, d, r, u "is not feasible". This concerns the displayed witness, not a claim about every possible witness. - CONFIRMED | degree 25 26 variables, a through z | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 5, degree-variables-badges. Jones p. 449: "degree 25 in 26 variables, a, b, c, ..., z". Both badges match. - CONFIRMED | 14 squared constraints | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 6, fourteen-badge. Jones Theorem 2.12 numbers the equations (1)-(14); p. 455 says "sum the squares of the equations". The supplied excerpt needs the numbered system as context, which was inspected. - CONFIRMED | 87 arithmetic operations | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 7, operations-badge. Jones p. 451, Theorem 5: "only 87 additions and multiplications". The page expressly uses the arithmetic-operation convention. - CONFIRMED | smallest positive value 2 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 8, smallest-badge. Jones p. 449: the positive range is "the set of all prime numbers 2,3,5,..."; hence its minimum is 2. - CONFIRMED | Choose an integer at least 2. The browser multiplies every factor modulo that integer. It never materialises the factorial, and it checks the result again by trial division. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 9, wilson-browser. HTML lines 1042-1104: "residue = (residue * factor) % n" and "const trial = isPrimeTrial(n)". The local browser-code audit independently ran all N=2..1000 and the endpoints; no factorial is materialised. - CONFIRMED | N is prime exactly when ((N - 1)! + 1) mod N = 0. N = 1 is excluded because it makes the remainder test meaningless. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 10, wilson-theorem. Jones Lemma 2.9 assumes k >= 1 and says "k + 1 is prime if and only if" k+1 divides k!+1. Set N=k+1. At N=1 the remainder is trivially 0, so it cannot distinguish primality; "meaningless" means useless as that test, not undefined arithmetic. - CONFIRMED | The slider is a convenience for 2 through 200. The number field accepts exact integers through 1,000,000. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 11, wilson-inputs. HTML line 742: min="2" max="200"; lines 1064-1066 reject values outside 2..1000000. audit-browser.mjs accepted 2 and 1000000 and rejected 1 and 1000001. - CONFIRMED | Integer N, from 2 to 1,000,000 | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 12, wilson-field-label. HTML lines 737-738 and 1064-1066 agree on 2..1000000. The boundary checks were recreated in audit-browser.mjs. - CONFIRMED | Integers 2 through 97, primes highlighted | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 13, prime-strip-label. HTML lines 1109-1115: "n = 2; n <= 97" and independent trial-division highlights. Recreated 96 buttons and 25 primes. - CONFIRMED | The remainder test still says “factorial.” Fourteen equations remove that word. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 14, factorial-encoding. Zheng p. 2: "encode the factorial function in Diophantine" equations, followed by Wilson. Theorem 1 lists fourteen equations containing no factorial notation. - CONFIRMED | Every residual, its square, their sum, and the polynomial output are recomputed with exact integer arithmetic. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 15, exact-recomputation. HTML lines 1177-1247 use BigInt coordinates, evaluate each residual, square it, and form "(tuple.k + 2n) * (1n - sumSquares)". Both named presets were evaluated and matched an independent arithmetic route. - CONFIRMED | Positivity is possible only when every residual is zero. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 16, positivity-all-zero. Jones p. 450: "M is a sum of squares and hence nonnegative". Since k+2 >= 2 and M is an integer, P>0 requires M=0, so each squared integer residual is zero. - CONFIRMED | P(a,...,z) = (k + 2) [1 - (alpha₁² + ... + alpha₁₄²)] | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 17, polynomial-form. Jones equation (4) is "(k + 2){1 - M(k, x1, ..., xn)}"; p. 455 constructs M by summing the fourteen squared equations. The p. 449 facsimile confirms the full expression. Mathematical typesetting is transcribed in plain text here. - CONFIRMED | All variables are nonnegative integers. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 18, nonnegative-domain. Jones Theorem 1: "as the variables range over the nonnegative integers". The browser enforces this domain. - CONFIRMED | The output-driving variable is k, so N = k + 2. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 19, shifted-k. Zheng p. 2: "replace k with k + 1; correspondingly, the prime becomes k + 2". This identifies the prime target when all constraints vanish, not every signed output. - CONFIRMED | The other 25 variables are existential witnesses, not knobs in a fast prime generator. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 20, auxiliary-witnesses. Jones Theorem 2.12 says "there exist numbers" and names all 25 coordinates other than k. Its existence statement supplies no efficient search for them; Zheng p. 5 illustrates the size obstacle. - CONFIRMED | Each field accepts 0 through 140 decimal digits. k is limited to 1,000,000 so every positive output can receive a separate trial-division check. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 22, coordinate-field-limits. HTML lines 1181-1185 reject non-digits, more than 140 digits, and k>1000000. Boundary tests passed. The wording "0 through 140 decimal digits" is read as nonnegative values of at most 140 digits; an empty field is rejected. - CONFIRMED | The 1976 paper states this bound and says it is calculated from the fourteen equations. It does not print an operation-by-operation ledger, so this strip counts the published total without inventing a distribution among equations. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 23, operation-provenance. Jones p. 451: "The number is easily calculated from the equations of Theorem 2.12." Full pp. 449-464 contain no per-operation ledger. Positive control: the same case-insensitive operation/addition/multiplication/ledger/87 search finds Theorem 5 and its 87 total. The strip has 87 cells. - CONFIRMED | An operation on a million-digit integer and an operation on a one-digit integer each occupy one cell. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 24, operation-cells-unit. HTML lines 1292-1299 append exactly one span for each of 87 indices; no operand size is attached. This describes unit-cost arithmetic counting, not an executed multiplication benchmark. - CONFIRMED | This is a bounded arithmetic proof, not a bounded running time or an 87-step practical primality test. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 25, arithmetic-vs-running-time. Jones Theorem 5 counts "87 additions and multiplications" and gives no bit-cost bound or witness-finding algorithm. Unbounded integer operands and finding their values are additional costs; this is a valid distinction from the theorem, not a quotation from it. - CONFIRMED | Finding the 25 auxiliary values remains the hard part. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 26, finding-witness-hard. Zheng p. 5: directly computing c, d, r, u "is not feasible". The claim is a qualitative limitation of this construction, not a formal computational lower bound for primality. - CONFIRMED | The witness for 2 will not fit here. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 27, witness-will-not-fit. Zheng p. 5 explicitly identifies c, d, r, u as too large to compute directly. The independently checked digit bound below substantiates the display limitation. - CONFIRMED | The actual four values are definitions in a Pell recurrence. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 29, four-recurrence-values. Zheng Claim 1, p. 4, gives c and d as quotients involving u, u=chi_a(4a psi_a(4a)), and r=psi_a(4a psi_a(4a))/(16a^2). These are exact compressed definitions. - CONFIRMED | e = 32 f = 17 a = 7901690358098896161685556879749949186326380713409290912 o = 8340353015645794683299462704812268882126086134656108363777 | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 30, materialised-seed. Zheng p. 4 gives exactly the displayed 55-digit a, 58-digit o, "e = 32", and "f = 17". Both long integers were compared digit for digit with the page and verifier. - CONFIRMED | a and o are published witness coordinates. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 33, published-a-o. Both constants appear in Zheng Claim 1, p. 4. The record correctly identifies them as published witness coordinates. - CONFIRMED | They are displayed constants, not derived by the browser. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 34, a-o-not-derived. HTML lines 1029-1030 contain literal "const SOURCE_A" and "const SOURCE_O" decimal strings. The browser derives x,y,v from them, but does not derive a or o. - CONFIRMED | chi_a(0)=1, chi_a(1)=a psi_a(0)=0, psi_a(1)=1 T(n+2)=2aT(n+1)-T(n) | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 35, pell-recurrence. Zheng p. 3 prints chi_a(0)=1, chi_a(1)=a, psi_a(0)=0, psi_a(1)=1, and T(n+2)=2aT(n+1)-T(n), with precisely these signs. - CONFIRMED | Every pair obeys the exact Pell identity | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 36, pell-every-pair. Zheng p. 3: "Moreover, all pairs (x, y) of this form are solutions." The universal assertion concerns the recurrence, not the verifier sample. - CONFIRMED | chi_a(n)² - (a²-1)psi_a(n)² = 1. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 37, pell-identity. Zheng p. 3 prints x^2=(a^2-1)y^2+1 and identifies the recurrence solutions. Rearrangement gives exactly the page identity. - CONFIRMED | That finite run tests the transcription; the cited proof supplies the universal lemma. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 39, pell-universal-lemma. Zheng p. 3 supplies the universal recurrence claim and attributes the divisibility and congruence lemmas to Davis (1973). The finite run is explicitly distinguished from these general results. - CONFIRMED | J = 4a psi_a(4a) u = chi_a(J) r = psi_a(J) / (16a²) y = 2a | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 40, constraint-seven-definitions. Zheng p. 4 defines precisely u=chi_a(4a psi_a(4a)), r=psi_a(4a psi_a(4a))/(16a^2), and y=2a. J is the page abbreviation for that same index. - CONFIRMED | The divisibility chain from the Pell sequence makes r an integer: | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 41, r-integrality. Zheng p. 5 applies Lemma 1 twice, concluding "16a2 | psi_a(4a psi_a(4a))" in mathematical typesetting. Dividing by 16a^2 therefore yields an integer; all terms are nonnegative. - CONFIRMED | psi_a(2)⁴ divides psi_a(4a)² divides psi_a(J). | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 42, r-divisibility-chain. Zheng p. 5 prints psi_a(2)^4 divides psi_a(2 psi_a(2))^2 = psi_a(4a)^2 divides psi_a(4a psi_a(4a)). Since psi_a(2)=2a and J=4a psi_a(4a), the displayed chain matches. - CONFIRMED | Then the Pell identity at index J is exactly residual 7: | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 43, seventh-residual-identity. Zheng p. 5 equation (1) substitutes 16a^2 r=psi_a(J) and u=chi_a(J). With y=2a, 16r^2 y^4=(16a^2 r)^2. This is exactly constraint 7, moved to the opposite side. - CONFIRMED | u² - 16(a²-1)r²y⁴ = 1. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 44, seventh-equation. Zheng equation (1), p. 5: u^2=16(a^2-1)r^2 y^4+1. Moving the product left reproduces the page equation. - CONFIRMED | r has more than 10^10⁵⁶ decimal digits. The lower bound is derived from 2a-1 > 10⁵⁵, 4a-1 > 10⁵⁵, and psi_a(n) at least (2a-1)^n-1. | git show 5333a8e3bd:research/prime-polynomial/verify-prime-polynomial.mjs; https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 45, r-digit-bound. Re-derived using Jones Lemma 2.1, p. 451: psi_a(4a)>(10^55)^(10^55)=10^(55*10^55), and 55*10^55>10^56. Thus J>4a*10^(10^56), and log10(r)>55(J-1)-112>10^(10^56), since 16a^2<10^112. The count of decimal digits therefore exceeds the stated target. The elementary integer inequalities also pass the verifier. - CONFIRMED | beta = a + u²(u²-a) c = (2beta² - x - 1) / u d = (2beta - n) / (4y) | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 46, constraint-eight-definitions. Zheng Claim 1, p. 4, supplies c=(2(a+u^2(u^2-a))^2-x-1)/u and d=(2(a+u^2(u^2-a))-n)/(4y). Substituting beta is exact. - CONFIRMED | With the quotient integrality supplied by the cited congruence lemmas, those definitions give | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 47, quotient-congruence-lemmas. Zheng p. 5 proves c integrality from a congruent to beta modulo u, and d integrality from u^2 congruent to 1 modulo 4y and n=2. It also establishes nonnegativity. The source supports both quotients, not just the identity after division. - CONFIRMED | x + cu = 2beta²-1 = chi_beta(2) n + 4dy = 2beta = psi_beta(2). | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 48, constraint-eight-pell-values. Zheng p. 5 equation (2) explicitly gives x+cu=2beta^2-1=chi_beta(2), n+4dy=2beta=psi_beta(2). - CONFIRMED | Residual 8 then becomes the two-step Pell identity. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 49, eighth-residual-identity. Substitution gives (2beta^2-1)^2-(beta^2-1)(2beta)^2=1, identically. Zheng p. 5 makes that substitution; the page does not infer the general statement solely from samples. - CONFIRMED | It does not pretend those samples reprove the general congruence lemmas. | git show 5333a8e3bd:research/prime-polynomial/README.md | N2 evidence carried forward: Entry 51, samples-not-general. README lines 68-72 explicitly says it does "not reprove" universal divisibility lemmas. The code checks finite loops and retains the external proof obligation. - CONFIRMED | Wilson's remainder uses modular multiplication, then trial division checks the same N by a separate route. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 52, check-wilson-routes. HTML functions wilson and isPrimeTrial use different calculations, modular factorial multiplication and trial divisors respectively. The browser-code audit obtained agreement on all 999 cases from 2 through 1000. - CONFIRMED | Every reachable tuple uses exact BigInt residuals. No floating-point number enters P. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 53, bigint-no-floats. HTML line 1183: "tuple[letter] = BigInt(raw)". Every arithmetic operand in computeResiduals and the final P expression is BigInt; the numerical Wilson input is bounded and converted before use. - CONFIRMED | 25 total polynomial degree | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 56, published-table-1. Jones p. 449 explicitly states "degree 25"; the largest residual degree is 12 and squaring then multiplying by k+2 yields degree 25. - CONFIRMED | 26 all variables a through z, including k | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 57, published-table-2. Jones p. 449 explicitly states "26 variables, a, b, c, ..., z". Independently collecting symbols from the fourteen page formulas gives all 26. - CONFIRMED | 14 squared integer residuals | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 58, published-table-3. The record excerpt about "degree 25 in 26 variables" does not itself establish 14. Repaired the support by inspecting Jones Theorem 2.12, p. 454, equations (1)-(14), and the p. 455 square-sum construction. The page claim is correct. - CONFIRMED | 87 additions and multiplications in the paper's proof convention | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 59, published-table-4. Jones Theorem 5, p. 451: "87 additions and multiplications". This is a published arithmetic count, not an 87-step bit algorithm. - CONFIRMED | 2 smallest positive value and witness target | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 60, published-table-5. Jones p. 449 identifies positive outputs with "2,3,5,..."; Zheng p. 4 supplies the displayed witness for 2. The record Jones excerpt supports the minimum; Zheng additionally supports the chosen witness target. - CONFIRMED | These five values are displayed from the 1976 paper. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 61, five-values-1976. 25, 26 and 2 occur explicitly on Jones p. 449; fourteen equations occur on p. 454 and are squared on p. 455; 87 occurs on p. 451. The excerpt alone omits the fourteen-equation passage, which was inspected. - CONFIRMED | The browser does not derive publication facts from its own code. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 62, publication-values-not-browser-derived. The badges and table are static HTML, and PUBLISHED_OPERATION_COUNT is a literal 87. The browser computes examples but does not infer what was published. - CONFIRMED | You choose N in the Wilson instrument. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 64, user-wilson-choice. HTML input and slider handlers at lines 1313-1317 call renderWilson with the selected value. The harness exercised both valid and rejected input values. - CONFIRMED | You choose all 26 polynomial coordinates. The three presets are conveniences, not samples with statistical meaning. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 65, user-coordinates-presets. buildVariables creates one editable input for every letter a..z. setPreset selects zero, successive indices, or the published witness coordinates deterministically. These are three conveniences, with no statistical sampling scheme. - CONFIRMED | The page limits coordinate fields to 140 digits and k to 1,000,000. Those are browser safety choices, not mathematics. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 66, safety-limits. parseTuple checks raw.length>140 and tuple.k>1000000n. These are imposed by the code, while Jones permits arbitrary nonnegative integers. - CONFIRMED | The residue trace shows at most its first 64 factors. The remainder above it still uses every factor. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 67, trace-64-factors. Only appending to trace is guarded by "trace.length < 64"; the multiplication loop still runs to n-1. At N=1000000, the browser reports "Showing the first 64 of 999998 factors. The exact remainder used all of them." - CONFIRMED | The 87-cell strip is a visual layout choice. Its count is published; its arrangement is not. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 68, strip-layout. The paper supplies "87 additions and multiplications"; HTML buildCircuit appends 87 spans and CSS arranges them. Neither source nor page identifies an operation-by-operation ledger. Positive control for the paper search is its Theorem 5 passage. - CONFIRMED | No measurement uncertainty or randomness occurs here. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 69, no-randomness. All three presets and all numerical routes are deterministic integer arithmetic. Searching the application script for Math.random/crypto/getRandomValues returns zero; the same function-name search finds wilson and computeResiduals. The claim concerns the mathematical instrument. - CONFIRMED | The finite Wilson sweep in the verifier is not the universal proof. Wilson's theorem and the positive-range theorem are cited results. | git show 5333a8e3bd:research/prime-polynomial/README.md | N2 evidence carried forward: Entry 70, wilson-proof-boundary. README: "The finite Wilson sweep is not a proof of Wilson's theorem." Jones provides both the Wilson citation and the universal positive-range theorem. The page labels them as distinct evidence. - CONFIRMED | The verifier does not expand u, r, c or d. It checks the algebraic closure and finite recurrence samples, then relies on the published divisibility and congruence lemmas. | git show 5333a8e3bd:research/prime-polynomial/README.md | N2 evidence carried forward: Entry 71, unexpanded-four. The code leaves u,r,c,d at zero for the finite preset, checks finite Pell sequences and the two-step identity, and the page gives the symbolic substitutions from Zheng. No gigantic integer expansion is claimed or performed. - CONFIRMED | A positive P is prime only on the stated domain of nonnegative integers. The polynomial also takes zero and negative values. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf; https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 72, domain-and-nonpositive-range. Jones p. 449 supports the nonnegative domain and negative outputs, but the supplied excerpt does not say zero. Zero is nevertheless attainable: in Zheng's full shifted witness, change only h=2,j=5 to h=3,j=3. Residual 1 becomes -1 and residual 2 stays (3+3)+3-9=0; all others stay zero, so S=1 and P=0. The zero tuple separately gives a negative value. - CONFIRMED | No density claim is made. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 73, density-claim-boundary. The README excerpt does not establish absence across the whole page. Inspected the full page: its only density/probability language is "No density claim is made" and the accompanying caveat. Positive control: that same search finds both occurrences. No quantitative sign frequency is asserted. - CONFIRMED | James P. Jones, Daihachiro Sato, Hideo Wada and Douglas Wiens, “Diophantine Representation of the Set of Prime Numbers,” The American Mathematical Monthly 83(6), June-July 1976, 449-464. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 74, citation-jones. PDF cover and Crossref agree on title, four authors, 83(6), 1976 and 449-464; DOI is 10.1080/00029890.1976.11994142. The automated initial warning is false: Crossref says given="James P.", family="Jones"; the page says "James P. Jones". The checker mistakes P. for a first initial. - CONFIRMED | The explicit formula, theorem, degree, variable count and operation count come from this paper. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 75, jones-formula-attribution. Jones Theorem 1 and its p. 449 polynomial supply the range, degree and variable count; Theorem 2.12 supplies the residual system; Theorem 5 supplies 87. All are in the named paper. - CONFIRMED | Yuri V. Matiyasevich, “Diophantine Representation of Enumerable Predicates,” Mathematics of the USSR-Izvestiya 5(1), 1971, 1-28. | https://api.crossref.org/works/10.1070%2FIM1971v005n01ABEH001004; https://www.mathnet.ru/php/archive.phtml?jrnid=im&option_lang=eng&paperid=1910&wshow=paper | N2 evidence carried forward: Entry 76, citation-matiyasevich. Crossref has title "DIOPHANTINE REPRESENTATION OF ENUMERABLE PREDICATES", volume="5", issue="1", page="1-28", issued 1971-02-28. Math-Net spells the author "Yu. V. Matiyasevich". "Ju V Matijasevič" in Crossref is a valid transliteration, so the DOI mismatch is a false alarm. - CONFIRMED | This is the completion of the Davis-Putnam-Robinson-Matiyasevich theorem, not a result caused by the 1976 polynomial. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf; https://www.mathnet.ru/php/archive.phtml?jrnid=im&option_lang=eng&paperid=1910&wshow=paper | N2 evidence carried forward: Entry 77, dprm-completion. Jones pp. 449-450 places the general theorem before the prime polynomial. The cited 1971 paper's Math-Net abstract explicitly concludes "every enumerable predicate is Diophantine" from Matiyasevich's construction and earlier Davis, Putnam and Robinson results. This verifies the actual paper, beyond the record's historical-context excerpt. - CONFIRMED | The compressed witness for 2 and its exact manageable coordinates come from this note. | https://www.ericzheng.org/files/pdf/prime.pdf | N2 evidence carried forward: Entry 79, zheng-witness-attribution. Zheng Claim 1, p. 4, gives the full explicit assignment and p. 5 checks the two huge constraints symbolically. The page correctly shifts his k=1 to the polynomial's k=0. - CONFIRMED | This object characterises primes through the positive part of a multivariable range. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 81, range-characterisation. Jones Theorem 1 identifies precisely the positive part of the multivariable polynomial range with the prime numbers. - CONFIRMED | It is not an efficient generator, a minimal polynomial, or a claim that every value is prime. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 82, not-efficient-minimal-all-prime. Jones p. 449 gives alternative variable/degree tradeoffs and explicitly says the polynomial takes negative values; Zheng explains infeasible coordinate expansion. The page denies three stronger properties the theorem does not supply. It does not assert a formal complexity lower bound. - CONFIRMED | This layer's check reads the bytes this page serves and asserts against them. | git show 5333a8e3bd:research/prime-polynomial/verify-prime-polynomial.mjs | N2 evidence carried forward: Entry 83, placard-reads-served-bytes. Verifier lines 8-11 read the shipped HTML and content Markdown; lines 246-266 assert several substrings. The claim is literally true. Its coverage is limited: a sentence-only S=1096 mutation survives, whereas empty HTML fails at check 1677. This placard does not promise detection of every changed sentence. - CONFIRMED | It is reading what you are reading. | git show 5333a8e3bd:research/prime-polynomial/verify-prime-polynomial.mjs | N2 evidence carried forward: Entry 85, placard-reading-same-page. The verifier reads public/strata/prime-polynomial/index.html. Live curl matches that article and application code; the only diff is injected pulse/Cloudflare scripts. The wording is about the checked article bytes, not a claim that the verifier fetches the network response. - CONFIRMED | Fourteen exact residuals wz + h + j - q | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 87, residual-1. Jones Theorem 2.12, p. 454: "(1) q = wz + h + j,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals wz + h + j - q depends on: w z h j q | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 88, residual-dependencies-1. Formula symbols are exactly "w z h j q". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals (gk + 2g + k + 1)(h + j) + h - z | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 89, residual-2. Jones Theorem 2.12, p. 454: "(2) z = (gk + g + k) · (h + j) + h,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals (gk + 2g + k + 1)(h + j) + h - z depends on: g k h j z | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 90, residual-dependencies-2. Formula symbols are exactly "g k h j z". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals 16(k + 1)^3(k + 2)(n + 1)^2 + 1 - f^2 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 91, residual-3. Jones Theorem 2.12, p. 454: "(3) (2k)³(2k + 2)(n + 1)² + 1 = f²,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals 16(k + 1)^3(k + 2)(n + 1)^2 + 1 - f^2 depends on: k n f | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 92, residual-dependencies-3. Formula symbols are exactly "k n f". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals 2n + p + q + z - e | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 93, residual-4. Jones Theorem 2.12, p. 454: "(4) e = p + q + z + 2n,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals 2n + p + q + z - e depends on: n p q z e | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 94, residual-dependencies-4. Formula symbols are exactly "n p q z e". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals e^3(e + 2)(a + 1)^2 + 1 - o^2 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 95, residual-5. Jones Theorem 2.12, p. 454: "(5) e³(e + 2)(a + 1)² + 1 = o²,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals e^3(e + 2)(a + 1)^2 + 1 - o^2 depends on: e a o | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 96, residual-dependencies-5. Formula symbols are exactly "e a o". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals (a^2 - 1)y^2 + 1 - x^2 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 97, residual-6. Jones Theorem 2.12, p. 454: "(6) x² = (a² − 1)y² + 1,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals (a^2 - 1)y^2 + 1 - x^2 depends on: a y x | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 98, residual-dependencies-6. Formula symbols are exactly "a y x". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals 16r^2y^4(a^2 - 1) + 1 - u^2 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 99, residual-7. Jones Theorem 2.12, p. 454: "(7) u² = 16(a² − 1)r²y⁴ + 1,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals 16r^2y^4(a^2 - 1) + 1 - u^2 depends on: r y a u | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 100, residual-dependencies-7. Formula symbols are exactly "r y a u". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals [(a + u^2(u^2-a))^2 - 1](n + 4dy)^2 + 1 - (x + cu)^2 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 101, residual-8. Jones Theorem 2.12, p. 454: "(8) (x + cu)² = ((a + u²(u² − a))² − 1) · (n + 4dy)² + 1,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals [(a + u^2(u^2-a))^2 - 1](n + 4dy)^2 + 1 - (x + cu)^2 depends on: a u n d y x c | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 102, residual-dependencies-8. Formula symbols are exactly "a u n d y x c". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals (a^2 - 1)l^2 + 1 - m^2 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 103, residual-9. Jones Theorem 2.12, p. 454: "(9) m² = (a² − 1)l² + 1,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals (a^2 - 1)l^2 + 1 - m^2 depends on: a l m | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 104, residual-dependencies-9. Formula symbols are exactly "a l m". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals ai + k + 1 - l - i | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 105, residual-10. Jones Theorem 2.12, p. 454: "(10) l = k + i(a − 1),"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals ai + k + 1 - l - i depends on: a i k l | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 106, residual-dependencies-10. Formula symbols are exactly "a i k l". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals n + l + v - y | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 107, residual-11. Jones Theorem 2.12, p. 454: "(11) n + l + v = y,"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals n + l + v - y depends on: n l v y | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 108, residual-dependencies-11. Formula symbols are exactly "n l v y". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals p + l(a-n-1) + b(2an+2a-n^2-2n-2) - m | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 109, residual-12. Jones Theorem 2.12, p. 454: "(12) m = p + l(a − n − 1) + b(2a(n + 1) − (n + 1)² − 1),"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals p + l(a-n-1) + b(2an+2a-n^2-2n-2) - m depends on: p l a n b m | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 110, residual-dependencies-12. Formula symbols are exactly "p l a n b m". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals q + y(a-p-1) + s(2ap+2a-p^2-2p-2) - x | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 111, residual-13. Jones Theorem 2.12, p. 454: "(13) x = q + y(a − p − 1) + s(2a(p + 1) − (p + 1)² − 1),"; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals q + y(a-p-1) + s(2ap+2a-p^2-2p-2) - x depends on: q y a p s x | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 112, residual-dependencies-13. Formula symbols are exactly "q y a p s x". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | Fourteen exact residuals z + pl(a-p) + t(2ap-p^2-1) - pm | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 113, residual-14. Jones Theorem 2.12, p. 454: "(14) pm = z + pl(a − p) + t(2ap − p² − 1)."; p. 455 instructs replacing k by k+1 and summing squares. Checked that shift, movement to one side, and any expansion term by term against the p. 449 polynomial and the browser evaluator. - CONFIRMED | Fourteen exact residuals z + pl(a-p) + t(2ap-p^2-1) - pm depends on: z p l a t m | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 114, residual-dependencies-14. Formula symbols are exactly "z p l a t m". audit-browser.mjs independently extracted the letter set from this formula and matched the dependency list; no missing or extra dependency. - CONFIRMED | A deterministic stress tuple. It has no special number-theoretic status and is not a random sample. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 115, counting-preset. setPreset assigns String(index) to letters a..z, deterministically 0..25. There is no random selection or claimed distribution; its three computed outputs were independently checked below. - CONFIRMED | Output is zero. The theorem makes no primality claim for zero. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 118, zero-output-message. The branch tests output===0n; Jones's theorem is explicitly about positive values. Zero is attainable by the h,j modification explained in domain-and-nonpositive-range. - CONFIRMED | Output is negative. The theorem makes no primality claim for negative values. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 119, negative-output-message. The else branch is reached only after excluding positive and zero outputs. The zero tuple reproduces the negative message and P=-2188; the cited theorem concerns positive values only. - CONFIRMED | empty product = 1 | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 120, empty-product. At N=2 the factors 2..N-1 form an empty list; the code initializes the product residue to 1n%n. Recreated display: "empty product = 1". This also matches 1!=1. - CONFIRMED | factors. The exact remainder used all of them. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 121, remainder-all-factors. The multiplication loop is not truncated by the display guard. Recreated N=1000000: "Showing the first 64 of 999998 factors. The exact remainder used all of them." - CONFIRMED | The first instrument computes Wilson's remainder for any chosen integer, with a separate trial-division check | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 128, markdown-instrument-1. renderWilson computes both routes for user selections in its explicitly displayed domain 2..1000000. "any chosen integer" is read in that instrument context, not as a promise of unbounded or negative inputs; the limits are stated on the page. - CONFIRMED | The second evaluates all fourteen Jones-Sato-Wada-Wiens residuals with exact integers, then opens the compressed Pell witness for 2 where twelve equations are materialised and two are certified symbolically | git show 5333a8e3bd:research/prime-polynomial/verify-prime-polynomial.mjs | N2 evidence carried forward: Entry 129, markdown-instrument-2. The browser evaluates all fourteen formulas. The witness preset has twelve exact zeros; the page's algebra panels, supported by Zheng pp. 4-5, give conditional symbolic closure of the other two. The browser does not expand c,d,r,u. - CONFIRMED | The page keeps the paper's universal theorem, its published operation count, and the browser's finite checks visibly distinct. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 130, markdown-instrument-3. The page separately labels "Recomputed now", "Published constants", and "Uncertainty and boundary". It expressly distinguishes finite tests from cited universal proofs; this is visible in the full page, beyond the verifier source. - CONFIRMED | Choose an integer, test its Wilson remainder, then open the fourteen constraints that turn a zero certificate into a positive prime. | git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: Entry 131, plain-description. The Wilson input, fourteen integer residuals and positive-range theorem are all present. With every residual zero, S=0 and P=k+2 is positive and prime by Jones; the phrase does not claim that the partial preset itself is a complete zero certificate. - CONFIRMED | Both hand you an existential Diophantine claim as an exact integer witness. The three-cubes page expands every published coordinate, while this page reaches the honest point where a witness must remain a checked Pell recurrence. | git show 5333a8e3bd:src/content/strata/three-mountains-leave-forty-two.md | N2 evidence carried forward: Entry 132, nearby-comparison-1. The compared Markdown says "exact BigInt arithmetic expands the published triples" and names 33 and 42. This page gives exact witness definitions, with four coordinates compressed. The comparison accurately states that distinction. - CONFIRMED | Both keep finite testing separate from a statement about every case. Past the Last Case compares browser checks with kernel proofs, while this page separates sampled Wilson checks from the published universal Diophantine theorem. | git show 5333a8e3bd:src/content/strata/past-the-last-case.md | N2 evidence carried forward: Entry 133, nearby-comparison-2. The compared page explicitly contrasts finite browser checks with Lean kernel proofs and describes the kernel-rerun limit. The prime-polynomial page separately states its finite and universal proof boundaries. - CONFIRMED | Both make a limit theorem operable through ordinary integer arithmetic before the integers become enormous. The Goedel page follows Goodstein growth and descending ordinals, while this page follows Pell recurrences into a fixed-length primality certificate with unbounded bit cost. | git show 5333a8e3bd:src/content/strata/godel-incompleteness.md | N2 evidence carried forward: Entry 134, nearby-comparison-3. The compared Markdown explicitly describes a runnable Goodstein machine and "descending shadow ordinals". The current page's Pell recurrence, 87-operation convention and unbounded coordinate sizes support the other half of the comparison. - CONFIRMED | “Almost always negative” would require a sampling measure the sources do not supply. | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf; https://www.ericzheng.org/files/pdf/prime.pdf; git show 5333a8e3bd:research/prime-polynomial/verify-prime-polynomial.mjs | N2 evidence carried forward: Entry 137, density-sampling-measure. The record leaves this without a source. It is justified as a mathematical caveat: a measure supported on the zero tuple gives probability 1 to negative output; one supported on a full prime witness gives probability 0. Thus the theorem alone supplies no frequency. Full-text measure/density/probability/random/almost searches returned zero in both papers; the same searches for polynomial/theorem returned 76 and 11 lines respectively. This is an inference from the range theorem and the computed example, not a verbatim source assertion. - CONFIRMED | psi_a(n) at least (2a-1)^n-1 | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf | N2 evidence carried forward: Entry 138, pell-growth-lemma. Jones p. 451, Lemma 2.1, verified visually: (2a-1)^n <= psi_a(n+1) <= (2a)^n. Replacing n by n-1 gives the stated lower bound for positive indices, which are the indices used in the witness. - CONFIRMED | (added) Wilson and factorial | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf; git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: HTML stage factorial selects residuals 1-3. Jones Lemma 2.11 and the necessity proof on p. 455 use (1),(2),(3) with Wilson to encode the factorial condition. The label was not in any source-record claim. - CONFIRMED | (added) growth bounds | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf; git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: HTML stage growth selects 4-5. Jones p. 454: equations (4),(5) with Lemma 2.3 force the bound on a. This stage label was omitted. - CONFIRMED | (added) Pell encoding | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf; git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: HTML stage pell selects 6-11. Jones p. 454 identifies these equations with the Pell sequence and its index constraints. This stage label was omitted. - CONFIRMED | (added) congruence closure | https://www.math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf; git show 5333a8e3bd:public/strata/prime-polynomial/index.html | N2 evidence carried forward: HTML stage congruence selects 12-14. Jones p. 455 applies Lemma 2.4 congruences to these three equations. This stage label was omitted. ## Findings - [fixed] X1, verifier-anchor-order (MINOR): replaced "The verifier begins here, before it reads a page value. It checks exactly that" with "The verifier's first assertion checks exactly that" in public/strata/prime-polynomial/index.html. The source reads the HTML and Markdown before asserting the independent witness anchor. No public correction line for this MINOR wording fix. - [fixed] X2, independent-variable-census (WRONG): removed the supplied-alphabet assertion from research/prime-polynomial/verify-prime-polynomial.mjs and corrected both public/strata/prime-polynomial/index.html and research/prime-polynomial/README.md to say that the verifier counts fourteen residuals and recovers degree 25, while the variable count of 26 is checked against a supplied constant. Before editing, the scratch mutation c * u to 0n * u still reported the variable census and PASS 1688 checks, confirming the false checking claim. Added "Corrected 2026-10-18" with "found by the assay line, 2026-10-18" to the HTML Corrections section and mirrored it at the end of src/content/strata/prime-polynomial.md. The published 26-variable mathematical claim remains correct. - [fixed] X3, zheng-title-article (MINOR): restored the source's words "An Nonnegative Integer Solution to the Jones-Sato-Wada-Wiens Polynomial" in the HTML citation and research README. The first page of https://www.ericzheng.org/files/pdf/prime.pdf says "An Nonnegative", "Eric Zheng", and "March 20, 2021". Author, date, and work identity were already correct. No public correction line for this MINOR restoration. - [declined] X4, verification-note-access (MINOR): the source notes and limits exist in research/prime-polynomial/README.md, with the formulas in its adjacent verifier, but the page gives no public note or runnable download link. N2 records HTTP 404 for both literal research URLs and HTTP 200 for the article as its control. A complete public runnable bundle must package the verifier with its HTML and Markdown inputs and preserve or adapt their paths, beyond a few words or a small code change. Listed under the Tier A rule; no page edit for this item. - [dated] X5, stale-modification-date (STALE; metadata-only fix): changed the HTML JSON-LD dateModified from 2026-07-30 to the requested revision date 2026-10-18. Git history records later revisions on 2026-08-01, 2026-09-27, and 2026-10-01. The explicit JSON-LD exception requires no Updated line; the WRONG correction dates this revision. This was the only STALE item, so no visible Updated line remains to group.