jensen_wedge: literature search for claims A, B and C (2026-10-19)

Nothing here bears on RH. This file records a bounded literature search, run 2026-10-19, for three results of hunt #135. It grades no mathematics: it says what the searched literature already contains. CLAUDE.md requires a stated search before anything is called new; MISSION.md forbids this hunt from declaring novelty, so the verdicts below use only the two forms "no prior instance found in the searched set" and "prior instance found".

The verdicts first

Both prior instances predate the hunt: it opened 2026-10-18, Sarnowski's deposits are dated 2026-08-20, and Savva's is dated 2026-09-03. Neither has been peer reviewed, and this search did not check their proofs. A prior instance means the claim is already in the literature, not that its proof there is right. Claims of RH strength found on the way (section 3) are listed and not assessed.

1. The searches

All on 2026-10-19. Every fetched page and PDF was treated as data. Downloads went to a scratch directory outside the tree and were not committed.

What the set does not cover. It includes no journal full-text search beyond MDPI and no MathSciNet. Zenodo was reached only through OpenAlex's index (its own API refused scripted requests), and only through titles and abstracts that OpenAlex holds. Sarnowski's other 33 deposits were not opened. Savva's Lean development and technical supplement were not read.

2. What was found, claim by claim

2.1 Claim A: Savva's two-thirds wedge

John Savva, A Two-Thirds Hyperbolicity Wedge for Jensen Polynomials of Riemann's Xi-Function, Version 1.1, 3 September 2026, Zenodo 10.5281/zenodo.22293642 (OpenAlex lists 10.5281/zenodo.22293641); repository github.com/aimathpapers/Jensen-2-Thirds. Its Theorem 1.1, in GORTTW's normalisation xi(1/2 + w) = sum gamma(n) w^(2n)/n!, states (paraphrased): for an absolute K > 0 and all d >= 1, n >= 0, the condition n^2 log(n+2) >= K d^3 implies that J^{d,n} has exactly d distinct negative real zeros.

Squared, the condition reads n^4 log^2(n+2) >= K^2 d^6. That is claim A without the log^12(d+2) factor, so Savva's statement, if correct, implies claim A. The route is the one RESULTS.md sections 11 and 12 follow:

• Holland's 3F2(-d, A, C; B, D) model with D free, fixed by four quotient coordinates and two normalisations so that six coefficients match;
• the limiting zero (alpha, t, w, delta) = (3, 2, 16/3, 1/3) of its matching map, that is A ~ 3nL, C ~ 2n, B - C ~ 16n/(3L) and D ~ n(1 + 1/(3L)), which are the leading-order values of section 11.3;
• a Banach contraction around that point (det DF = -1/144 in Savva's coordinates), the role H1 plays in H1_H3.md section 4;
• the observation that Holland's localisation hypothesis (C - D)/D <= 1/4 fails on this branch, where the ratio tends to 1 (section 11.3 has (C - D)/D -> 1), and a replacement through a shifted 3F2 recurrence where section 12 uses Lemmas A to C;
• a six-node complex Hermite-Genocchi remainder at radius sqrt(nd), giving d^3/(n^2 log n), the role of Proposition 2.2_6 in section 12.1.

Status as Savva states it: written with substantial AI assistance, mainly from one named OpenAI model, and with no human mathematical review or peer review claimed. The Lean development is conditional on literature inputs entered as typed records (Jacobi, Martinez-Finkelshtein-Morales-Perales, Marcus-Spielman-Srivastava). This search did not check the proof.

A second, weaker prior instance concerns the exponent heuristic only. Sarnowski's Paper 134Y (20 August 2026) shows that five matches plus a fifth-derivative bound on a sqrt(nd) disk reproduce Holland's 3/5, and Paper 134Z's conditional 3/4 and 4/5 wedges are the rule d <~ n^(1 - 2/m) at m = 8 and 10. This is the heuristic MISSION.md derives under Q1, there marked as derived in-tree.

2.2 Claim B: Sarnowski's diagonal Pade spines

Michael Sarnowski, Paper 134Z: Multi-Jacobi Protected Spines and Higher-Order Matching in the Riemann xi Jensen Hierarchy, Zenodo 10.5281/zenodo.22023893, 20 August 2026; and Paper 134AA: Jacobi Cancellation Skeletons and All-Large-Shift Geometry of Multi-Jacobi Protected Spines, Zenodo 10.5281/zenodo.22025447, 20 August 2026. Read: 134AA in full, 134Z in abstract.

134Z builds a rank-r rational quotient spine by diagonal rational interpolation of the adjacent normalised coefficient ratios. It matches 2r + 2 coefficients and factors into Jacobi strands joined by finite-free convolution. A model 3F2(-d, A, C; B, D) has adjacent coefficient ratio (A + j)(C + j)/((B + j)(D + j)), a [2/2] rational function of j, so the rank-2 spine is Holland's two-factor family with D free. That identification is read from 134AA's definitions; 134Z's rank-2 text was not read. 134AA proves, for every fixed r and all large shifts N:

• the rescaled spine tends to the diagonal [r/r] Pade approximant of (1 + y)^alpha_N, with alpha_N = 1 - eps_N and eps_N ~ 2/L_N. This is section 11.1's statement that matching is Pade agreement with the binomial f_eps;
• at alpha = 1 numerator and denominator share the Jacobi factor P^(1,1)_(r-1), which 134AA calls the cancellation skeleton. At r = 2 its single zero gives the interior node lambda = 2, which is section 11.3's Lobatto (Simpson) limit with nodes at 0, 1/2 and 1 in the variable w = n/p;
• one escaping pole with eps_N A_(r,N)/N -> r(r + 1): 6 at r = 2, so A ~ 3NL, as in section 11.3; and B_1/N -> 1, section 11.3's D ~ n;
• the first unprotected derivative obeys N^(2r+1) E^(2r+2)(0)/eps_N -> -C_r with C_r = (r+1)(r!)^4/(r (2r)!). At r = 2, C_2 = 1, so E^(6)(0) ~ -2/(N^5 L): section 11.4's leading-order R_6 defect E_S(6) ~ -2/(n^5 L), sign and constant included.

Sarnowski's Paper 134AE (10.5281/zenodo.22026880, 20 August 2026; abstract read) adds section 11.3's Stieltjes argument: an exact positive Beta-Stieltjes representation of the binomial comparison, the diagonal Pade approximant as a Gaussian quadrature, and pole-zero interlacing. Savva (section 2.1) reaches the same six-match point in Holland's literal parametrisation, without the Pade language.

Not found in what was read, and therefore still without a located prior instance: that phase 0's bisected theta_star (the sign change of E_F(5) along Holland's D-fixed family) is this Pade point (section 11.3); the measured reflection symmetry a1 + b2 = b1 + a2 = 1; the restricted-class obstruction of section 11.5; and the Davenport-Heilbronn gate of section 15. They are details of claim B, not claim B itself. Sarnowski states that his own deposits have mixed-precision, non-interval diagnostics, no effective starting shift, and no new hyperbolicity region.

2.3 Claim C: explicit constants

No searched source gives a number for Holland's K, for GORTTW's c, or for the constant of any wedge at exponent 3/5 or 2/3.

• Savva makes one part explicit: K_geometry = 522255954073519803473068032000000000000000001 (about 5.2e44). The final constant is max{K_geometry, C_mult C_B6, K_finite} with N_0 = max{N_analytic, N_explicit}. C_B6 and N_analytic come from the sectorial saddle proof and are not computed, so the K of his wedge is not explicit.
• Sarnowski says 134Y does not determine Holland's constants and 134AA gives no effective starting shift.
• Ning, An Effective d^3-Scale Criterion for the Hyperbolicity of Jensen Polynomials Associated with the Riemann xi-Function, Zenodo 10.5281/zenodo.19891455, 29 April 2026, Theorem 9.4: an absolute C_0 with n + d >= C_0 d^3 sufficient. It is a polynomial wedge (d <~ n^(1/3)) that predates Holland, but C_0 is only taken large enough, never computed. Holland's eight references (read in arXiv:2608.08682v1) include O'Sullivan but not Ning or Planat.
• Planat, Mathematics 14 (2026) 1884, prints C_0 ~ 0.020 for n >= C_0 d^4. That is not Holland's K or GORTTW's c, and section 4 explains why it is not an explicit constant for the standard family either.

A remark derived here, unreviewed, and recorded because it bears on how much claim C is worth: GORTTW's c is the cheap half. GORTTW Corollary 1.3 covers every d <= 9.36e20 at all n. For larger d and n >= e^(d/2), n^3 log^2(n+2) >= e^(3d/2) (d/2)^2, which exceeds K d^5 whenever K <= e^(3d/2)/(4 d^3), a quantity far above e^(1e21) at d = 9.36e20 and increasing from there. So any proved explicit bound K <= e^(1e21) on Holland's K would make c = 1 admissible in GORTTW Theorem 1.1, in both its v3 form c e^(d/2) and its published form c e^d. The substantive explicit target is K.

3. Other 2026 work met on the way

None of these is a prior instance of A, B or C. The last three claim results of RH strength, or close to it, that would subsume Holland's wedge if correct. All four are unreviewed deposits, and this search did not assess them.

Older work checked for claim C: O'Sullivan, Res. Math. Sci. 8 (2021) 46 (arXiv:2007.13582). His Theorem 1.3 makes a Hermite-modified family P_{d,n}, not J^{d,n}, hyperbolic for n/log^2 n >= d^(3/4)/2 once d is large enough. There is no explicit threshold. Kim and Lee, J. Korean Math. Soc. 59 (2022) 775 (Zbl 1494.30013): by its review, an improvement of GORZ for derivatives; no explicit wedge was found in the review.

4. Planat 2026, read critically

Two articles by Michel Planat, both in MDPI Mathematics: Asymptotic Hyperbolicity of Jensen Polynomials and the Finite-Strip Obstruction to the Riemann Hypothesis, 14 (2026) 1884, 28 May 2026, doi 10.3390/math14111884; and Parity Bifurcation, PIII(D6) Topology, and a Stieltjes Framework to Jensen Polynomial Hyperbolicity, 14 (2026) 2240, 23 June 2026, doi 10.3390/math14132240. Both were read in full in a browser.

What 1884 states. Theorem 3 (paraphrased): there is a constant C_0^inf > 0 such that J^gamma_{d,n} is hyperbolic for all d >= 1 and n >= C_0^inf d^4, with C_0^inf ~ 0.020 given numerically. Theorem 4 bounds the onset index by n*(d) <= C_0^inf d^4 and gives the formula C_0^inf = (6/pi)(C_2^eff + C^tail + C^bulk) ~ 0.0195.

Is it uniform in d? One constant serves every d, but the threshold grows like d^4. That is a wedge d <~ n^(1/4), weaker than Holland's n^(3/5), and GORTTW Corollary 1.3 already covers every d <= 9.36e20 at all n. It is not "for all n >= C" independent of d. The summary that credited such a statement misread n >= C_0^inf d^4.

What is proved and what is asserted.

• The d^4 exponent is chosen, not derived. Remark 5 notes that a cruder estimate gives d^(5/2) and sets it aside because it disagrees with the observed onset scaling. In Step 3 of the proof the bulk constants C_{d,k} depend on d and k and are summed without a uniform bound.
• C_0^inf uses an effective K_tau ~ 0.62 fitted on n <= 23 (the paper's own analytic limit is K_tau = 1), and components evaluated at the single reference point (d, n) = (8, 4).
• Proposition 2(iii)'s bound |eps_n| < 2.9/(n+1), on which Lemma 1 rests for n >= 10, is checked numerically for n = 10..50 and asserted beyond.

Normalisation. The paper sets M_n = int_0^inf Phi_1(u) u^(2n) du, where Phi_1 is twice the first term of the theta series, and identifies gamma(n) = M_n although its own definition of gamma(n) carries a 1/(2n)!. Constant factors and a rescaling t -> 2t do not matter for hyperbolicity, but the dropped (2n)! does, and so, slightly, do the dropped k >= 2 terms. The family is then used two ways:

• Lemma 1's b_n > (2n+1)/(2n+3), with b_n = M_(n+1)^2/(M_n M_(n+2)), is exactly the Turan inequality for GORTTW's gamma(n), which is proportional to n! M_n/(2n)! (derived here: gamma(n+1)^2/(gamma(n) gamma(n+2)) = b_n (2n+3)/(2n+1)).
• Remark 2 computes the d = 2 discriminant from raw M_n, finds it negative because moments are log-convex (b_n < 1), and concludes that J_{2,n} has no real zeros at any n.

Measured here, once, by mpmath quadrature at 25 digits on one route (not pinned by a test): with the full kernel, b_n is 0.35828, 0.63765, 0.75307 and 0.81515 at n = 0..3, so b_n < 1, and the Turan ratio of the standard gamma(n) is 1.0748, 1.0627, 1.0543 and 1.0481. The standard J_{2,n} is hyperbolic at those n, so Remark 2 holds for the raw-moment family and fails for the standard one. Keeping only the first theta term moves M_0 by a relative 3.5e-4. The paper also places a positive onset at every d >= 9, which for the standard family contradicts GORTTW Corollary 1.3 (n*(d) = 0 for d <= 9.36e20) and Chasse (d <= 2e17). So the family on which its onset numbers were measured is not the standard J^{d,n}, and Theorem 3 does not transfer to Holland's or GORTTW's polynomials as written.

Comparison with Holland or GORTTW. None. 1884 has 12 references, and the only Jensen work among them is GORZ 2019. Holland postdates both articles. 2240 cites GORZ and Planat 1884.

2240. A numerical study of an onset for 5 <= d <= 16, again positive where the standard family is hyperbolic at every n. It offers conjectures only (Conjectures 1 and 2), no hyperbolicity theorem. Its Pade approximants belong to a cumulant generating function B(w), with poles near the squared zero ordinates. That is unrelated to claim B's comparison family.

5. What this changes for the hunt

Claims A and B already have prior instances, so the hunt's phase 1 result is an independent re-derivation of results deposited 6 to 9 weeks earlier, not a delta against Holland that the lab could claim. Two parts of it still differ from what was found:

• it is conditional where Savva states an unconditional theorem;
• it carries a log^12 d loss that Savva's statement does not.

Phase 2 (MISSION Q2, explicit constants) has no located prior instance and is the open target. Savva's K_final structure is the nearest prior work and could serve as a comparison: an explicit K for Holland's wedge or for Savva's wedge would be a delta against both. Per section 2.3, an explicit bound on K also settles GORTTW's c at once. Whether to redirect phase 2 is the owner's decision, and this file does not make it.