Vor-ι′ 7D: canonical positive bounded-transform cross-bridge fails Prime-2 exact calibration - #97
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Leitfaden für ReviewerDieser Entwurf fügt eine kanonische positive 7D-Cross-Bridge mit beschränkter Transformation unter Verwendung vorhandener P11-Operatoren hinzu und verwendet anschließend ein 200-Bit-Arb/Chebyshev-Zertifikat, um rigoros zu zeigen, dass ihre R=1-Prime-2-Antwort das exakte Weil-Kalibrierungsziel nicht erreichen kann. Das Ergebnis ist ausdrücklich auf einen einzelnen Zeugen in einem endlichen Fenster beschränkt und erhebt keine weitergehenden No-Go-Ansprüche. Sequenzdiagramm für die Arb/Chebyshev-ZertifizierungsequenceDiagram
participant Checker
participant Spectral as SpectralBoxes
participant Cheb as ChebyshevResolver
participant Arb
participant Firewall as SupportFirewall
Checker->>Spectral: spectral_boxes()
Spectral->>Arb: certify ||H*H|| < 16 and ||A|| < 32
Arb-->>Spectral: certified bounds
Checker->>Cheb: cheb_resolvent_defect(a, G_apply, 16, 13)
Checker->>Cheb: cheb_resolvent_defect(a, A_apply, 32, 13)
Cheb->>Arb: evaluate coefficients and tail bounds
Arb-->>Cheb: Arb enclosures
Checker->>Firewall: certify_final_disjoint(P_Ha, P_Hb, P_Ra, P_Rb)
Firewall-->>Checker: support gaps exceed 2*EPS
Checker->>Arb: compare Xlo with Xreq
Arb-->>Checker: Xreq < Xlo
Checker-->>Checker: report d-exact FAIL
Ablaufdiagramm für die zertifizierte Prime-2-Kalibrierungs-Firewallflowchart TD
W["R=1 odd Prime-2 witness (a,b)"] --> D["P_H = H*H(I+H*H)^(-1)\nP_R = A(I+A)^(-1)"]
D --> X["X_7D(a,b) = <P_Ha, P_Rb> + <P_Ra, P_Hb>"]
X --> C["Degree-13 Chebyshev approximation\n200-bit Arb arithmetic"]
C --> E["Certified enclosure:\n[-0.0911347959..., -0.0520968085...]"]
R["Exact target X_req = -0.1172764645..."] --> S{"Target below enclosure?"}
E --> S
S -->|"Yes; gap > 0.02614"| F["d-weak PASS; d-exact FAIL"]
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Original review guide in EnglishReviewer's GuideThis draft adds a canonical positive 7D bounded-transform cross bridge using existing P11 operators, then uses a 200-bit Arb/Chebyshev certificate to rigorously show that its R=1 Prime-2 response cannot reach the exact Weil calibration target; the result is explicitly confined to a single finite-window witness with no broader no-go claims. Sequence diagram for the Arb/Chebyshev certificationsequenceDiagram
participant Checker
participant Spectral as SpectralBoxes
participant Cheb as ChebyshevResolver
participant Arb
participant Firewall as SupportFirewall
Checker->>Spectral: spectral_boxes()
Spectral->>Arb: certify ||H*H|| < 16 and ||A|| < 32
Arb-->>Spectral: certified bounds
Checker->>Cheb: cheb_resolvent_defect(a, G_apply, 16, 13)
Checker->>Cheb: cheb_resolvent_defect(a, A_apply, 32, 13)
Cheb->>Arb: evaluate coefficients and tail bounds
Arb-->>Cheb: Arb enclosures
Checker->>Firewall: certify_final_disjoint(P_Ha, P_Hb, P_Ra, P_Rb)
Firewall-->>Checker: support gaps exceed 2*EPS
Checker->>Arb: compare Xlo with Xreq
Arb-->>Checker: Xreq < Xlo
Checker-->>Checker: report d-exact FAIL
Flow diagram for the certified Prime-2 calibration firewallflowchart TD
W["R=1 odd Prime-2 witness (a,b)"] --> D["P_H = H*H(I+H*H)^(-1)\nP_R = A(I+A)^(-1)"]
D --> X["X_7D(a,b) = <P_Ha, P_Rb> + <P_Ra, P_Hb>"]
X --> C["Degree-13 Chebyshev approximation\n200-bit Arb arithmetic"]
C --> E["Certified enclosure:\n[-0.0911347959..., -0.0520968085...]"]
R["Exact target X_req = -0.1172764645..."] --> S{"Target below enclosure?"}
E --> S
S -->|"Yes; gap > 0.02614"| F["d-weak PASS; d-exact FAIL"]
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Waschtl904
marked this pull request as ready for review
September 12, 2026 08:25
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Scope
Finite-window, single-witness destructive audit at
R=1. This PR studies one canonical, parameter-free pre-Schur/Mediator bridge built only from existing P11 data. It does not claim a universal cross-term/mediator no-go, an Object-X no-go, or anything about RH.This is new relative to merged PR #96, whose explicit nonclaims left nontrivial mediators and pre-Schur nonorthogonal Hub/Rest cross terms open.
7D bridge
With
T = \widetilde R_1,A=T^*T=R_1^*R_1,B=(I+A)^{-1},H=H_1, defineThe two bounded transforms have norm at most
1/2, henceThe same-source cross correction is the anticommutator of the two positive resolvent defects
Prime-2 firewall
For the same odd PR-#91 witness used by PR #96, exact Weil calibration requires
The hardened degree-13 Chebyshev/Arb certificate gives
Thus the target lies rigorously outside the certified enclosure:
The checker uses
python-flintArb balls at 200-bit precision, no small-amplitude pruning, certified cutoff decisions, and a final2*epsilonsupport-separation firewall.Reproduction
A separate pre-push cloud reproduction using
python-flint 0.9.0reproduced the degree-13 central value, analytic tail, target separation, and the relevant support-gap diagnostics. Exact-head destructive review of the committed script remains the next governance gate.Files
audits/P11_VOR_IOTA_PRIME_7D_2026-09-12/README.mdaudits/P11_VOR_IOTA_PRIME_7D_2026-09-12/audit.mdaudits/P11_VOR_IOTA_PRIME_7D_2026-09-12/provenienz.mdscripts/check_vor_iota_prime_7D_harden.pyNonclaims / governance
Zusammenfassung von Sourcery
Bestätigt, dass die kanonische 7D-beschränkte Transformations-Cross-Bridge bei R=1 die exakte Prime-2-Kalibrierung verfehlt, während die Positivität erhalten bleibt und die Schlussfolgerung auf das angegebene Finite-Window-„Witness“ beschränkt wird.
Neue Funktionen:
Verbesserungen:
Dokumentation:
Tests:
Aufgaben:
Original summary in English
Zusammenfassung von Sourcery
Bestätigt, dass die kanonische beschränkte 7D-Transformations-Cross-Bridge positiv bleibt, jedoch für den angegebenen R=1-Zeugen keine exakte Prime-2-Kalibrierung erreichen kann.
Neue Funktionen:
Verbesserungen:
Dokumentation:
Tests:
Aufgaben:
Original summary in English
Summary by Sourcery
Certify that the canonical 7D bounded-transform cross-bridge remains positive but cannot achieve exact Prime-2 calibration for the stated R=1 witness.
New Features:
Enhancements:
Documentation:
Tests:
Chores: