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Engineering Record · Second Arc Convergence v1.0 2026-07-25 CERTIFIED_RADIUS_1.78E-6

Local Interval Green Position Cover

Local Interval Green Cell Cover v1.0 — Strictly elevates the conservative uniform position radius of 2×10⁻¹⁵ from v0.9 by 890 million times to 1.78×10⁻⁶, and precisely marks the boundary between "passed" and "inconclusive" for the current prover: it fails at h=1.8×10⁻⁶. This is the technical convergence node of the second research arc.

RH_CLAIM = False — The document within the package explicitly states "this is a local position quantifier certificate in the abstract Green model, not an actual zeta zero occupancy certificate... all relevant flags remain false", reproduced as is. The pass/inconclusive boundary does not mean the true positivity critical value lies between them.

Connections

This package elevates the fixed atomic certificate of v0.7 and the conservative radius of v0.9 into a replayable covering box certificate, quoting its boundary audit as-is.

"The interval lower bound of the final Sylvester determinant for h=1.8×10⁻⁶ is negative, so the certificate is indeterminate... This table only provides the pass/indeterminate brackets of the current interval prover... It does not imply that the true positivity critical value lies between the two." — Excerpt from RESULTS.md in this package.

Technical Notes

Main Document — 58-dimensional position box certificate construction, radius step boundary audit, adversarial corner testing, 890-million-fold improvement over v0.9, and technical convergence judgment.

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Theorem

From THEORY.md in the package.

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Result Data

Main certificate strict bound table, complete radius ladder (pass/inconclusive/failure type), and improvement multiplier over v0.9, from RESULTS.md within the package.

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Trust Boundaries

From TRUST_BOUNDARY.md within the package.

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Files

Large interval certificates (local_green_cell_certificate_h178e-8.json, adversarial_corner_point_certificate_h1e-3.json, each about 140 KB) and the inherited parent node data are not listed individually; they are all in the complete zip file.

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Download Complete Package (204.9 KB)

sha256 495b6d185ac53f9179d395aab35d5dcb340f7686e312f5dd3a47fb5be5d8ea93