Occupancy Operator Family and Covering Green Certificates

Occupancy Operator Family v0.9 — No longer collapses the unknown zero locations into a single scalar count, but preserves the positional uncertainty, using exact rational numbers to prove the joint positive definiteness of the operators for the entire family of allowed locations (radius 2×10⁻¹⁵); simultaneously honestly quantifies the proof budget gap of about 8 trillion times compared to the floating-point intuitive scale.

RH_CLAIM = False — The files in the package self-report exact_synthetic_occupancy_family=true and conditional_abstract_clamped_family=true, but actual_zeta_occupancy_family=false and global_rh_certificate=false, reproduced here as-is.

Connections

This package formally builds the "positional quantifier" problem discovered in the previous package into a three-tier replayable object, quoting its honest gap as is.

"Floating-point adversarial corner diagnostics still yield a threshold of about 1.0004702 at a cell radius of 0.016, and about 0.9880614 at 0.017. This is not a universal certificate, but it shows a proof-budget gap of approximately 8×10¹² between the exact micro-radius and the floating-point local scale." — Excerpted from "Exact Results of This Round" in the README of this package.

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Technical Notes

Main document — Exact occupancy-to-operator transfer theorem, fully rational Dirichlet Green–Schur adaptive cover, exact rational lower bound of the 58-cell micro-radius certificate, and drop quantification of floating-point adversarial corner points.

Theorem

From THEORY.md in the package.

Result Data

Exact semantic bridge, adaptive bisection cover results, 58-cell micro-radius certificate, and floating-point corner diagnostics, from RESULTS.md within the package.

Trust Boundaries

From TRUST_BOUNDARY.md within the package.

Files

The large interval certificates (140 KB) inherited from v0.7 are not listed individually; they are included in the complete zip file.

Download Complete Package (124.3 KB)

sha256 bc5f204e1f6f441d8e20b4463f92968df18017dc1736067a1a595372ecc7a113