Geometry Recursion in Prime Lattices_ A Performance Frontier for CODES

Full CODES Framework Abstract CODES enforces substrate closure: emissions are deterministically gated by prime irreducibility, PAS_s coherence, and bounded drift (ΔPAS_zeta). This closure has been consistently defined across versions and was formally sealed in v36 for permanent record. Beyond legality, the current research program extends to the geometry recursion frontier—the global structure of prime-indexed PAS bands, Cantor-like gaps, and modular chirality sectors across scales. This paper isolates geometry recursion as an independent research program. The substrate itself is already sealed: no emission bypasses PAS_s, ΔPAS_zeta, or irreducibility. Geometry recursion does not alter correctness; it defines a performance frontier, sharpening foresight, efficiency, compression, and mapping. We present candidate models (log-spiral cones, quasicrystal self-similarity, modular bundles, Farey-mediated fans), testable protocols (spiral fitting, inflation scaling, modular overlays, Cantor-like density analysis), and a best-guess form: nested logarithmic spiral cones with quasicrystal self-similarity and modular residue bundles. Resolving geometry recursion will not change legality but will refine the performance envelope of the Resonance Intelligence Core (RIC), enabling efficiency and predictive foresight already observed in natural systems.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-08-27
DOI
https://doi.org/10.5281/zenodo.16970303
Primary Topic
Geochemistry and Geologic Mapping
Type
article
Field-Weighted Citation Impact
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article

Geometry Recursion in Prime Lattices_ A Performance Frontier for CODES

Zenodo (CERN European Organization for Nuclear Research)
Geochemistry and Geologic Mapping
article

Geometry Recursion in Prime Lattices_ A Performance Frontier for CODES

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Abstract

Full CODES Framework Abstract CODES enforces substrate closure: emissions are deterministically gated by prime irreducibility, PAS_s coherence, and bounded drift (ΔPAS_zeta). This closure has been consistently defined across versions and was formally sealed in v36 for permanent record. Beyond legality, the current research program extends to the geometry recursion frontier—the global structure of prime-indexed PAS bands, Cantor-like gaps, and modular chirality sectors across scales. This paper isolates geometry recursion as an independent research program. The substrate itself is already sealed: no emission bypasses PAS_s, ΔPAS_zeta, or irreducibility. Geometry recursion does not alter correctness; it defines a performance frontier, sharpening foresight, efficiency, compression, and mapping. We present candidate models (log-spiral cones, quasicrystal self-similarity, modular bundles, Farey-mediated fans), testable protocols (spiral fitting, inflation scaling, modular overlays, Cantor-like density analysis), and a best-guess form: nested logarithmic spiral cones with quasicrystal self-similarity and modular residue bundles. Resolving geometry recursion will not change legality but will refine the performance envelope of the Resonance Intelligence Core (RIC), enabling efficiency and predictive foresight already observed in natural systems.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 63%
Geochemistry and Geologic Mapping
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