From FCHP to PSOC4(3) Hyperelastic Phase-Spatial Resolution

A bridge paper on the relation between the Finsler Coherence Hyperelastic Principle and PSOC4(3). FCHP describes coherence as a hyperelastic field under directional closure cost. PSOC4(3) appears when that deeper strain resolves into one phase degree and three spatialorientation degrees, forming the local phase-spatial grammar of physical disclosure.FCHP → directional closure cost → closure strain resolution → PSOC4(3) → physical disclosure PSOC4(3) = U(1) ⊕ SO(3) = Q + Jₓ + Jᵧ + J_z This bridge paper clarifies the relation between the Finsler Coherence Hyperelastic Principle (FCHP) and PSOC4(3). FCHP is treated as the deeper constitutive principle governing coherence strain, hyperelastic resistance, and directional closure cost within Finsler phaspace. PSOC4(3) is treated as the local phase-spatial closure grammar that appears when that deeper strain resolves into one phase degree and three spatial-orientation degrees. The paper therefore does not frame FCHP and PSOC4(3) as competing structures, but as two levels of one disclosure architecture: FCHP supplies the deep law of coherence strain; PSOC4(3) supplies the local algebra of phase-spatial physical.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-27
DOI
https://doi.org/10.5281/zenodo.20951277
Primary Topic
Elasticity and Material Modeling
Type
preprint
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From FCHP to PSOC4(3) Hyperelastic Phase-Spatial Resolution

Philip Lilien
Zenodo (CERN European Organization for Nuclear Research)
Elasticity and Material Modeling
preprint

From FCHP to PSOC4(3) Hyperelastic Phase-Spatial Resolution

Philip Lilien
preprint en

Abstract

A bridge paper on the relation between the Finsler Coherence Hyperelastic Principle and PSOC4(3). FCHP describes coherence as a hyperelastic field under directional closure cost. PSOC4(3) appears when that deeper strain resolves into one phase degree and three spatialorientation degrees, forming the local phase-spatial grammar of physical disclosure.FCHP → directional closure cost → closure strain resolution → PSOC4(3) → physical disclosure PSOC4(3) = U(1) ⊕ SO(3) = Q + Jₓ + Jᵧ + J_z This bridge paper clarifies the relation between the Finsler Coherence Hyperelastic Principle (FCHP) and PSOC4(3). FCHP is treated as the deeper constitutive principle governing coherence strain, hyperelastic resistance, and directional closure cost within Finsler phaspace. PSOC4(3) is treated as the local phase-spatial closure grammar that appears when that deeper strain resolves into one phase degree and three spatial-orientation degrees. The paper therefore does not frame FCHP and PSOC4(3) as competing structures, but as two levels of one disclosure architecture: FCHP supplies the deep law of coherence strain; PSOC4(3) supplies the local algebra of phase-spatial physical.

Zenodo (CERN European Organization for Nuclear Research)
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Elasticity and Material Modeling
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From FCHP to PSOC4(3) Hyperelastic Phase-Spatial Resolution — Philip Lilien · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS