Coherence Calculus: An Operator Calculus for Finite Observability under Horizon Projections

This record is the v0.10 preprint release of Coherence Calculus. Coherence Calculus studies operator application under finite observability: when a system is restricted to a horizon, what visible law survives, what defect is returned from the hidden complement, and which closure classes are forced by that projection? It develops a horizon-based operator calculus for exactifiable incidence, presentation, elimination, returned defect, and scale-law closure. Version v0.10 is a substantial structural revision. Part I refactors the front end from direct Closure Balance wording to Exact Observation, exactifiable incidence, presentation calculus, lower observables, and the first scalar counting realization. The counting equation is recovered on that first scalar counting surface, rather than treated as the primitive bedrock closure axiom. Part II introduces Boundary Balance as an explicit three-clause physical-law hypothesis and derives carrier-level consequences from it. Under later endpoint-rigidity and representative hypotheses used for carrier identification, the manuscript recovers recognizable Schrödinger, wave/Klein-Gordon, Maxwell, and Einstein equation forms as conditional normal-form identifications of one common selected state-field law on a shared selected realization, rather than as independent starting laws or empirical derivations from Part I alone. The uploaded artifacts include the monograph PDF, flattened LaTeX source, generated dashboard, and concise audit summaries for Blueprint-compatible theorem/proof linkage, appendix proof-chain validation, dashboard validation, Lean pipeline status, and lean-assumptions boundary auditing. The assumption-boundary audit is performed with lean-assumptions, an external Lean 4 dependency-surface inspection tool: https://github.com/Rodbourn/lean-assumptions. The present scope does not include coupling constants, mass ratios, or the particle spectrum. The manuscript should be read as an active research preprint. Part I develops the mathematical operator calculus; Part II derives law-side consequences only under the stated physical-law hypotheses and representative assumptions. This manuscript release is supplemented by the corresponding v0.10 public source snapshot for GitHub release cc-v10-source in Rodbourn/coherence-calculus, archived at https://doi.org/10.5281/zenodo.20024197.