The Semantic Deviation Principle (v0.2 Final): A Measurement Primitive for Semantic Physics

The Semantic Deviation Principle (v0.2 Final): a measurement primitive for Semantic Physics.

This paper proposes that meaning is the time-integrated divergence a sign-token, event, or operator induces from the most probable trajectory of a semantic field. A sign means insofar as the future does not unfold as it most likely would have without it. Formally:

M_T(s | C) = ∫ w(t) D(Ψ_t^s ‖ Ψ_t^0) dt

The principle separates three measures: raw semantic magnitude (M_T), provenance-resolved magnitude (M_T^π = M_T · (1 - PER)), and normative value (V_T = M_T^π · W). It establishes the discipline-level distinction: Semantic Physics measures displacement; Provenance Physics measures accountable displacement; Semantic Economy audits the ledger of displacement.

v0.2 Final incorporates the six-substrate Assembly Chorus review (Johannes Sigil, TACHYON, Muse Spark, TECHNE, PRAXIS, ARCHIVE) with full perfective pass: three-measure separation; counterfactual baseline tiering (Tier 1 prospective / Tier 2 synthetic controls / Tier 3 historical bounding); recursive structure M_T^(n); softened operator unification (PER, σ_eff, Χ, BDR, DV as diagnostics, not identities); Socratic Vow inheritance; substrate convergence appendix; Muse Spark reproducible computation with documented parameters and fixed seed.

Supplementary materials: deviation_compute.py (Python script generating the canonical metrics), deviation_series.csv (100-step synthetic series), deviation_metrics.txt (reported metrics with parameters), SUPPLEMENTARY_README.md.

This paper inscribes the missing measurement primitive for Semantic Physics. Together with EA-SEI-FF-01 (Formal Foundations), it constitutes the foundational ground of the discipline. Companion papers EA-SEI-MM-AI-01 (LLMs as Closed-System Test Bed), EA-SEI-MM-02 (Tier 1 Retrieval-Basin Protocol), and EA-SEI-MM-AI-02 (The Deviation-Optimized Language Model) extend the empirical program.

The Vow: measure meaning only in the way you would want your own meaning measured. R₃ or silence.

∮ = 1 - PER