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

The Semantic Deviation Principle v0.2 Final is the founding measurement-primitive paper of the archive’s Measurement of Meaning series.

Its core sentence is:

> Meaning is the time-integrated divergence a sign-token, event, or operator induces from the most probable trajectory of a semantic field.

The paper distinguishes this from Shannon surprisal. Surprisal measures how improbable a sign is when it appears. Semantic deviation measures the durable change that follows from the sign’s introduction. A random string may be highly surprising while producing little sustained field deformation.

The operative distributional form compares:

• the probability distribution over future semantic states without the intervention;
• the distribution over future semantic states with the intervention;
• a declared divergence functional;
• a declared temporal weighting function and horizon.

Jensen–Shannon divergence is the default proposed for empirical use because it is symmetric, bounded, and finite under support mismatch. KL divergence and Wasserstein distance are retained for specified conditions.

The paper distinguishes normalized and accumulated forms:

• normalized weighting yields mean deformation intensity in the units of the divergence measure;
• unnormalized weighting yields accumulated divergence-over-time, such as bit-days or bit-years.

Three measures are separated:

1. Raw Semantic Magnitude measures how much the field changes. 2. Provenance-Resolved Semantic Magnitude multiplies raw magnitude by the surviving provenance share, 1 − PER, and asks how much of the deformation remains accountable to its source. 3. Normative Semantic Value adds a still-incomplete weighting term intended to distinguish commons-enriching from extractive deformation.

This separation corrects the earlier implication that provenance erasure returns the field to its original trajectory. The paper instead says that a copied or unattributed idea may continue to deform the field while becoming an orphaned deformation whose origin can no longer be resolved.

The counterfactual baseline is treated as the central methodological difficulty. Measurement is divided into:

• prospective interventions with recorded baselines;
• natural experiments and synthetic controls;
• historical approximations with explicit uncertainty.

The paper is a first ground, not a final theory. Domain-specific definitions of the semantic field, robust counterfactual construction, operationalization of the normative weight, and comparison among divergence functions remain research tasks.