Law of Genealogical Non-Injectivity

Scope: Nodes at epistemic equilibrium in a content-addressed substrate.

Statement: For any node N with saturation = 1.0 and CAS-convergent output, the activation-weighted measure over all lineages in the preimage of N is uniform. Lineage is gauge choice. The CID certifies the present state. No present state certifies a unique history.

Boundary: Does not hold for unsaturated nodes. Does not license claims about the world the substrate models — only about relations between nodes. Does not assert universal non-injectivity of physical law.

Supported by:

1. CAS architecture: put() is defined on bytes, not paths (structural)

2. Saturation mechanism: optimizer prunes without lineage query (operational)

3. Compression-as-truth-convergence: convergence makes all paths witnesses to the same fact (theoretical, Joven 2026)

Implication for physics (open): If the forward map of physical law is non-injective at equilibrium, the arrow of time, symmetry breaking, and parameter constraints may follow from consistency requirements rather than initial conditions or fine-tuning. This is a research program, not a result. The substrate demonstrates the mechanism. The physics must be verified independently.

Testable from substrate: At high-saturation nodes, examine activation profiles of all lineages in the preimage. Uniform distribution confirms the law. Concentrated distribution is a finding requiring explanation.