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A mass shell admits the same product form.
The correspondence is exact inside a bounded special-relativistic parameterization. The physics is inherited and credited. Mapping the factors to seeing and doing is our interpretation, not a result of relativity.
The claim, exactly
For a massive timelike on-shell particle, define φ = (E + pc)/(mc²) and ν = (E − pc)/(mc²). Then the inherited mass-shell equation gives φ·ν = 1. Calling those factors seeing and doing is a separate wager.
The seam, undressed
One factorization, stated exactly.
Start with the special-relativistic mass shell for a massive particle and factor it:
Here w is rapidity along the selected boost direction. The normalized factors are reciprocal because the mass-shell relation makes their product one. This is inherited special-relativistic algebra [A]. It excludes the massless case, for which division by m is unavailable. No ethical or person-level conclusion follows from the factorization.
The dictionary
Word for word, the mapping.
Why the algebra matches
A declared hyperbolic parameterization.
The match occurs because both descriptions use positive reciprocal factors. Special relativity supplies them through rapidity and the factored mass shell. The Emergentism chart deliberately reuses that normalized product form. Reuse is a mathematical correspondence, not evidence that coherence, capability, persons, or institutions are relativistic particles.
The algebra is inherited and exact in scope. The seeing/doing interpretation is our wager.
Why this matters to you
A calibration, not a proof.
Finding a known algebraic form does not validate the framework or make its variable meanings non-arbitrary. It gives one precise comparison to audit. The open question is whether independently defined person-level variables predict anything beyond the chosen normalization; that remains unestablished and belongs in the trial record.
One more discipline, printed wherever it appears: the seam (φ·ν = 1 in the declared parameterization) is never the score (B = 2/(φ + ν) = sech w here) and never the finite-node law. Seam, score, and node remain distinct.
Live animation: rapidity rising, the clock-rate falling — real hyperbolic functions of one slider, drawn on a family of tori: horn at rest, spindle in motion, a sphere as the limit approached and never occupied. The relativity is computed first and painted onto the geometry; the torus rendering is an emblem of the algebra, not its derivation (its mouth is a cusp, not the light cone — 151_HORN_TORUS_SR_FORMAL_AUDIT_2026_07_20.md; the strong claim is in our graveyard, dated).
The passage. What the slider walks — horn, then spindle, then the sphere-limit it never reaches — is a story of its own, told at its tier: The Crossing · [I] emblem riding credited geometry.
Held against adversarial audit — see the trial record.
[A] mass-shell factorization inherited from special relativity · [I]/[C] seeing/doing mapping — interpretive and unvalidated