nucleation

CLAIM-161: A system persists as the same self over an interval when a coherence measure is approximately conserved along its own trajectory, not merely matched by some map between its states

2 min read

Properties8
StatusProposed
Version2
Rolethesis
Warrantinterpretive
Tagspersonhood, self, complex-systems
Linedistributed-agency
ComplementsCLAIM-287 — What persists when a self persists through inactivity is the capacity to reinstate an organization, not its continuous running, and continuity of that kind can branch and merge, so it is not an identity relation, CLAIM-329 — A collective that replaces all its members persists, when it does, by causal transmission of the organization that produces it, not by resemblance: an organization of the same kind that arises independently is not its continuation, and a lapse in its coherence need not end it
UsesTERM-046 — notation for the threshold, drive and unity criteria, TERM-045 — self, and which sense

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The claim

From MOM-CLM-153. The condition “there exists φ with γ(S) ≈ γ(φ(S))” holds of my system at noon and yours at midnight, so it is no condition. Replace “some φ” with the system’s own evolution: γ(Φ_Δt(S(t))) ≈ γ(S(t)) for Δt in the interval of interest. The self (TERM-045) is then the region of state space on which γ stays level. The defect, sup over Δt of |γ(Φ_Δt(s)) − γ(s)|, is measurable (notation as in TERM-046).

Why this record files it, and why Proposed

It gives the person across time (the reluctant writer’s afternoons, CASE-013; the child and adult reader, CASE-048) a test that can fail. That is what this record’s diachronic material lacked. It also matches the corporate case’s drift and cadence (CASE-050): a firm whose coherence decays between events conserves γ only over short windows. That bearing is this record’s.

It stays Proposed because everything rests on γ, and MOM’s source defines γ elsewhere as a representational alignment score, not as a dynamical quantity. Until γ is fixed, the claim says what form a persistence criterion must take, not which one is right.

What it does not say

  • That a conserved γ is sufficient for being a self. It is a persistence condition, in the sense ADR-024 keeps apart from being a subject.
  • Which γ. Different choices give different selves. CLAIM-152’s target-relativity applies.
  • Over what window, and with what tolerance. If γ is an information quantity, its value averaged over an interval and its value at a moment can disagree in sign (THEORY-268, LIT-953, NOTE-756). “Approximately conserved” then needs a window and a tolerance for negative local values that average out. That is this record’s application, not the paper’s claim.

Note of 2026-10-30: what holds it back

Kept Proposed by the eighteenth status review. γ is unspecified, as the body says (QUESTION-043), and the second disjunct of the defeat condition is met as written by any constant γ, under which every trajectory conserves it, so the condition can fail only once γ is fixed or constrained. CLAIM-287, Active, qualifies it for a trajectory with a gap, where what is conserved is a capacity to reinstate an organization and not a running quantity, and the title does not yet say so.

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