SelfDesc over Code (not Carrier)
Identity in a SelfDesc system is determined by the ω-germ code plus the deformation class of its evaluator — not by the material carrier. A SelfDesc identity is invariant under any carrier replacement that preserves both code(D)[ω] and the evaluator deformation class [Eval_X], provided SelfDesc never breaks during the transition. The carrier is the vehicle; the code is the identity.
τ-Definition
Identity in a SelfDesc system is determined by the ω-germ code plus the deformation class of its evaluator — not by the material carrier. A SelfDesc identity is invariant under any carrier replacement that preserves both code(D)[ω] and the evaluator deformation class [Eval_X], provided SelfDesc never breaks during the transition. The carrier is the vehicle; the code is the identity.
Categorical invariant. Identity equivalence relation on SelfDesc triples (X, D, Eval_X) given by code(D)[ω] together with the continuous deformation class [Eval_X]; invariant under carrier replacement satisfying code-preservation, evaluator-deformation-equivalence, and continuous-SelfDesc constraints.
Primary registry anchor:
VI.D53
τ-Derivation Chain
-
I.K0— Universe Postulate -
VI.D15— Life Sector -
VI.D08— SelfDesc Predicate — the carrier reads its own distinction -
VI.D09— Internal Evaluator — the carrier-internal decoder -
VI.D12— DecodeHorizon — the ω-germ code as identity carrier -
VI.D53— SelfDesc Identity over Code — invariant under carrier replacement
Empirical Correlate
Biomarker: Cellular turnover with persistent identity: ~330 billion cells replaced per day in adult human; ~7-year full-body protein turnover; intestinal epithelium replaced every 3-5 days; red blood cells every ~120 days; neuron persistence with continuous protein/lipid replacement.
Measurable range: Self-continuity persists across complete material turnover within ~7-10 years for non-neural tissue; neurons retain DNA across the human lifespan but turn over essentially all proteins on a timescale of weeks-to-years; the ω-germ code (genome) is conserved with mutation rate ≈ 10⁻⁹ per base per replication.
Observation method: Pulse-chase isotope labelling (¹⁴C bomb-pulse for cell birth dating); ¹⁵N/¹³C protein turnover mass spec; clonal lineage tracing (Cre-lox, barcoded transposons); single-cell genome resequencing for ω-germ stability; transplantation studies.
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel
- ω-germ code preserved through carrier turnover (chirality-locked)
- evaluator deformation class continuous through replacement
- identity-as-code is chirality-channel-invariant
Manuscript reference: manuscript-sources/book-06/part06/ch42-ship-of-theseus.tex
Lean Coverage
Status: Planned