Neural Hayflick Bound
The neural Hayflick bound (VI.D91) is the τ-categorical horizon at which the neural defect tower (VI.D88) exhausts its repair budget — the structural limit on cognitive lifespan. Per level, H_i = R_max(i) / r_i, the ratio of the Level-i repair budget (VI.D45) to the net Level-i defect accumulation rate. The overall cognitive Hayflick bound is H_neural = min(H_1, H_2, H_3, H_4) — the system fails at its weakest level. The geometric decay rate (1 − ι_τ)^n governs the baseline.
τ-Definition
The neural Hayflick bound (VI.D91) is the τ-categorical horizon at which the neural defect tower (VI.D88) exhausts its repair budget — the structural limit on cognitive lifespan. Per level, H_i = R_max(i) / r_i, the ratio of the Level-i repair budget (VI.D45) to the net Level-i defect accumulation rate. The overall cognitive Hayflick bound is H_neural = min(H_1, H_2, H_3, H_4) — the system fails at its weakest level. The geometric decay rate (1 − ι_τ)^n governs the baseline.
Categorical invariant. H_neural = min_{i∈{1,2,3,4}} R_max(i) / r_i, the level-wise quotient of repair-budget capacity over net accumulation rate, with the minimum across levels giving the system-level horizon. Specializes the universal repair-budget exhaustion proposition (VI.P16) to the neural τ³-computer.
Primary registry anchor:
VI.D91
τ-Derivation Chain
-
I.K0— Universe Postulate -
VI.D15— Life Sector -
VI.D45— Repair Budget — finite restoration capacity -
VI.P16— Repair Budget Exhaustion — universal Hayflick-type proposition -
VI.D52— Neural Architecture as τ³ Computer -
VI.D88— Neural Defect Tower — provides the four Δ_i -
VI.D91— Neural Hayflick Bound — H_i = R_max(i) / r_i; H_neural = min_i H_i -
VI.T54— Neurodegeneration as Hayflick Crossing — disease onset = first level to cross H_i
Empirical Correlate
Biomarker: Cognitive lifespan: median onset of mild cognitive impairment ~70–80 yrs in unaffected populations; early-onset disease (familial Alzheimer's APP/PSEN mutations, Huntington's CAG repeats) correlates with elevated r_1 → reduced H_1. Maximum recorded cognitive lifespan with intact function: ~110–115 yrs (super-centenarian neurology). Sleep-deprivation accelerates H_1 crossing per VI.P24.
Measurable range: Healthy population: H_neural typically governed by H_1 (molecular) or H_3 (circuit) depending on genotype. Familial early-onset Alzheimer's: H_1 reduced to ~40–55 yrs. Idiopathic Parkinson's: H_3 typically 60–80 yrs. Idiopathic ALS: H_3 (motor circuit) typically 50–70 yrs. Repair-budget delta from chronic short sleep: ~10–20% reduction in δR_1 per night skipped, compounding monotonically.
Observation method: Longitudinal cohort studies (Framingham, Rotterdam, ADNI) tracking biomarker trajectories vs. clinical onset. Genetic risk stratification (APOE-ε4, APP/PSEN, LRRK2, SNCA) correlating with predicted H_i. Twin studies isolating r_i contributions. Animal models with accelerated r_i (Aβ-overexpressing mice, PD α-synuclein lines) for cross-validation.
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel
- stereochemistry-dependent r_i: misfolding rates of L-amino-acid proteins set r_1
- L-handed receptor turnover sets r_2; dopaminergic neuron loss kinetics set r_3
Manuscript reference: manuscript-sources/book-06/part06/ch40-neural-systems.tex
Lean Coverage
Status: Planned