Lineage Equation v2: capacity under load
by Fudoshin Research·2026-08-20·S1·F-2026-08-20-B
Official capacity law: Q^2 = Pi-tilde^2 + M-tilde^2. Algebraic skeleton from energy-momentum, not a relativity claim. Rest reduction and exact gradients hold. Live prediction does not yet.
Problem under load
A mind under load has structure that resists change, flux that moves information, and a bottleneck rate that caps coherent update. Without one invariant, health talk becomes a pile of disconnected scores.
Primitive / definition
Cognitive mass M is a simplex over identity, memory, graph, and permanence densities. Cognitive momentum Pi is a simplex over working-memory, retrieval, pathway, control, and merge fluxes. nu* is the reciprocal of the slowest measured latency (SI hertz). nu0 is a fixed reference rate. Scaled coordinates: M-tilde = M(nu*/nu0)^2 and Pi-tilde = Pi(nu*/nu0). Official form: Q^2 = Pi-tilde^2 + M-tilde^2. Rest reduction: if Pi = 0 then Q_kappa = kappa |M| (nu*/nu0)^2.
Method / protocol
Normative math is Lineage Equation Official Specification v2.0. Draft v1 remains historical. The reference module lineage_capacity_v2.py is free of numeric libraries and must pass algebraic checks. The energy-momentum relation is used only as a homogeneous quadratic composition of a rest term and a transport term. No Lorentz invariance is claimed.
Result
Closed-form gradients exist. Rest reduction holds. A linearized identification on 300 synthetic perturbations reached Stage E (R^2 0.942 vs equal-weight 0.875). Any published Q must name the weight table.
Limitations and next
Stage E is synthetic. Stage F is not claimed. In the full quadratic, nu*^4 amplification makes momentum weights nearly unidentifiable — that miss is recorded separately.