Original ledger status
SEAM.ATTRACTOR.01
SEAM.ATTRACTOR.01
Unique attractor: a gapped boundary transport selects ONE fixed point [I]/[L]. The boundary transport spectrum {1,(2/3)^6,(1/3)^6} has spectral gap Delta=-log(2/3)^6=6 log(3/2)=2.4328>0. By Perron-Frobenius a primitive gapped operator has a UNIQUE dominant eigenvector and iteration converges to it geometrically at rate lambda2/lambda1=(2/3)^6, independent of initial state (demonstrated: two different starts -> same fixed direction, cos=1). This is the dynamical-systems content of 'parameter-free via fixed point' - the realized state is an ATTRACTOR, not a tuning; the convergence rate is the SAME (2/3)^6 of flavor+horizon (v54). Coxeter rotation lives in |mu4|=4 invariant planes (exponents pair m+(30-m)=30); sum exps=120=|R+(E8)|; #roots=rank*h=240. Entropy reset = the gap: T^n/lambda1^n -> rank-1 projector (only boundary law survives). Cyclic-cosmology reading is [P], not included
Recorded status: Identity/Lie [I]/[L]
Dependencies, status detail and source
Canonical status: Identity/Lie [I]/[L]
Dependencies: SEAM.HORIZON.01; SEAM.CYCLE.01; v54; v55
Scripts: v56_unique_attractor.py
Location: origin_theory;tfpt_3
Original CSV, line 133