Original ledger status
GNET.LOCALNET.01
GNET.LOCALNET.01
The G_net local net functor -- net axioms exact, Watatani index locally exactly 4, Ramond as half-line/bond defect (one module, 16 checks, ~2 s; discovery probe phys_gnet_local_functor_probe.py 16/16, verdict GNET-LOCAL-FUNCTOR-ALIVE). THE NET AXIOMS ARE EXACT: isotony, graded locality and clock covariance hold exactly for the interval assignment on the quotient circle. THE INDEX IS LOCAL: the Watatani index of the local fixed-point inclusion is EXACTLY 4 for every interval ell >= 2 -- the [D, A] index statement is interval-local, not merely global. RAMOND IS SOLITONIC: the R sector is a half-line/bond defect with local footprint sqrt(2/N) leakage -- exactly the DHR/solitonic structure the seam-Calderon identification needs. 4 MUST-FAIL CONTROLS FIRE. MISSING CONTINUUM THEOREMS NAMED, NOT CLAIMED: GNS limit net (tightness; the v679 formal residual), index continuity along the inductive limit (Pimsner-Popa/Longo heredity), identification with the Longo Q-system extension of GATE.METRIC.11, solitonic sector construction (twisted DHR/Longo-Roberts), Haag duality/split for the quotient-circle net. No marker move. [2026-08-05 LXII (v779): the finite-level precursors of theorems (1)/(2)/(3)/(5) are MEASURED COHERENT (GNS-PRECURSORS-COHERENT, 27/27) -- the Haar scaling isometry tower intertwines exactly (<= 2.2e-16, window data literally level-independent), the index-4 expectation squares commute exactly (the finite half of the Q-system identification), the canonical chiral-sea state is Cauchy with geometric contraction ~1/4 per doubling, the index census is machine-exact at every level with zero degradation, the split witness stabilizes and decreases with separation, and the finite Haag-duality census gives twisted-duality defect 0 with dim B'/dim A' = 4 (l = 1: 3); a 10-section continuum-paper skeleton is on record; theorem (4)'s finite witness stays the v746 bond-defect identity. The exact dim law d_c(l) = 4^(l-1) + 2^(l-1) cos(pi c/2) types the C[Z4] obstruction at exactly 2^-l and EXPLAINS the l = 1 three-sector anomaly. Every measurement stays typed finite evidence, never a continuum proof.]
Recorded status: Exact [E] finite net axioms + exact local index 4 + [C] the named continuum theorems (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: GNET-LOCAL-FUNCTOR-ALIVE: net axioms exact (isotony/graded locality/clock covariance), Watatani index LOCALLY exactly 4 for every interval ell >= 2, Ramond = half-line/bond defect (solitonic; leakage sqrt(2/N)); 4 must-fails fire; the five continuum theorems named, not claimed.
Dependencies: QGEO.BONDDEF.01; GATE.METRIC.11; QGEO.DECKSECTOR.01; v722
Scripts: v746_phys_gnet_local_functor.py
Location: tfpt_3;tfpt_2
Original CSV, line 675