Original ledger status
GATE.UWALL.05
(U_wall) FINAL leg-assignment test (honest result): (i) delta=1/2 resolvent reproduces lepton c=(16/7,4/3,7/6) exactly => Lambda=(0.475,1.107,0.917); (ii) Lambda_mu=1.107>1 RULES OUT amplitudes=unitary holonomy moduli (modulus bound); (iii) SUGGESTIVE: harmonic-frame |diag M~_0|=(0,1/2,1/2), the 1/2 = delta=1/2 => geometry supplies delta (point observation, genericity future); (iv) CLEAN NEGATIVE: (I-1/2 M~)^-1 != amplitude vector. VERDICT: amplitudes are the combinatorial delta=1/2 resolvent; holonomy supplies delta+leg not magnitude; c_u/c_d NOT obtained from holonomy alone (no fabrication)
Recorded status: Numerical (honest negative + suggestive link)
Dependencies, status detail and source
Canonical status: Numerical (honest negative + suggestive link)
Dependencies: GATE.UWALL.04; v20; v40
Scripts: v41_leg_assignment.py
Location: tfpt_research_contracts
Original CSV, line 65Original ledger status
GATE.UWALL.06
TORSION NORMAL FORM + THE DELTA = 1/2 THEOREM (executes the GATE.UWALL.05 'genericity future work'; the distinguished lepton transport value delta = 1/2 stops being a point observation): (1) FLATNESS = mu4 TORSION [I, symbolic generic M] - prod_k U^k M U^{-k} = (MU)^4 exactly, so the Z4-family flatness constraint of the (U_wall) bundle IS the torsion statement 'T = MU is a fourth root of unity': the mu_4 atom appears as the ORDER of the twisted cusp generator. (2) DELTA = 1/2 THEOREM [I, both directions]: on the involutive branch (T^2 = 1) T is a Hermitian reflection 2vv^dag - 1 and the cusp trace condition 2v^dag U^{-1}v = 1 splits exactly into |v1|^2 = 1/2 (real part) + |v2| = |v3| (imaginary part), forcing diag M = (0, i/2, -i/2) with spec M = {1, w, w^2} AUTOMATIC (unitary + tr 0 + det 1 => char poly lam^3 - 1): delta = |M_22| = 1/2 EXACTLY AND CONSTANTLY on the whole 2-parameter branch - the value v20 used by hand and v40/v41 observed at the explicit point is a mu4-torsion identity. (3) REFLECTION LEMMA [I]: the D4 reflection forces diag M = (r, z, zbar) with r real and Re z = -r/2 - the D4 diagonal freedom is ONE real parameter, delta = 1/2 <=> r = 0. (4) BRANCH CENSUS [N, seeded scipy sampling, Python-only]: the full D4-fixed flat cusp locus realises only tr(MU) in {1, -1}; the involutive branch has diagonal CONSTANT (0, 1/2, 1/2) to 1e-15 across all samples; the {1, i, -i} branch has d1 varying over [0, 1] and the explicit v33/v40 point sits in its d1 = 0 slice - the same delta value. (5) RESIDUE [P] (recorded): whether the anchor splitting type O(-2)+O(-1)^2 (Mehta-Seshadri side) forces the d1 = 0 slice or selects the involutive branch is the remaining question; delta = 1/2 itself is no longer open
Recorded status: Identity [I] (symbolic theorems) + Numerical [N] (branch census) + Physical [P] (residue)
Dependencies, status detail and source
Canonical status: Theorem: delta = 1/2 is a mu4-torsion identity on the involutive branch; flatness = (MU)^4 = 1 normal form; residue = bundle-side branch selection
Dependencies: GATE.UWALL.04; GATE.UWALL.05; FLAV.DELTA.01; v20; v30; v33
Scripts: v114_torsion_delta.py
Location: tfpt_research_contracts
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