Original ledger status
QGEO.REDUCE.01
QGEO.REDUCE.01
DEEPER REDUCTION OF THE TWO OBLIGATIONS (an honest attempt at QGEO.MARKS.01 + QGEO.KERNEL.01; NEITHER is closed -- they are genuine constructive-geometry/AQFT statements, not finite computations -- but each finite/algebraic CORE is now closed [E] and each obligation is reduced to ONE sharper irreducible premise [O]): (1) MARKS FINITE CORE [E] -- given a genus-0 double with an order-4 clock rho (conjugate to z->iz, fixed points {0,infinity}) and sheet reflection tau, the parabolic marks are a generic rho-orbit {1,i,-1,-i}=mu4 (|mu4|=4=e1(a), NOT the fixed points), DISTINCT iff b1=(#marks)-1=3=N_fam (any collision drops b1 below N_fam, excluded by the family count), and tau:z->1/z gives tau.rho.tau=rho^{-1} and permutes the marks => <rho,tau>=D4 of order 8, faithful; so MARKS reduces from 'produce the whole marked D4 boundary' to the SINGLE topological/clock premise 'the seam double is genus-0 and the seam clock is an order-4 conformal automorphism whose marks form one orbit'. (2) KERNEL FINITE CORE [E] (dissolves the spectrum-vs-operator worry on the finite block) -- on the 3-dim H^1 character space the mu4 characters (weights (1,2,3) -> i,-1,-i) are DISTINCT, so by Schur a mu4-equivariant operator is forced DIAGONAL (commutant of distinct-eigenvalue U = diagonal algebra) and is COMPLETELY DETERMINED by its eigenvalue per character; hence two such operators with the same forced transfer spectrum {1,(2/3)^6,(1/3)^6} (v162) and the unique residue-normalised basis Phi (v177) are EQUAL as operators, not merely isospectral -- the 'C_Sigma=U^{-1}C_mu4 U vs same spectral list' distinction VANISHES on the multiplicity-free H^1 block; so KERNEL reduces from the full operator identity to the SINGLE full-operator-reduction premise 'the full seam Calderon DtN on L^2 reduces to this 3-dim gapped mu4-moving transfer block plus the fixed rank-8 Calderon polarisation K_Sigma' (principal symbol universally |k|, Lee-Uhlmann/v156; c=8 fixed point isolated, no relevant/marginal drift, v158). NET (honest): neither obligation closed; both sharpened to milder premises, finite cores [E]; the structural residual of the whole theory is exactly {the topological clock premise, the full-operator-reduction premise}
Recorded status: Deeper reduction [E] (finite cores) + [O] (the two sharper irreducible premises)
Dependencies, status detail and source
Canonical status: Deeper reduction [E]/[O]: MARKS + KERNEL finite cores closed; each reduced to one sharper premise (topological clock / full-operator reduction); neither obligation closed
Dependencies: QGEO.MARKS.01; QGEO.KERNEL.01; QGEO.TREE.01; v156_seam_net_construction.py; v158_fixed_point_stable.py; v162_seam_transport_identification.py; v177_seam_marking_kernel.py
Scripts: v178_marks_kernel_attempt.py
Location: tfpt_research_contracts
Original CSV, line 258