TFPT scientific source excerpt
Original repository path: verification/v1000_spin2_sk_witnesses.py
Original file SHA-256: 80e90cd79c3db8f4a0a5691c47392ec800536175e21c34264508d4a3b438342d
Inclusive original lines: 1-26
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000001 | """v1000 -- GRAV.SPIN2.EMERGENCE.01 + FTRANSFER.SK.RHO0.01
000002 | [O updates: quadratic Hamiltonian half executed; SK mechanism executed].
000003 | Provenance: experiments/tfpt-discovery/spin2_hamiltonian_lattice_probe.py
000004 | + sk_rho0_mechanism_probe.py (review wave 4, 2026-08-29).
000005 | 
000006 | THE POINT.  Two independent executed halves of two open contracts.
000007 | 
000008 |   GRAV.SPIN2.EMERGENCE.01 (quadratic Hamiltonian, lattice-fundamental):
000009 |   [E] positivity exact; 2 TT helicities at all 5852 nonzero momenta
000010 |       (N=6..12); omega = |q| with q_i = 2 sin(k_i/2); axis expansion
000011 |       omega = k - k^3/24 exact.  Spectrum {0 x8, q^2 x2, 1 x2}.
000012 |   Still [O]: spectral-action Hessian identification, nonlinear Ward,
000013 |       universal coupling.  Display stays [O].
000014 | 
000015 |   FTRANSFER.SK.RHO0.01 (finite SK / rho_0 mechanism):
000016 |   [N] KMS/FDT on the exact Bohr grid ~1e-17.
000017 |   [N] rho_0-dependence contrast ~3.5e-3 vs static ~1e-16.
000018 |   [C] saddle 5-fold degenerate; 3pi/5 unique in the chosen mu4 lift.
000019 |   Display stays [O]; no cosmological solve.
000020 | 
000021 | MUST-FAIL: mass term gaps TT; wrong-sign kinetic term gives 2 negative
000022 | directions; SK product-state contrast is O(1) relative to the KMS pulse.
000023 | 
000024 | HONEST SCOPE (firewall): quadratic free graviton on a periodic N^3
000025 | lattice; finite 96-dim 1+1D W[J] sector.  Neither contract closes.
000026 | Python-only / Wolfram mirror deferred.