TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/RECOVERED-NATIVE-SOURCE-v486-run.txt
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Inclusive original lines: 1-8
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | v486  HYP.REWRITE.02: the full transfer spectrum from the unique lazy Z2-pair walk
000002 |   [PASS] UNIQUENESS [E]: the symmetric Z2-pair rule M(s,h) has survival spectrum {s+h, s-h}; demanding the PHYSICAL pair {2/3, 1/3} (v54/v221) forces UNIQUELY (stay, hop, leak) = (1/2, 1/6, 1/3) = (1/|Z2|, 1/(|Z2| N_fam), 1/N_fam) -- the lazy Z2-pair walk; atom form recorded (direction: spectrum -> rates)
000003 |   [PASS] SIX-HAND GENERATION [E]: over the order-6 = 2 N_fam = |R+(A3)| hand the rule generates EXACTLY the physical spectrum eig(B^6) = {64/729, 1/729} = {(2/3)^6, (1/3)^6}; decay gaps 6 ln(3/2) (the recovery gap, v76) and 6 ln 3 (the subdominant gap, now generator-full)
000004 |   [PASS] SUPERSESSION [E]: v327's uniform rule (1/3, 1/3) has spectrum {2/3, 0} -- the zero mode persists under every power, so NO iterate can produce the (1/3)^6 mode: the uniform rule stays the correct lambda_2 story (2/3 = |Z2|/N_fam from the arity) but is superseded as generator of the FULL spectrum
000005 |   [PASS] STOCHASTIC SANITY [E]: the lazy rule is sub-stochastic (rates >= 0; row sums {1, 2/3, 2/3}), symmetric on the pair (detailed balance), and keeps the absorbing democratic family attractor of v327/v317 (eigenvalue 1)
000006 |   [PASS] HONEST RESIDUAL [O]: the arity {|Z2|, N_fam} = {2, 3} stays the anchor input (as in v327); the lazy split (1/2, 1/6) vs uniform (1/3, 1/3) is SELECTED by the physical spectrum, not yet derived from a first principle -- named candidate: 'stay = 1/|Z2|' as the sheet-symmetric choice of the Z2 involution (recorded, not claimed)
000007 | --- v486 HYP.REWRITE.02: the FULL transfer spectrum {1,(2/3)^6,(1/3)^6} has one local generator -- the unique lazy Z2-pair walk (stay, hop, leak) = (1/2, 1/6, 1/3) = (1/|Z2|, 1/(|Z2| N_fam), 1/N_fam); over the order-6 hand eig(B^6) = {64/729, 1/729} exactly; the previously generator-less (1/3)^6 mode gets its origin (subdominant gap 6 ln 3); v327's uniform rule = degenerate {2/3, 0} case, superseded as full-spectrum generator; arity + split selection stay [O]: 5 passed, 0 failed ---
000008 |