Original ledger status
SEAM.CFIN.KMSMIX.01
THE CHANNEL-MIXING CANDIDATE STATE (constructed 2026-08-09, round CXIII; promoted round CXV in v898): the v896 demand -- a channel-mixing state realizing the block Wick functor's value level -- now has a CONSTRUCTED CANDIDATE on the deployed 16-dim one-particle space. (1) THE KMS ROUTE: the C6-covariant mixing KMS state EXISTS -- K = i h with h = -(A16_dep + A_int/8) at beta = 1 (the FIRST point of the frozen grid) passes ALL gates: CAR strict (smax 0.668), exact C6 block covariance with the v896 forced zeros, all 15 duad cross-blocks at the frozen floor, the q*/sheet grading carried exactly (5/5 vacuum + 10/10 carrier FULL), all 15 block Wick monomials nonzero with the CANONICAL Pf4 sign pattern of G_c; ROBUST at beta = 2; the hermitian O16-commutant measured exactly (112 = 62 sym + 50 antisym; the mixing slice is the 33-dim v896 block space). (2) SEAM.CFIN.SCHURMIX.01 (EXACT sympy): boundary elimination of the coupled diagonal state A_full = [[kappa A_CC, t V], [-t V^T, m J3]] (kappa = m = 1/2, t = 1/20, validity proven exactly) gives A_eff = kappa A_CC + (t^2 m/(1-m^2)) V J3 V^T EXACTLY, and S = V J3 V^T GENERATES all 10 carrier duads (uniform 3J block, canonical Pf4 signs) from the BARE DIAGONAL state -- the SAME Schur/Feshbach elimination that creates the RH port creates the carrier mixing: on both fronts the real correlation lives in the ELIMINATED boundary. (3) THE FROZEN 15-SIGNATURE TABLE is the registered prediction any physical seam state realizing the block functor must reproduce. (4) RP typed honestly: NO spatial/OS theta is deployed on the 16-dim space; the Majorana real structure Theta_0 satisfies the v426/v440 dictionary automatically; the OS-positivity under a SPATIAL theta is the NAMED OPEN CHECK RP-THETA-OPEN. THE [O] PREMISE IS UNMOVED: candidate states + frozen signatures; whether the ACTUAL seam realizes any of them is untouched. No marker moves. RP NOTE (2026-08-10, rounds CXXIV/CXXXI-CXXXIII; promoted in v903): RP-THETA-OPEN is now MEASURED at family level and the answer is an EXCLUSION -- strict OS positivity under both deployable spatial reflections forces t = 0 (OS <=> a_J = 0 <=> the mixing floor falls: RP and the mixing floor are mutually exclusive on this family), the complete C6-twisted census is exclusionary (0/6), and the parent-dilation route yields only a MARGINAL cone-boundary witness (whose Schur compression carries the full mixing with the exact identity t^2 * 3m/(1-m^2) = 1/200) while the strict collar route is family-wide obstructed by an exact linear 2t law (SEAM.STATE.DERIVATION.01 / SEAM.CFIN.TWISTED.RP.01 / SEAM.CFIN.RP.DILATION.01, v903_seam_rp_exclusion.py); a measurement on the complete finite candidate set, not a universal no-go; the [O] premise stays unmoved.
Recorded status: Constructed candidate + exact generation identity [Numerical/Identity]: the mixing demand answered at candidate level; RP-THETA-OPEN measured exclusionary at family level (v903); the [O] premise unmoved
Dependencies, status detail and source
Canonical status: CONSTRUCTED: the C6-covariant mixing KMS state passes all block-functor gates; exact Schur generation of all 10 carrier duads; RP-THETA-OPEN measured exclusionary at family level (v903); [O] unmoved
Dependencies: SEAM.CFIN.WICKFUNCTOR.01; v888; v113; v426; v440
Scripts: v898_kms_schur_mixing.py
Location: tfpt_1;tfpt_research_contracts
Original CSV, line 727Original ledger status
SEAM.STATE.DERIVATION.01
THE RP/MODULAR CARVING OF THE SEAM STATE SPACE (measured 2026-08-10, round CXXIV; promoted in v903): on the v898 family the reflections and the modular route CARVE for the first time. (1) THE REFLECTION CENSUS: two spatial thetas are deployable on the 16-dim one-particle space (the sheet swap theta_S = the 16-dim lift of the v440 collar reflection, and the orientation-REVERSED 2-cycle theta_abT); the untwisted 2-cycle is NOT an OS reflection (Gram non-hermitian 0.924 already at t = 0); the v519 twist eta = +i is again FORCED. (2) THE INCOMPATIBILITY: the odd-sector Gram eigenvalues are EXACTLY +-|a_J| of the {4,5} duad (worst identity 2.2e-16) -- OS positivity <=> a_J = 0 <=> the v898 gate G3 (all 15 blocks at the floor) FALLS: reflection positivity and the block-functor mixing floor are MUTUALLY EXCLUSIVE on this family; strict RP forces t = 0 under BOTH reflections (t = 0 marginal PSD); u >= t is FORCED with u_c = t exact in the deployed region (SPEC-v2 amendment disclosed fail-first: the corner (t=1/4, beta=4) gives u_c = 0.3627 > t, law re-typed u_c >= t) -- u = 0 is RP-EXCLUDED, correcting the round-57 'u unforced' reading. (3) THE STRUCTURE OBJECT: det(A16_dep + t A_int) = (t-1)^2 (3t^2-1)^2 (9t^3+21t^2-t-1)^2 EXACT (sympy); the three positive roots organize everything measured (1p RP boundary = t/u = 1; hermitized boundary t_c(beta) -> t_gap; the ground-state modular transition at the SAME root); NO root is 1/8 -- the deployed value stays UNPINNED by state demands. (4) THE MODULAR ROUTE: D(0, beta) = |beta - 2pi|/(2pi) exact (ward 1.1e-16); the 2pi-KMS locus of the boundary reduction is EXACTLY the point (t = 0, beta = 2pi) -- the geometric temperature KILLS the mixing instead of pinning it; off-axis EMPTY. (5) THE THERMAL CURVE: order-parameter peak at beta = 1.6730 +- 5e-4 (round-57 'peak at beta = 2' corrected: coarse-grid argmax); distinguished-point census at 0.5 percent: NO HIT (DISTINGUISHED-ABSENT, typed as a reading census). The v898 [O] premise unmoved. NO RH claim. UPDATED 2026-08-27 (v972): the exclusivity is TYPED RAY- and REFLECTION-relative -- the v903 statement concerns the v898 RAY (all 33 covariant coordinates moving together), not the slice: the full 33-dim census (SEAM.STATE.RPMIXING.01) shows theta_abT kills exactly ONE coordinate (a_J, kernel value -1/(1+c^2) = -0.8240271368 at c = tanh(1/2)), leaving a 32-dim marginal RP hyperplane, and theta_S leaves a 17-dim first-order-neutral subspace with strict finite-s witnesses. The v903 anchor is reproduced exactly (odd Gram eigenvalues +-|a_J|, a_J = +0.04068013); the carving itself is UNMOVED.
Recorded status: Measured carving [Numerical/Identity]: RP and mixing mutually exclusive; u >= t forced; the modular locus is one point; no marker move
Dependencies, status detail and source
Canonical status: MEASURED: strict RP forces t = 0 (mixing and RP mutually exclusive); u >= t forced; 2pi-KMS locus = (t=0 beta=2pi); no root is 1/8
Dependencies: SEAM.CFIN.KMSMIX.01; SEAM.CFIN.WICKFUNCTOR.01; v898; v440; v519; v526
Scripts: v903_seam_rp_exclusion.py
Location: tfpt_1;tfpt_research_contracts
Original CSV, line 728Original ledger status
SEAM.CFIN.MIXING.NORMALIZATION.01
DEAD READING (negative result, first-class; measured 2026-08-10, round CXVI; promoted in v903): 'THE MIXING STRENGTH t = 1/8 = 2pi c3/|Z2| IS A COMPILER VALUE' IS A DECORATION, NOT A DERIVATION -- the seat audit is clean (the chain beta-angle x c3/|Z2| = 2pi x (1/(8pi))/2 = 1/8 is EXACT and via v813 equivalent to 1/(I_Jones |Z2|); c3 = P1 axiom, the angle 2pi MEASURED (v526/v519/v239), |Z2| = 2 deployed (v53/v456/v44)) but the COMBINATION IS FREE: no vN module composes the three factors into a mixing strength, and the decisive scan shows ALL 55 t values pass ALL frozen v898 gates (grid 0.01-0.50 + the exact rationals + decades; CAR strictness is a THEOREM tanh < 1, the apparent onset is float64 saturation, MARGIN-ARTIFACT typed) -- the allowed set is mathematically (0, infinity), u in {0,...,2} (incl. u = 0) and beta in {1/2,...,4} pass too: the v898 gates force NOTHING about (u, t, beta) beyond t > 0. PIN-ABSENT: no frozen functional distinguishes 1/8 (uniformity/entropy argmax at 0.005, support/vacuum-mass argmin at 0.207, 1-crossing at 1.091); the anti-numerology census finds 4 equally-cheap deployed-constant readings of 1/8 -- the arithmetic is cheap, content could only live in seats + a future pinning demand. THE NEW STRUCTURE FACT kept: the channel mixing is THERMAL (mass peaks near beta = 2 and DIES to the ground state, 0/15 cross-blocks at beta = 100 -- the beta -> infinity limit returns to SEAM-DIAGONAL). HONEST UPDATE (same round family): SEAM.STATE.DERIVATION.01 subsequently measured u >= t as the FIRST non-decorative normalization demand -- the reading stays a registered decoration with typed seats. Zero RH content.
Recorded status: Dead reading registered [Numerical] (negative result): the t = 1/8 reading is a decoration -- allowed set unbounded and pin absent; no marker move
Dependencies, status detail and source
Canonical status: NEGATIVE: t = 1/8 is a decoration (55/55 t pass all frozen v898 gates; allowed set (0 infinity); PIN-ABSENT); thermal mixing kept as structure fact
Dependencies: AX.P1.01; SEAM.CFIN.KMSMIX.01; v813; v526; v898
Scripts: v903_seam_rp_exclusion.py
Location: tfpt_research_contracts
Original CSV, line 729Original ledger status
SEAM.CFIN.MINIMAL.MEDIATOR.01
DEAD READING (negative result, first-class; measured 2026-08-10, round CXVII; promoted in v903): 'N_fam = 3 IS THE MINIMAL BOUNDARY-MEDIATION RANK' IS REFUTED at theorem grade for this finite size (a census/sign-level theorem, not a search negative). PREMISES SHARPENED: O16 is EXACTLY the identity on the A3 boundary -- C6 covariance constrains only the COUPLING (24-dim, orbit-repeated 2x6 blocks, projector ward + symbolic both ways); the expected orbit-count obstruction against r < 3 CANNOT exist. THE STRUCTURE THEOREM (39 symbols, exact sympy): under covariant coupling the 10 carrier blocks of S' = V M V^T take exactly THREE values -- the full requirement (10/10 populated, canonical Pf4 signs, CAR-scalable) reduces to (gamma_ab != 0, gamma_cde != 0, det B_x > 0). RANK-1 EXHAUSTION AS A THEOREM: det(B_x) = gamma_ab gamma_cde symbolically for EVERY symplectic-rank-1 mediator, so the ONLY rank-1 obstruction is the sign law gamma_ab gamma_cde <= 0; the explicit integer witness J(+)0(+)0 with the deployed coupling passes the requirement COMPLETELY (10/10, 0 wrong signs); seeded census 2000/2000 agrees; exhaustion r in {0, 1, 2, 3} complete, only r = 0 fails. PREMISE CORRECTION: rank(V J3 V^T) = 2 EXACTLY and S = 1_5 (x) 3J EXACTLY -- the coupling fold collapses the deployed 3-level mediator to ONE effective carrier level ('<= 3' was true but empty). WHAT 3 REALLY PINS (measured): boundary NON-DEGENERACY -- pure boundary ground state <=> matrix rank 6 <=> symplectic rank 3 = N_fam, honestly typed as DIMENSION BOOKKEEPING (dim(A3) = 6 = |Z2| N_fam), not a mediation theorem: the mediation demands are already met at rank 1. Controls: rank 0 dead 10/10; covariance break reaches provably-unreachable signs; the fold-cancel rank-4 mediator is dead 10/10 (mediation capacity is NOT rank-monotone). Zero RH content.
Recorded status: Dead reading registered [Identity/Numerical] (negative result): rank 1 suffices -- the minimal-mediation reading of N_fam = 3 is refuted; purity pins 3 as dimension bookkeeping; no marker move
Dependencies, status detail and source
Canonical status: NEGATIVE: N_fam = 3 as minimal mediation rank REFUTED (rank 1 suffices by exact sign law + integer witness; deployed S rank 2 exactly); purity = dimension bookkeeping
Dependencies: SEAM.CFIN.KMSMIX.01; SEAM.CFIN.WICKFUNCTOR.01; v898
Scripts: v903_seam_rp_exclusion.py
Location: tfpt_research_contracts
Original CSV, line 730Original ledger status
SEAM.CFIN.TWISTED.RP.01
THE COMPLETE TWISTED-OS CENSUS IS EXCLUSIONARY (measured 2026-08-10, round CXXXI; promoted in v903): the COMPLETE census of C6-twisted reflections Theta_g = U_g o theta (2 bases x 6 C6 powers x 4 degree twists = 48 candidates) admits EXACTLY 16 involutions (Theta^2 = 1 <=> 3 | k, eta-independent; the law q^2 = img^{2k} verified indexwise -- the 3-cycle of pi forces k in {0, 3}), of which 6 are Gram-hermitian at the bare point (eta = +-i for (S,0), (S,3), (abT,0)), and ZERO of 6 admit strict RP at ANY t > 0: no selection -- TWISTED-RP-EXCLUSIONARY; the g^3 transport twist of the sheet swap is not a rescue but a NEW obstruction (its 1p Gram is indefinite already at t = 0, lam_min = -0.4621 for BOTH eta signs -- the twist degenerates the eta sign). The enumeration is provably complete at finite size (C6 = <g>, generator pin re-verified; the U_g = O16^k are exact symmetries of every scanned KMS state at 1.1e-15); the scalar character axis collapses measured (chi = -1 negates the Gram, chi = i breaks hermiticity); eta = -i flips the 1p Gram exactly against +i -- at most ONE eta sign per side-exchanging candidate can carry strict positivity, and at the marginal abT bare point both pass and both fall for every t > 0. SMOKE CORRECTIONS disclosed fail-first (the expected within-side mechanism for the side-fixing (abT, k=3) does NOT exist -- hermiticity-dead at the bare point for every eta; lam_max 0.4973 < the expected 0.5 bar). RP and the v898 mixing floor remain mutually exclusive under EVERY C6-compatible involutive twist -- a MEASUREMENT on this complete finite candidate set, no universal no-go. Zero RH content; the [O] premise unmoved.
Recorded status: Measured complete census [Numerical] (negative result): 0 of 6 admissible twisted reflections admit strict RP at t > 0; no marker move
Dependencies, status detail and source
Canonical status: MEASURED: twisted census 16/48 involutive and 6 admissible; 0/6 with strict RP at t > 0 (TWISTED-RP-EXCLUSIONARY); exclusion survives every C6 twist
Dependencies: SEAM.STATE.DERIVATION.01; SEAM.CFIN.KMSMIX.01; v898; v519
Scripts: v903_seam_rp_exclusion.py
Location: tfpt_research_contracts
Original CSV, line 731Original ledger status
SEAM.CFIN.RP.DILATION.01
THE DILATION ROUTE SPLITS (measured 2026-08-10, round CXXXII; promoted in v903): on the explicit C6-covariant parent family over the v898 split 16 = 10 (+) 6 the dilation mechanism is REALIZED for the 2-cycle reflection -- every one of the 28 CAR-valid s = 0 points is theta_abT-MARGINAL RP (parent a_J = 0, 1p Gram eigenvalues EXACTLY {0, 0}: the cone boundary), and the Schur compression of the v898 M2 parent (kappa = m = 1/2, t = 1/20) carries the FULL Pfaffian mixing (10/10 carrier duads, uniform J block = the round-51/52 FLOOR as the EXACT rational identity t^2 * 3m/(1 - m^2) = 1/200, canonical Pf4 signs) while the effective carrier RP falls exactly by the +-|a_J| law (a_J = 1/200): parent RP above and effective RP failure below COEXIST -- the round-58 incompatibility is pushed one level up, not resolved; BUT the STRICT collar sheet swap is family-wide obstructed: 0/78 CAR-valid lattice points pass strict theta_S RP, and at the M2 parent the obstruction is EXACT -- 30 defect entries, ALL of magnitude 2t = 1/10, ALL on (empty monomial <-> mixed carrier-boundary pair) positions: a linear coupling law, not noise. The witness is end-to-end EXACT rational arithmetic (symbolic Schur identity in all 5 parameters, PD/PSD by exact LDL pivots); the parent KMS typing binds exactly via CAR strictness (the -2 artanh spectral map; the disclosed smoke correction: the first draft used arctan and was killed by the roundtrip ward); orbit selectivity measured (W1-only mixes exactly 1/10, W2-only exactly 3/10, full mixing needs BOTH orbits); the compression lives on the uniform J ray, NOT the A_int ray of the KMS family (the FLOOR value is hit, the covariant DIRECTION differs -- typed, not hidden). The marginal witness sits ON the RP cone boundary (not strict); the strict-collar obstruction is family-level (no universal no-go); the v898 [O] premise stays [O]. Zero RH content.
Recorded status: Measured split [Numerical/Identity]: a marginal cone-boundary witness with the exact 1/200 floor; the strict collar route obstructed by an exact linear law; no marker move
Dependencies, status detail and source
Canonical status: MEASURED: DILATION-SPLIT -- marginal theta_abT witness on the cone boundary; t^2*3m/(1-m^2) = 1/200 exact; strict collar obstructed (defect magnitude 2t)
Dependencies: SEAM.STATE.DERIVATION.01; SEAM.CFIN.TWISTED.RP.01; SEAM.CFIN.KMSMIX.01; v898
Scripts: v903_seam_rp_exclusion.py
Location: tfpt_research_contracts
Original CSV, line 732Original ledger status
SEAM.CFIN.GAP.PENCIL.01
t_gap IS THEOREM-SHAPED (measured 2026-08-10, round CXXXIII; promoted in v903): t_gap = 0.2309488708... is the UNIQUE positive root of the irreducible cubic q(t) = 9t^3 + 21t^2 - t - 1 (exact Sturm count: 1 on (0, infinity) and 1 on (0, 1/4] -- the root is interior to the deployed region), which divides the EXACT Pfaffian of the FIXED integer pencil: Pf(A_dep + t A_int) = -(t-1)(3t^2-1) q(t) EXACTLY (degree <= 8 identity certified at 9 rational points by exact Fraction-Pfaffian recursion; sign fixed by Pf(A_dep) = +1 at t = 0) -- t_gap is a finite GENERALIZED EIGENVALUE of (A_dep, A_int) with kernel dimension EXACTLY 2 (exact argument: q squarefree => det vanishes to order exactly 2; antisymmetric => even rank) and minimal polynomial q of degree 3; the pencil is strictly-singular typed (deg det = 12 < 16). THE THREE KNOWN CRITICAL SURFACES ARE PROJECTIONS OF ONE VARIETY: (1) the 1p gap closes at t_gap (2.6e-17) and NOWHERE else in (0, 1/4]; (2) the beta -> infinity ground state jumps there by EXACTLY a rank-2 occupation flip (||Delta||_F = 2 sqrt(2), persistent to delta = 1e-5; exact sign flip q(23/100) < 0 < q(6/25)); (3) the hermitized RP boundary t_c(beta) climbs monotonically to the pencil root (t_c(1) = 0.2205 measurably BELOW with gap 1.04e-2; t_c(30), t_c(60) coincide with t_gap below float resolution 1.4e-15 -- a LIMIT statement, typed). INVARIANCE in strongest form: the C6 lift O16 fixes BOTH pencil members ENTRYWISE (exact integer); gauge congruences preserve det P(t) identically; scaling covariance exact. THE COUPLING IS LOAD-BEARING: zeroing the carrier-boundary coupling or perturbing coupling wires kills t_gap as a root (exact polynomial remainder mod q != 0, 3/3 seeded draws). SMOKE CORRECTIONS disclosed fail-first (the Pfaffian sign first guess +1 killed by the t = 0 evaluation; the strict-below gate at beta = 30 not float-resolvable, typed as a limit statement). t_gap remains a property of THIS integer pencil; the RP boundary meets the root only in the beta -> infinity limit. Zero RH content; no marker moves.
Recorded status: Measured exact pencil identity [Identity/Numerical]: t_gap as a generalized eigenvalue with Sturm uniqueness; three surfaces one variety; no marker move
Dependencies, status detail and source
Canonical status: MEASURED: Pf(A_dep + t A_int) = -(t-1)(3t^2-1)(9t^3+21t^2-t-1) exact; t_gap unique in (0 1/4] (Sturm); kernel dim exactly 2; coupling load-bearing
Dependencies: SEAM.STATE.DERIVATION.01; SEAM.CFIN.RP.DILATION.01; v898
Scripts: v903_seam_rp_exclusion.py
Location: tfpt_research_contracts
Original CSV, line 733Original ledger status
SEAM.CFIN.MARGINAL.STABILITY.01
STRICT 2-CYCLE RP IS IMPOSSIBLE ON THE WHOLE COVARIANT CLASS (measured 2026-08-10, round CXXXVIII(60); promoted in v908): the closure-vs-isolated dilemma of the v903 marginal witness is REFUTED AS A DILEMMA -- the theta_abT sector Grams see ONLY the channel-{4,5} 4x4 seat (ward 1e-14), covariance allows there EXACTLY the J coordinate (integer defect 2 for I/X/Z units, 0 for J; c4 = c5 forced), and the exact symbolic seat law M1 = [[aJ+aX, aI-aZ],[aI+aZ, -aJ+aX]] reduces covariantly to M1 = diag(a_J, -a_J) with det M2 = -a_J^2: strict theta_abT RP is IMPOSSIBLE on the WHOLE covariant class (the RP set = {a_J = 0} = the cone boundary, interior EMPTY); the marginal witness is NOT a limit of covariant strict equilibria (there are none) and NOT isolated (the whole s = 0 family is a positive-dimensional MARGINAL STRATUM: margin exactly 0 on all 16 CAR-valid lattice points at full 10/10 canonical mixing); the decisive scalar sup(RP-margin x mixing) = 0 EXACT. THE KERNEL ANATOMY (exact rational arithmetic): at the M2 parent the 1p Gram is IDENTICALLY 0 and the deg-2 Gram is exactly [[1, i/2], [-i/2, 1/4]] with eigenvalues {0, 5/4} -- the vacuum bound to the a-pair; both kernels forced by the SAME pure-J covariance law whose only visible coordinate a_J is exactly the strict-route obstruction. THE TRANSVERSAL ESCAPE + ITS EXACT PRICE: the ONLY hermiticity-preserving strict-enabling seat direction is the covariance-BREAKING X coordinate: at every eps > 0 the parent is STRICTLY RP (1p eigenvalues {eps, eps} exact, deg-2 det = eps^2 exact), covariance defect EXACTLY 2 eps (linear price law), mixing 10/10 with the J coordinate 1/200 UNCHANGED, margin exponent 2.000 -- TRANSVERSAL. FLOOR-EXCHANGE (the sharpest exact object): Pf4_{45}(eps) = (eps - 1/200)(eps + 1/200) and the effective 2-cycle odd Gram is diag(eps + 1/200, eps - 1/200) EXACTLY -- the canonical sign gate IS the negative effective RP margin (the same polynomial factor): one level down the exclusion survives the transversal escape, with the crossover EXACTLY at the 1/200 floor. SPEC v2 with ONE disclosed amendment (fail-first preserved: the v1 gate 'all 18 s=0 points CAR-valid' fell at the two m = 3/4 corners; v2 reads the 16 CAR-valid points, the marginality held on all 18). Reading typed: 'physical as a limit of equilibria' is unrealizable within the symmetry class -- strict 2-cycle RP needs symmetry breaking (price 2 eps) or a different reflection. Controls: the I direction violates RP for BOTH signs, Z breaks 1p hermiticity, the 1/200 identity regresses rationally, 3/3 seeded scrambles break the covariance ward. The v898/v903 [O] premise stays [O]. Zero RH content.
Recorded status: Measured covariant exclusion [Identity/Numerical]: interior empty (exact +-a_J law), floor exchange Pf4 = (eps - 1/200)(eps + 1/200); escape only by symmetry breaking at price 2 eps; no marker move
Dependencies, status detail and source
Canonical status: MEASURED: strict 2-cycle RP impossible on the whole covariant class (M1 = diag(a_J, -a_J) exact); the s = 0 stratum is marginal not isolated; Pf4(eps) = (eps - 1/200)(eps + 1/200) -- crossover at the 1/200 floor
Dependencies: SEAM.STATE.DERIVATION.01; SEAM.CFIN.RP.DILATION.01; SEAM.CFIN.KMSMIX.01; v898; v903
Scripts: v908_seam_equilibrium_wiring.py
Location: tfpt_1;tfpt_research_contracts
Original CSV, line 734Original ledger status
SEAM.CFIN.NESS.PARENT.01
NO NESS NEEDED -- THE PRICE OF THE MIXING IS EXACTLY ZERO ENTROPY PRODUCTION (demand closed as NOT-NEEDED; measured 2026-08-10, round CXXXIX(60); promoted in v908): strict theta_S (collar) hermiticity is a TWO-SEAT LINEAR LAW of the coupling -- the 1p seat A_{x+1,y} + A_{x,y+1} kills the X-, the deg-2 empty seat A_{x,y} + A_{x+1,y+1} the I-subblock coordinates; exact rank 12, kernel 12 = the {J, Z} coordinates of the 24-dim covariant coupling space = the v898 T-count. THE DEPLOYED SEAM WIRING V = A_int[C, B] IS PURE-I (every 2x2 subblock exactly -I2) = a MAXIMALLY obstructed covariant direction -- explaining the v903 strict-collar law ('30 entries, magnitude 2t') EXACTLY as 15 mixed pairs x 2 Gram positions. THE KERNEL CONTAINS EQUILIBRIUM WITNESSES: the uniform J-coupling parent V_J (kappa = m = 1/2, t = 1/20) passes strict theta_S RP in EXACT arithmetic (Grams exactly hermitian, PD by exact LDL; float lam_min 0.3064/0.1532) while its Schur compression carries the FULL canonical Pfaffian mixing -- S_J = V_J J3 V_J^T = 3J on ALL 25 channel blocks (integer identity), J coordinate EXACTLY t^2 3m/(1 - m^2) = 1/200 = the same rational floor identity as the v903 witness, Pf4 canonical 10/10; V_Z is a SECOND witness (S_Z = -3J, J coordinate -1/200). THE NESS SIDE HONEST (FINITE-NESS-NOGO): at finite size every exactly stationary quasi-free state has [h, A] = 0 => ALL block currents Phi_r = (1/4) tr(h0_r [h, A]) = 0 => sigma = beta_C Phi_C + beta_B Phi_B == 0 (exact; energy ward 7e-18) -- 'NESS with positive entropy production' is category-inapplicable; the weakest meaningful positivity = RP of the stationary covariance, EXACTLY what is tested; the two-temperature Cesaro states (frozen grid) are exactly stationary (3e-16), covariant, CAR-valid, with vanishing t = 0 product currents. THE PRICE CURVE IS FLAT-OPEN: the 15/15 canonical block census is open at EVERY drive point INCLUDING zero drive, the theta_S hermiticity defect stays PINNED (0.0982) and the PSD margin degrades monotonically -- the minimal entropy production at which the mixing gates open is EXACTLY ZERO: DRIVE BUYS NO RP, NESS-NOT-FORCED -- the demand closes as NOT-NEEDED. Kernel membership is NECESSARY, not sufficient: J/Z mixtures pass hermiticity + PD but break the canonical sign census (4/10) -- the canonical gate selects the uniform J (or Z) ray; orbit selectivity reproduced (single boundary pair: both orbits 10/10 with J coordinate exactly lambda t^2 = 1/600). THE REGISTERED NEXT CONTRACT: SEAM.STATE.WIRING.SELECTOR.01 -- is PURE-I compiler-forced? The deployed IOTA wiring comes from the vacuum-orbit construction of A_int; whether the orbit/edge rules admit a {J, Z}-kernel alternative at equal C6 covariance and equal Pf pencil is exactly answerable -- only then is it decidable whether the strict-collar obstruction is a compiler theorem or a deployment choice. The witnesses live on a DIFFERENT covariant coupling direction than the deployed A_int wiring -- whether the actual seam allows them is untouched; the v898/v903 [O] premise stays [O]. Controls: global-KMS regression reproduces the round-58/59 equilibrium obstruction (defect 0.0982); 3/3 seeded permutations break covariance + canonical census; PURE-I regression (0.1, 30 entries); the I-orbit switch-on fires WITHIN the covariant class. Zero RH content.
Recorded status: Demand closed NOT-NEEDED [Identity/Numerical]: equilibrium J/Z witnesses carry the full 1/200 mixing at zero entropy production; the deployed wiring is PURE-I (maximally obstructed); wiring-selector contract registered; no marker move
Dependencies, status detail and source
Canonical status: CLOSED (NOT-NEEDED): stationary => sigma == 0 exactly and drive buys no RP; V_J/V_Z equilibrium witnesses with J coordinate exactly 1/200; PURE-I is the maximally obstructed direction -- SEAM.STATE.WIRING.SELECTOR.01 registered next
Dependencies: SEAM.CFIN.MARGINAL.STABILITY.01; SEAM.STATE.DERIVATION.01; SEAM.CFIN.KMSMIX.01; v898; v903
Scripts: v908_seam_equilibrium_wiring.py
Location: tfpt_1;tfpt_research_contracts
Original CSV, line 735Original ledger status
SEAM.STATE.WIRING.SELECTOR.01
THE WIRING FREEDOM THEOREM -- IS PURE-I COMPILER-FORCED? ANSWERED: NO -- DEPLOYMENT-CHOICE, NOT COMPILER THEOREM (the v908-registered contract, closed 2026-08-12, rounds 69-71 notes CCXIII/CCXV/CCXXI; promoted in v911). (1) THE EXACT GROEBNER CENSUS (30/30, WIRING-DEGENERATE): the C6-equivariant commutant of the coupling space is EXACTLY 24-dim (the boundary C6 action is the identity), the IOTA rule subspace 8-dim with the deployed PURE-I point; the constraint classes E1 (unit law), E2 (CAR/KMS), E3 (Pfaffian pencil, anchored by the symbolic Schur identity on all of W), E4 (orientation propagation det u > 0), E5 (covariance + seat stack) leave EXACTLY ONE admissible component mod rule gauge -- the rotation cell C_rot (dim 3; certified real decomposition, cofactor certificates, mixed branches real-point-free); pure-I is an INTERIOR point, NOT a vertex, and the INTEGER gauge (+)_5 J2 (+) I6 (preserving A_CC, C6, W and the ideal) connects pure-I and the pure-J ray; C_refl falls at EXACTLY ONE class -- orientation (det u = -(b^2 + d^2) < 0 identically): Z/X wirings are edge-illegal; SELECTOR THEOREM: rules + strict-collar Hermiticity would force PURE-J uniquely (up to flips/scale), pure-I sits at the maximally obstructed angle (defect 2t). (2) THE COLLAR-FRAME DECISION (26/26, THETA-CONVENTIONAL): no compiler-side demand distinguishes the theta_S sheet-swap frame within the 9-dim rule-gauge algebra -- five demand classes (mu4/C6, CAR/state, pencil/orientation, doily combinatorics, the round-59 census property) all COMPATIBLE-NOT-FORCING / SILENT-ON-ANGLE (the bare covariance tanh(beta u/2) A16 is exactly torus-invariant; the refined doily stabilizer is 9 OF 9; the round-59 spectra are constant on the orbit with closed forms tanh(1/2) / tanh^2(1/2)); the deployed parent (pure-I) PASSES strict collar RP EXACTLY in the integer-conjugated frame and fails at theta_S with defect 0.1 = 2t -- the round-58/59 strict-collar obstruction is FRAME-RELATIVE; the CXXXIX question closes as a compiler-FREEDOM theorem: freedom group = the rule-gauge frame orbit (tangent 7/9), selection quotient = the delta-circle, the only gauge-invariant datum of (frame, wiring) is the relative angle. (3) THE GAUGE-COVARIANCE AUDIT (21/21, RP-FRAME-COVARIANT, lead-ordered): theta' = g_int theta_S g_int^{-1} both directions exactly; the kernel-covariance law holds SYMBOLICALLY on the full torus (g^T A(V) g = A(g_C^T V g_B) identically), so strict-collar RP depends only on the relative angle delta (defect law 2t |a cos delta + c sin delta|); the pure-I exclusion is the lead's OPTION (2): a statement at the FIXED theta_S frame, NOT a wiring no-go; the Z/X exclusion IS genuinely orbit-invariant (det u frame-transport-invariant; the only det-flipping orthogonal element flips the vacuum and leaves the rule gauge). THE CANONICAL SENTENCE (frozen verbatim, sha 79950314): the compiler determines the wiring ORBIT; pure-I is a DEPLOYMENT REPRESENTATIVE; strict Hermiticity in the theta_S frame would select pure-J, the same demand in the integer-conjugated frame selects pure-I; a canonical wiring selection requires an ADDITIONALLY DERIVED physical frame. FORBIDDEN from now on: 'pure-I is compiler-forced' (and equivalents without the frame qualifier). HONEST SCOPE: the census covers the FIVE enumerated demand classes -- a compiler demand outside the list is not excluded; whether the actual seam physics derives a specific collar frame remains outside the formalized rules; the v898/v903 [O] premise stays [O]. Controls fire 6/6 + 6/6 + 5/5; exact integer/rational sympy, float64 only in disclosed wards, RNG only in declared controls. Zero RH content.
Recorded status: Contract closed as measured freedom theorem [Identity/Numerical]: one admissible wiring orbit (C_rot), Z/X excluded gauge-invariantly; pure-I = deployment representative; RP exclusion frame-relative (option 2); 'pure-I is compiler-forced' FORBIDDEN; [O] premise of v898/v903 unmoved; no marker move
Dependencies, status detail and source
Canonical status: CLOSED (DEPLOYMENT-CHOICE): exactly one admissible wiring component mod rule gauge; pure-I interior + integer-gauge-connected to pure-J; theta_S conventional (five demand classes silent); strict-collar RP exactly frame-covariant, exclusion = frame statement; Z/X exclusion orbit-invariant
Dependencies: SEAM.CFIN.NESS.PARENT.01; SEAM.CFIN.MARGINAL.STABILITY.01; SEAM.STATE.DERIVATION.01; v898; v903; v908
Scripts: v911_wiring_freedom.py
Location: tfpt_1;tfpt_research_contracts
Original CSV, line 736Original ledger status
CCC.SEAM.KINEMATICS.01
THE CCC CROSSOVER KINEMATICS DICTIONARY [E] (rounds DL-DLV, notes 2026-08-24; promoted 2026-08-24). EXACT (v957; six probes 28/28 + 29/29 + 18/18 + 21/21 + 14/14 + 7/7 embedded byte-exact, hashes pinned): (1) Penrose's reciprocal gauge Omega*tau(Omega) = -1 is the element tau = rho^2 sigma of the proven mu_4 Moebius stabiliser D_4; tau reverses the clock (= the Z_2 sheet parity), swaps the aeon poles {0, inf}, fixes +-i; the crossover locus |Omega| = |tau(Omega)| is the unit circle carrying all four marks. (2) The clock alone leaves exactly one constant-curvature conformal modulus on the 2D seam and the reciprocal Z_2 kills it (Liouville-exact; so(3,1) commutant dims 2-with-1-boost / 0). (3) The v221 transport is CPTP not unitary; its Stinespring isometry is explicit (V^dag V = 1_3), ||T^n - P_star||_2 = (2/3)^{6n} exactly, the global overlap is invariant and the environment retains full distinguishability -- the entropy reset of the cyclic reading is a REDUCED CHANNEL, no information destroyed. (4) The kinematic uplift: stereographic(Hopf(v)) = z1/z2 exactly; the v492 deck acts freely, so the crossover X = S^3/Z_4 is the smooth lens boundary of the corpus A_3 ALE; clock and reciprocal lift normalise the deck and descend; the four marks lift to four Hopf fibre circles paired into the two Z_2 sheet orbits with Gauss linking 1; the so(4,1) deck-commutant is 4-dimensional, ALL Killing, boost content 0 (infinitesimal Yamabe rigidity with no extra condition; global uniqueness on the explicit Obata boost family, 200-axis scan bounded below); the inversion x -> x/|x|^2 is a conformal involution of the cone C^2/Z_4 fixing the unit lens pointwise and swapping the aeon ends; the Lorentzian bridge (1/cos^2 T)(-dT^2 + g_{S^3}) is Einstein R_ab = 3 g_ab (symbolic Ricci) with a spacelike round-S^3 crossover and Omega_hat*Omega_check = -1, Omega_check = -cos T vanishing to first order. (5) KMS/modular closure at the free level: detailed balance exact, spec(-ln T) = {0, 6 ln(3/2), 6 ln 3}, T = e^{-H_mod}, OS Gram PSD; the v526 normalisation beta_angle = 2 pi = 1/(4 c3) equals the Gibbons-Hawking normalisation on the crossover fibre. (6) Holonomy dictionary: pole strings carry the full mu_4 monodromy (chi(D) = i), every seam string carries exactly the 2-torsion chi(D^2) = -1 = the v522 GSO/fermion-parity wrap (typed [C] structural correspondence). (7) Selector necessity: the admissible reflections of M(delta) close to D_4 iff delta = pi/2 (the clock factorises into admissible reflections only at mu_4); at Majorana operator level with fermionic signs the clock-axis cuts are Theta-real ONLY at k = 4 and asymmetric couplings break reality -- the uniqueness half of the v534 selector is DERIVED as a Theta-reality necessity (survival + coupling sign stay v534's nonperturbative toy facts, cited; reality is sign-blind, checked). (8) The frozen Gate-6 kernel: two decay modes ln(729/64) and ln(729) (ratio 2.709511), frozen defect-class overlap table, disc radius theta_max = eta_rec/(eta_0 - eta_rec) ~ 1.16 deg, kappa derived from the v526 KMS normalisation up to a declared convention band (u_rec <= 8.3e-5, contrast <= 3.3e-4): the template degenerates robustly to the sharp causal top-hat disc -- feeds the preregistered search experiments/ccc-crossover-disc (no CMB data touched).
Recorded status: Certified kinematics dictionary [E] (fine types Identity/Formal (Moebius/D_4 algebra, Stinespring isometry, Hopf equivariance, commutant dimensions, symbolic Einstein/Weyl checks, KMS/detailed-balance identities, Theta-reality censuses -- exact on corpus objects) and Numerical (linking integrals, Obata scans, band arithmetic pinned); the CCC/cyclic READING itself stays [C] and is NOT upgraded; WOIT.OS.TWISTOR.01 stays [O] with all kill tests live)
Dependencies, status detail and source
Canonical status: Kinematics certified [E]: reciprocal-in-D_4 + conformal rigidity (2D needs tau, 3D automatic) + Stinespring reduced-channel reset + lens-crossover uplift + KMS closure (tick = e^{-H_mod}) + holonomy dictionary (seam strings = GSO 2-torsion) + selector-uniqueness necessity + frozen top-hat kernel; the cyclic/CCC reading stays [C]; the dynamics stay WOIT.OS.TWISTOR.01 [O]
Dependencies: QGEO.CONF.01 (the seam premise); v221 (transport); v492 (deck/clock, A_3 ALE); v519/v521/v522 (Theta, side-blindness, GSO wrap); v526 (KMS normalisation); v529/v534 (straddle law + selector, cited); VGEO.TORSOR.01 (unit calibration untouched); rounds DL-DLV
Scripts: v957_ccc_crossover_kinematics.py
Location: origin_theory;tfpt_research_contracts
Original CSV, line 737Original ledger status
CCC.SEAM.CROSSOVER.01
THE CCC CROSSOVER CONTRACT [O] (registered 2026-08-24 from the external TFPT-vs-CCC adjudication of the six gates; the kinematic base is CCC.SEAM.KINEMATICS.01 [E]/v957). DEMAND (the dynamical crossover, in order): (D1) the interacting seam algebra A_hol realised ON the lens crossover X = S^3/Z_4 with reflection positivity protected on the mid-gap cut class while the aeon transfer uses the through-mark class (the two D_4 classes whose product is the clock; the v529 straddle law is this separation at toy level; = WOIT.OS.TWISTOR.01 gamma in the crossover geometry); (D2) the aeon-transfer channel as a Stinespring isometry at FIELD level (the v957 finite-dimensional dilation lifted to the reconstructed net) -- fundamental unitarity + rank-1 attractor in the visible channel + microstate record in the complement; (D3) the cosmology fork DECIDED: exactly one active story (Starobinsky r = 12/N^2 in [0.0033, 0.0048] vs crossover/GW epoch vs computed hybrid) -- priced decidable by LiteBIRD/CMB-S4-class sigma(r) ~ 0.001; (D4) the preregistered disc search experiments/ccc-crossover-disc EXECUTED per its frozen hypotheses (top-hat template, sign-pairing statistics, kill criteria K1-K6, BH-q < 0.01 + replication decision rule) -- EXECUTED 2026-08-24 with a ROBUST NULL on the Planck PR3 SMICA map (first data contact; freeze intact 3/3 hashes, frozen-kernel guards 5/5 BEFORE data contact; map integrity 2013312960 bytes, SHA-256 pinned in results.json; seed 20260824, reruns bit-identical): max|SNR| 5.119 on data vs null mean 5.20 over 100 Gaussian LCDM sims (matched mask + spectrum), p_global = 0.673, p_counts = 0.446, BH-q_min = 0.673 -- the q < 0.01 threshold CLEARLY missed; 171 candidates |SNR| >= 4 with 83 pos / 88 neg (no sign excess); injection recovery 100 percent (20 x 200 muK discs at 1.16 deg -- the search is well-powered, the null is a REAL null); K1-K6 all NA (they fire only on a resolved relic; none exists); replication legs (half-mission, Commander/NILC) not required for a null per the frozen decision rule, available for future candidates; three amendments disclosed (seed pinning of the unseeded synfast preflight, reporting fields, the documented estimator l-weighting) -- statistics, thresholds and kill criteria unchanged; results machine-readable in experiments/ccc-crossover-disc/results/results.json. KILL CRITERIA (frozen): a free fitted conformal factor anywhere; failure of the mid-gap RP protection on the interacting algebra (kill test 2 of WOIT gamma); the interacting level breaking the v522 wrap = (-1)^F identification (reopens the deck fork); r measured incompatible with the surviving cosmology branch; a resolved crossover relic violating the frozen template class (K1-K6, incl. the K6 contrast bound killing the derived-kappa chain); mu_4 marks identified with Hawking-point counts (typed numerological, forbidden). FENCES: the cyclic/CCC reading stays [C] regardless; the executed D4 null does NOT damage the compiler core (the kernel was OUTPUT of the [E] kinematics, not input) and no kill criterion fired; the contract stays OPEN via D1-D3; nothing here asserts CCC follows from TFPT in either direction.
Recorded status: Open contract [O] (research contract; the kinematic base [E] via v957; the dynamics = WOIT.OS.TWISTOR.01 gamma on the crossover geometry; D4 executed 2026-08-24 with a robust preregistered null -- no kill fired, no type change; the contract stays open via D1-D3)
Dependencies, status detail and source
Canonical status: Open [O]: D1 interacting algebra on the crossover (WOIT gamma) + D2 field-level Stinespring + D3 cosmology fork decision = the remaining demands; D4 EXECUTED with a robust null (p_global 0.673, BH-q 0.673, injection recovery 100 percent, K1-K6 NA; results.json) -- no kill fired; kinematic base certified in v957
Dependencies: CCC.SEAM.KINEMATICS.01 (the certified base); WOIT.OS.TWISTOR.01 (gamma = D1); SEAM.THERMAL.KMS.01 (the kappa chain); v529/v534 (the straddle fence); experiments/ccc-crossover-disc (the frozen search)
Scripts: v957_ccc_crossover_kinematics.py
Location: tfpt_research_contracts
Original CSV, line 738Original ledger status
DIMENSION.UPLIFT.FIREWALL.01
THE DIMENSION-UPLIFT FIREWALL (registered 2026-08-27 from the external deep review: 'chiral 1+1D seam net does NOT imply a local, interacting 3+1D quantum world'). STANDING RULE, in force immediately: (F1) no theorem whose hypotheses live in 1+1D (chiral net, VOA, lattice collar, seam circle) may be cited as CLOSING a claim about 3+1D physics; (F2) every contract closure must state the spacetime dimension of its hypotheses AND of its conclusion (dimension typing, same discipline as the markers). Audit census at registration: SEAM.EQUIV.01 and both routes are 1+1D in and out (OS/MMST scaling limit arXiv:2107.13834 treats 1+1D free lattice fermions; AMT OS-reconstruction arXiv:2407.18222 treats 2D full VOAs; L2 claims a chiral c=8 CFT and nothing more) -- even a FULLY PROVED SEAM.EQUIV.01 is a rigorous boundary building block, not the 4D theory; the WOIT.OS.TWISTOR.01 target IS the uplift demand and stays [O] with all kill tests live; the kinematic 2D->3D->4D uplift (v957, ccc_uplift_4d_probe self-labelled kinematic) does NOT close the firewall (a metric uplift is not an interacting local quantum theory); the anomaly-inflow bulk of the c_-=8 edge is an invertible/topological bulk (Witten-Yonekura arXiv:1909.08775, Hsieh-Tachikawa-Yonekura arXiv:2003.11550), never to be silently equated with the physical 3+1D spacetime bulk. ROUTE ORDERING (programme skeleton): (1) seam stays an internal/topological boundary module; (2) genuine 4D Euclidean lattice theory (TFPT fixes reps/charges/coupling relations/boundary conditions); (3) QFT4D.OS.RECON.01; (4) CHIRAL4D.NOMIRROR.01 in the same 4D model; (5) only then BW/CHM + entanglement gravity (GRAV.NONCIRCULAR.01); (6) then bulk-seam equivalence (SEAM.BULK4D.RECON.01). The twistor/celestial alternative is riskier (boundary correlators do not guarantee bulk locality, cf. arXiv:2602.04223) and stays a named parallel route.
Recorded status: Firewall (standing discipline rule, in force; the uplift theorems it names stay Open)
Dependencies, status detail and source
Canonical status: Firewall in force: no 1+1D theorem closes a 3+1D claim; every closure carries dimension typing of hypotheses and conclusion; route ordering registered
Dependencies: SEAM.EQUIV.01; WOIT.OS.TWISTOR.01; CCC.SEAM.KINEMATICS.01 (kinematic only)
Scripts: See original ledger entry
Location: tfpt_research_contracts
Original CSV, line 739Original ledger status
SEAM.BULK4D.RECON.01
THE SEAM-TO-BULK 4D RECONSTRUCTION CONTRACT [O] (registered 2026-08-27): the theorem previously only implicit between the SEAM.EQUIV.01 conclusion (a chiral c=8 boundary object, 1+1D) and the WOIT.OS.TWISTOR.01 goal (a Poincare-covariant causal chiral 4D theory) is made explicit as its own named target. DEMAND: from seam data alone construct a 4D family of local algebras (equivalently Schwinger functions) and prove (B1) 4D locality/microlocality, (B2) Poincare covariance + positive energy spectrum, (B3) spin-statistics + CPT, (B4) BOTH helicities (the anti-self-dual completion), (B5) cluster decomposition, (B6) a nontrivial S-matrix (interacting, not generalized-free), (B7) a UNIQUE seam<->bulk operator dictionary (not character-level only). KILL TESTS: every 4D extension is generalized-free; the inflow bulk is provably only invertible/topological with no local propagating completion; the dictionary is non-unique at operator level (OPE mismatch). A Hopf-fiber uplift / 4D cone / Einstein metric (v957) does NOT close this. Route-agnostic: WOIT.OS.TWISTOR.01 and the DIMENSION.UPLIFT.FIREWALL.01 constructive-lattice ordering are the two candidate proofs. NOTHING in the corpus closes any part of it. SPECTATOR OBSTRUCTION (2026-09-04, v1020): B7 as worded is unsatisfiable -- boundary(B(x)C) = boundary(B) for any decoupled anomaly-free C with trivial boundary; finite free-fermion witness in v1020; uniqueness is re-scoped to BULK.PRIME_COMPLETION.01 (prime/seam-generated completions, trivial relative commutant); status unchanged [O]
Recorded status: Open (research contract)
Dependencies, status detail and source
Canonical status: Open: the named seam->bulk 4D reconstruction theorem (seven demands B1-B7); no corpus result closes any part
Dependencies: DIMENSION.UPLIFT.FIREWALL.01; SEAM.EQUIV.01; WOIT.OS.TWISTOR.01; QFT4D.OS.RECON.01; CHIRAL4D.NOMIRROR.01
Scripts: See original ledger entry
Location: tfpt_research_contracts
Original CSV, line 740Original ledger status
DYN.MARKOV.EMBED.01
THE MARKOV EMBEDDING CONTRACT (registered 2026-08-27; 'three meanings of dynamics' split, step (a)->(b)). FINITE KERNEL HALF [E] (v971, sympy-exact): for the v221 seam transfer kernel T (spectrum exactly {1, 64/729, 1/729}) the principal logarithm Q = log T is an EXACT classical Markov generator -- e^Q = T by exact spectral calculus; row sums symbolically zero; off-diagonals exactly {ln(9/8), 2 ln 3, 2 ln 3} = {0.117783, 2.197225, 2.197225} > 0 (the reviewer's independently verified numbers), diagonals -ln(81/8), -ln(81/8), -4 ln 3; uniformization certificate Q + (4 ln 3) I >= 0 entrywise (diagonals ln 8, ln 8, 0, exact) => e^{tQ} positivity-preserving doubly stochastic for ALL t >= 0, T embeddable, every root T^{1/n} stochastic; spec(Q) = -spec(H_mod) = {0, -6 ln(3/2), -6 ln 3} (gap = Delta = 6 ln(3/2)); detailed balance w.r.t. the uniform state. NEGATIVE CONTROL: second eigenvalue -1/10 gives det = -1/200 < 0 -- provably NOT embeddable (det e^Q = e^{tr Q} > 0 always); embeddability is not generic, the RP/OS spectral positivity (CONTRACT.F.01 axiom 3) is the enabling fact. WHAT STAYS [O]: the same embedding statement at FIELD level (reconstructed net / quasi-local algebra, uniform in system size). FIREWALL: e^{tQ} is irreversible statistical dynamics (H-theorem), NOT unitary evolution -- step (b)->(c) is the separate contract DYN.UNITARY.DILATION.01; the shared F_transfer relaxation shape is a universal CONTRACTION CLASS, not one physical clock (v723/v724/v777). Python-only per GATE.WOLFRAM.02 (matrix-log/spectral identities; the exact rationals 64/729, 1/729 already mirrored).
Recorded status: Contract [E] (finite kernel embedding, sympy-exact; v971) + [O] (field level)
Dependencies, status detail and source
Canonical status: [E] the finite kernel half: Q = log T is an exact Markov generator (row sums 0, off-diagonals ln(9/8), 2ln3, 2ln3 > 0, uniformization positivity for all t >= 0); [O] the field-level embedding
Dependencies: v221 (kernel); v957 (T = e^{-H_mod}); CONTRACT.F.01 (axiom 3 positivity); v723/v724/v777 (external clocks)
Scripts: v971_markov_embedding_generator.py
Location: tfpt_research_contracts
Original CSV, line 741Original ledger status
DYN.UNITARY.DILATION.01
THE UNITARY DILATION CONTRACT [O] (registered 2026-08-27; 'three meanings of dynamics' split, step (b)->(c)). The continuous semigroup e^{tQ} (DYN.MARKOV.EMBED.01) is irreversible statistical dynamics; fundamental quantum dynamics needs T = e^{-aH} -> (OS) -> U(t) = e^{-itH} with H positive self-adjoint. DEMAND: (D1) a Stinespring/Hamiltonian dilation of the semigroup with (quasi-)local generator; (D2) size consistency (compatible with the thermodynamic limit -- no pathologically growing environment); (D3) a Lieb-Robinson bound (finite propagation speed of the dilated dynamics); (D4) the OS analytic continuation to a unitary one-parameter group on the reconstructed Hilbert space. KILL TESTS: every dilation of the seam semigroup is provably nonlocal; the Lieb-Robinson velocity diverges in the scaling limit; the OS continuation fails on the interacting algebra. RELATION: demand D2 of CCC.SEAM.CROSSOVER.01 (Stinespring isometry at field level) presupposes this contract -- named here as its prerequisite. NOTHING here is closed by the finite v971 result. [2026-08-27 lift-structure note (v976/v977, marker UNCHANGED): the dilation the corpus actually deploys (K_ij = sqrt(T_ij)|i><j|, the CCC Stinespring reading of the v221 kernel) is PROVABLY entanglement breaking (measure-and-prepare; quantum capacity 0; C_0 = 0) -- it cannot carry the coherent transport this contract demands, so any closing dilation must be a genuinely different object. The classical kernel admits the full lift trichotomy {EB dilation | random-permutation fibre with the hidden circulation parameter t (v976) | reversible unistochastic macro-gate with the hidden orientation bit sgn J = +-1/27 (v977)} -- the same classical data, three inequivalent quantum dynamics; and no fixed microstep unitary generates the relaxing sequence (Dirichlet recurrence witness), so repeated steps REQUIRE environment/dephasing between steps -- exactly the D1-D4 demand.] EXECUTED UPDATE (2026-08-28, v987): the OS/dilation LADDER is executed at kernel + free-field + interacting-kernel + quantum-coupled band level -- B = P1+(2/3)P2+(1/3)P3 > 0, H = -log B PSD (gap log(3/2)), T(t) semigroup inside the stochastic cone, U(t) = e^{-itH} with Wick anchor U(-in) = B^n (n=1..6); size-uniform free-band gap; congruence interacting family SPD; quantum SWAP coupling d(theta)~theta^2, CPTP, LR radius 1. MUST-FAIL: v971 negative kernel has no real half-step; one-sided mutant K B^(x L) is not symmetric. FIREWALL: continuous field-level OS reconstruction, thermodynamic-limit branch selection and any 3+1D reading stay [O]. Python-only / Wolfram mirror deferred. EXECUTED UPDATE (2026-08-29, review wave 4, v999): the finite ladder is now COMPLETE -- discrete / kernel / field-free / interacting-classical / quantum-coupled / CONTINUOUS-TIME. Weak-collision Hudson-Parthasarathy: generator extraction Richardson 1.098e-10, diag(L_GKSL)==Q=log B symbolic, e^Q=B exact, GNS splitting defect 0, locality 1.355e-20, strong-collision singularity contrast rank 9/81. Open = thermodynamic field limit only. Display stays [O]; no marker move.
Recorded status: Open [O] + finite ladder complete [E]/[N] (discrete/kernel/field-free/interacting-classical/quantum-coupled/continuous-time; open = thermodynamic field limit only)
Dependencies, status detail and source
Canonical status: [E] (2026-08-28, v984): discrete collision/QCA-band dilation. [E] (2026-08-28, v987): kernel OS continuation exact + size-uniform free band + interacting congruence family + quantum SWAP coupling (d(theta)~theta^1.99, CPTP, LR radius 1). [O] continuous field-level OS reconstruction, thermodynamic-limit branch selection, any 3+1D reading; no marker move. | 2026-08-29 v999: finite ladder COMPLETE (incl. continuous-time weak-collision HP); open = thermodynamic field limit only. Display stays [O].
Dependencies: DYN.MARKOV.EMBED.01; CCC.SEAM.CROSSOVER.01 (D2); QFT4D.OS.RECON.01
Scripts: v984_markov_qca_dilation.py, v987_os_dilation_package.py, v999_weak_collision_hp.py
Location: tfpt_research_contracts
Original CSV, line 742Original ledger status
TRANSFER.HIDDEN.CIRCULATION.01
THE HIDDEN CIRCULATION CONTRACT, executed half (registered 2026-08-27; external-review round, companion of the DYN.MARKOV.EMBED.01/DYN.UNITARY.DILATION.01 split). [E] (v976, sympy/Fraction-exact): (1) the Birkhoff fibre of the seam single step B (exact sixth root of the v221 kernel; B = (1/2)I + (1/18)P12 + (2/9)P13 + (2/9)P23 bit-exact) is EXACTLY a one-parameter line w_t, t in [0, 1/18], because the decomposition map on R[S3] has the 1-dim kernel (even - odd); the hidden parameter is the sign-character Fourier coefficient w_t-hat(sgn) = 6t; populations are exactly t-free and no fibre member is chiral (w(C123) = w(C132) forced -- the typed obstruction for any chirality reading). (2) THE DISCRIMINATOR: one-step coherence dynamics is the weighted left regular S3 representation with spectrum {1, 6t, 2/3 x2, 1/3 x2} exactly; the triangle loop current A is an exact eigen-observable Psi_t(A) = 6t A (population-blind; one step + one current readout measures t, no ancilla; one-step tomography rank 6 determines all six weights). (3) CONTRAST-QUBIT CHOI LAW: spec(Choi^{T2}) = {-3t/2, 1/6+3t/2, 1/3+3t/2, 1/2-3t/2} symbolically; CRITICALITY lambda_min = (1 - lambda2 - lambda3 - 6t)/4 with lambda2 + lambda3 = 2/3 + 1/3 = 1 EXACTLY: t = 0 sits precisely ON the entanglement-breaking boundary (mutated spectra {2/3,1/2}/{1/2,1/3} miss by -1/12/+1/12 -- criticality not generic); the squared channel is PPT on the whole range (endpoint minima 1/9, 1/12). (4) FULL-LEVEL NPT PERSISTENCE: lambda_min(Choi(Psi_t^n)^{T2}) = -(1/3)(2/3)^n, t-independent (exact eigenvalue for n in {1,2,6}; float minimum n = 1..8) -- the 3-level family is never EB at tested n (pinned by the invariant coherent state (1,1,1)/sqrt3). (5) THE NO-GO for DYN.UNITARY.DILATION.01: the deployed Kraus dilation K_ij = sqrt(T_ij)|i><j| is measure-and-prepare (one step kills every coherence, fully symbolic), its Choi is diagonal => entanglement breaking => quantum capacity 0; C_0(T) = 0 exactly (T entrywise > 0); the Kraus channel is NOT in the Birkhoff fibre. (6) BINARY MESSAGE (KKT, 50 digits): p* = (1/2, 1/2, 0) exactly capacity-achieving for BOTH T and B; C(T) = 0.00835801913781 bit, C(B) = [13 log2(13/7) - log2 7]/18 = 0.4890415237 bit, ratio 1.709%. [C] literature-typed: PPT<=>separable in 2x2 (Peres-Horodecki), separable Choi <=> EB (Horodecki-Shor-Ruskai quant-ph/0302031), EB index (Lami-Giovannetti 1411.2517) => qubit n_EB = 1 (t = 0) / 2 (t > 0). [C] VALUE COINCIDENCE (observation, NOT a theorem): the t = 0 weights (9,1,4,4)/18 = (3^2,1^2,2^2,2^2)/18 hit the v652 c = 0 defect-ladder values 2*Delta = g^2/18 including w(I) = 1/2 = 2*Delta(gt=3); multiplicity matches only at g = 2; the forcing functor (CFT defect dimension -> Birkhoff weight) is the OPEN half, named TRANSFER.DEFECT.BIRKHOFF.01. OPEN: the physical selection of a fibre point t; any 4D/flavor reading. Python-only per GATE.WOLFRAM.02 (channel/Choi/Birkhoff algebra; the exact seam rationals already mirrored).
Recorded status: Identity [E] (executed half: fibre line, discriminator, criticality, EB no-go, KKT) + literature [C]; fibre-point selection open
Dependencies, status detail and source
Canonical status: [E] the Birkhoff fibre of B is the sign-character line t in [0,1/18]; loop-current discriminator Psi_t(A) = 6t A; qubit Choi law -3t/2 with EB criticality 2/3 + 1/3 = 1; full-level NPT -(1/3)(2/3)^n; the deployed Kraus dilation is EB (Q = 0, C_0 = 0); binary-message KKT certificates; [C] defect-Birkhoff value coincidence (forcing functor OPEN as TRANSFER.DEFECT.BIRKHOFF.01)
Dependencies: DYN.UNITARY.DILATION.01; DYN.MARKOV.EMBED.01; QEC.SEAM.01; v221_seam_qecc.py; v652_orbifold_arf.py
Scripts: v976_seam_lift_birkhoff.py
Location: tfpt_research_contracts
Original CSV, line 743Original ledger status
TRANSFER.COHERENT.WILSON.01
THE COHERENT WILSON CONTRACT, executed half (registered 2026-08-27; external-review round, companion of TRANSFER.HIDDEN.CIRCULATION.01). [E] (v977, sympy-exact): (1) UNISTOCHASTICITY: the seam single step B equals |U_ij|^2 entrywise for an exact U in SU(3); the angles are forced by B (sin^2 th13 = 2/9, sin^2 th12 = 1/14, sin^2 th23 = 2/7), cos delta = -4/sqrt(65) is uniquely solved, so the complete lift set up to rephasing is the two-branch family {U, U*} with e^{i delta} = (-4 +- 7i)/sqrt(65). (2) THE WILSON DATA ARE CLASSICAL UP TO ONE SIGN: J = 1/27 exact, Re of every plaquette fixed by B through unitarity (Re Q_{12;12} = -5/324, J^2 = 1/729 from B alone) -- the classically invisible datum is the Z2 orientation bit sgn J (U* lifts the same B with J = -1/27); minimal observable = the plaquette interference readout Im(U11 U22 U12* U21*). (3) THE 5-12-13 CODE: Q_{12;12} = (-5+12i)/324, normalized (-5+12i)/13 with 5^2 + 12^2 = 13^2 (atoms 5 = g_car, 12 = dim g_SM, 13 = Delta_Q = N(3+2i)); all nine plaquettes close on four Gaussian phase types with norms exclusively {10, 13, 130, 169} = {2*5, 13, 2*5*13, 13^2}; every plaquette has Im = +-1/27; the four fundamental plaquettes generate all nine via exact B-weighted composition. (4) THE CENTER BRIDGE: disc chi_A = 65 = det(A-I)^2 + (det A/2)^2 = 4^2 + 7^2 for the v530 atom matrix A = [[8,2],[5,3]], and e^{i delta} = (-det(A-I) +- i det A/2)/sqrt(disc chi_A) equals the transport-lift phase EXACTLY; -4+7i = (1+2i)(2+3i) with Gaussian norms 5, 13 (the v738 tower primes); NEGATIVE controls: the v530 siblings A_K (disc 48 vs identity 13) and A_Q (disc 13 vs 13/4) FAIL the identity -- the bridge selects the atom quotient A. (5) POWER LAW + RATIONALITY SELECTION: J_n^2 = (1-b)^2(1+2b-3a^2)/108 (a = (2/3)^n, b = (1/3)^n), every B^n unistochastic with its own U_n (U_6 built, |U_6|^2 = T exact); |J_6| = 0.0951088904 = 0.9884006 J_max; the uniform limit lifts to the Fourier matrix F3 at J_max = 1/(6 sqrt 3) exactly; J_n is RATIONAL ONLY at n = 1 (the deployed step hits 3(1+2b-3a^2) = 1 exactly, so J = 1/27) -- the Gaussian-Pythagorean code selects the single step. (6) NO FIXED MICROSTEP: B^2 != |U^2|^2 exact, and the Dirichlet recurrence witness n* = 967909 has min diag |U^{n*}|^2 = 0.999999 while B^{n*} is uniform to 5.6e-17 -- no single closed unitary generates the relaxing sequence; repeated steps require dephasing between steps, the six-step macro-gate U_6 is NOT U_1^6 (the coherent sharpening of the k5 clock-vs-walk verdict). (7) SELECTIVITY (hard kill passed): the obstruction certificate J^2 = -1/64 < 0 fires on the classic non-unistochastic control; mutated spectra give irrational J; census over 238 valid family points: 4 rational-J, EXACTLY ONE full 5-12-13 code point = the deployed (2/3, 1/3) (0.42% << the preregistered 10% kill). (8) PMNS NEAR-MISS stays NEGATIVE: branch phase 240.2551 deg near the deployed 240 deg (4pi/3, v270) but J_tr = -1/27 = -0.037037 != J_PMNS = -0.02965 and all three angles differ -- NO PMNS derivation. [C] literature: coherification by a reversible unitary iff unistochastic (Dunkl-Zyczkowski 0909.0116; Korzekwa et al. 1710.04228); a unitary lift carries quantum capacity log2 3. OPEN: the physical selection of sgn J; the A -> angles intertwiner (the bridge fixes the PHASE from A-invariants, the ANGLES come from B alone); any CP/time-orientation reading. Python-only per GATE.WOLFRAM.02 (SU(3)/plaquette/center-bridge symbolic algebra with nested radicals).
Recorded status: Identity [E] (executed half: unistochastic lift, Wilson code, center bridge, selectivity census) + literature [C]; branch selection and intertwiner open
Dependencies, status detail and source
Canonical status: [E] B unistochastic with exact SU(3) lift {U, U*}, J = +-1/27; 5-12-13 plaquette code (norms {10,13,130,169}); center bridge disc chi_A = 65 = det(A-I)^2 + (det A/2)^2 with sibling negatives; rationality selection (J_n rational only at n = 1); census unique full-code point = deployed (2/3, 1/3); no fixed microstep (Dirichlet witness); [C] coherification literature; PMNS near-miss stays negative; sgn J and the intertwiner OPEN
Dependencies: TRANSFER.HIDDEN.CIRCULATION.01; DYN.UNITARY.DILATION.01; v530_center_quotient_compiler.py; v738_hecke_mod_ramified.py; v270_pmns_jarlskog_assembly.py
Scripts: v977_transfer_unistochastic_wilson.py
Location: tfpt_research_contracts
Original CSV, line 744Original ledger status
QFT4D.OS.RECON.01
THE 4D OSTERWALDER-SCHRADER PACKAGE CONTRACT [O] (registered 2026-08-27; step (3) of the DIMENSION.UPLIFT.FIREWALL.01 route ordering). INPUT: TFPT fixes the discrete data (representation content, charge lattice, coupling relations, boundary conditions -- the seam as internal/topological boundary module); the genuine 4D Euclidean lattice carries spacetime, gauge fields, Higgs, fermions. DEMAND: (O1) reflection positivity of the lattice measure; (O2) Euclidean covariance restoration (hypercubic -> full Euclidean group); (O3) clustering; (O4) uniform bounds (uniform in lattice spacing and volume); (O5) continuum limit; (O6) OS reconstruction of the Wightman/Haag-Kastler theory. BINDING PHRASING RULE (the perturbative firewall): QFT4D.EG.ALLORDER.01 (v381) is a LOCAL PERTURBATIVE CONSTRUCTION UNDER THE STATED EG/BRST HYPOTHESES and no more -- the weak adiabatic limit for massless particles is the cited Duch theorem (arXiv:1801.10147) whose hypotheses must be verified for the concrete TFPT model; a seam-transfer gap does not substitute for the IR structure of massless photons/gluons; even full EG/BRST success yields NONE of: confinement/hadron spectrum, Yang-Mills mass gap, asymptotic charged states in QED, nonperturbative Higgs vacuum, controlled full S-matrix.
Recorded status: Open (research contract; binding phrasing rule in force for the perturbative leg)
Dependencies, status detail and source
Canonical status: Open: the nonperturbative 4D OS package (RP, Euclidean covariance, clustering, uniform bounds, continuum limit, reconstruction); the all-orders EG/BRST leg is fenced as local-perturbative-under-hypotheses
Dependencies: DIMENSION.UPLIFT.FIREWALL.01; QFT4D.EG.ALLORDER.01 (fenced perturbative leg)
Scripts: See original ledger entry
Location: tfpt_research_contracts
Original CSV, line 745Original ledger status
CHIRAL4D.NOMIRROR.01
THE CHIRAL 4D LATTICE MATTER CONTRACT [O] (registered 2026-08-27; step (4) of the firewall route ordering). The seam's c_- = 8 and Chern/inflow structure are a boundary-ANOMALY signal, not yet 4D matter. DEMAND: an explicit chiral lattice operator (Ginsparg-Wilson/overlap type) for the TFPT representation content with proofs of (C1) a local gauge-invariant fermion measure; (C2) perturbative AND global anomaly freedom; (C3) no Witten SU(2) anomaly; (C4) no mirror generation in the physical spectrum (mirror decoupling surviving the continuum limit); (C5) correct index and charges (TFPT charge lattice, N_fam generations); (C6) a stable continuum limit compatible with QFT4D.OS.RECON.01. CALIBRATION (state of the art): Mastropietro arXiv:2303.02790 -- weakly coupled 4D U(1) with a MASSIVE gauge field; the TFPT target (chiral SU(3)xSU(2)xU(1), three generations, massless nonabelian fields, EWSB and confinement downstream) is far stronger. KILL TESTS: mirror fails to decouple (WOIT kill test 3 at lattice level); Witten anomaly obstructs the carrier SU(2); every gauge-invariant measure is provably nonlocal. CONSISTENCY (ledger wins): the celestial-branch scope fence honestly lists interacting RP, mirror decoupling, internal SU(2), both helicities, local matter fields, EWSB, confinement as NOT closed; the contradictory 'zero open internal mechanisms' phrase in docs/OPEN_PROBLEMS.md is corrected in the same change. EXECUTED UPDATE (2026-08-28, v989): chiral Gauss census on a two-species Z4 Hamiltonian (factorized 16 x 256, 4096 never materialised) -- single-exponent Gauss iff q_L = q_R; two-exponent Gauss always (lattice Dirac doubling); V^4 = I; mutant (g_L,g_R)=(1,0) on vectorlike fails. NOT the TFPT representation content and not 3+1D. Contract stays [O]. Python-only / Wolfram mirror deferred. EXECUTED UPDATE (2026-08-28, completeness wave, v997): FK SMG toy theorem -- N=8 unique Spin(7)-singlet ground state, Schmidt rank 1, volume-independent gap 14 at L=1,2,3; N=4 contrast 2^L-degenerate; physical chiral edge keeps its pi/L spectrum exactly. SMG mechanism toy-proved [E]; 4D Spin(10) theorem stays [O]. Contract stays [O]. Python-only / Wolfram mirror deferred. WAVE-5 KILL (2026-08-29, v1002): number-preserving Casimir projector route excluded -- singlet census one 16 = {N=0:1, N=16:1} (none at N=8); k=2 half-filling multiplicity 27; k=3: 1463 (exact Weyl alternation, |W(D5)|=1920); uniqueness fails at every cluster size. The DET16 number-violating projector is a SEPARATE candidate (CHIRAL4D.MIRROR.DET16.01 [C]). EXECUTED UPDATE (2026-09-05, v1023): child CHIRAL4D.MIRROR.DFILTER.BLOCK.01 proves the finite derivative-filtered 2x2 singular-value block, exact ker(D_GW) preservation and the adiabatically mirror-continuated high branch. The bare mirror variable is not invariant, the low branch is quadratic (z=2), and no bare-mirror response gap, Weyl cone, DET16/DET32 realization, interacting parent, local measure/anomaly/index control or 3+1D continuum theorem follows. Parent status stays Open [O]. ROUND-4 CURRENT: v1027 repairs canonical DET excitations under the singlet premise and preserves signed z=1 dispersion for fixed c-number gauge fields. It changes flatDeltaQ to additiveDeltaNa. No hard bare-mirror gap, quantum-link CAR diagonalization, chiral SM or continuum closure; [O] unchanged.
Recorded status: Open (research contract; 1+1D chiral Gauss census executed; SMG mechanism toy-proved [E]; Nielsen-Ninomiya as Gauss statement; 4D Spin(10) theorem stays [O]; no 3+1D closure) | Round-3 v1023 adds an exact finite block lemma [E]/conditional GW reading [C]; NOMIRROR remains Open [O].
Dependencies, status detail and source
Canonical status: Open: explicit GW/overlap chiral lattice operator for the TFPT content. EXECUTED (v989): 1+1D Gauss census (single-exponent iff vectorlike; two-exponent always). No 3+1D closure. EXECUTED (v997): SMG mechanism toy-proved [E] (N=8 unique Spin(7) singlet, gap 14 volume-independent; N=4 2^L contrast; physical edge pi/L exact). 4D Spin(10) theorem stays [O]. No 3+1D closure. WAVE-5 (2026-08-29, v1002): number-preserving Casimir projector route excluded (census N=8:0, k=2:27, k=3:1463, |W(D5)|=1920). Display unmoved Open. | ROUND3 2026-09-05: finite derivative-filtered block only; no invariant mirror-response gap, Weyl cone, many-body realization or 4D closure. Display stays [O]. | ROUND-4 CURRENT: v1027 repairs canonical DET excitations under the singlet premise and preserves signed z=1 dispersion for fixed c-number gauge fields. It changes flatDeltaQ to additiveDeltaNa. No hard bare-mirror gap, quantum-link CAR diagonalization, chiral SM or continuum closure; [O] unchanged.
Dependencies: DIMENSION.UPLIFT.FIREWALL.01; QFT4D.OS.RECON.01; WOIT.OS.TWISTOR.01 (kill test 3)
Scripts: v989_lattice_gate_battery.py, v997_spin2_smg_witnesses.py, v1002_spin10_mirror_projector.py, v1023_derivative_filtered_wall.py
Location: tfpt_research_contracts
Original CSV, line 746