Original ledger status
GATE.METRIC.19
PREMISE (A) MAXIMAL HONEST CLOSURE (the two residual gates A2 + R1 pinned to their floor; (A) carries ZERO independent open content): (1) A2 (NET EXISTENCE) CLOSES BY ASSEMBLY [C] - every ingredient is a constructed object: 16 free Majoranas => free-fermion conformal net (Buchholz-Mack-Todorov / Boeckenhauer-Evans), holomorphic c=8 lattice net = (E8)1 (Frenkel-Kac-Segal VOA / Dong-Xu net / Kawahigashi-Longo machinery), mu4 simple-current extension = Longo Q-system index 4 (v125), KLM mu(B)=16/16=1 => holomorphic, modular data checked 248=120(NS)+128(R), character E4/eta^8=j^{1/3} (v156); the ONLY TFPT-specific identification (seam Calderon kernel = free-fermion 2-point function) is DONE since the DtN/Calderon symbol is universally |k| (Lee-Uhlmann, v156/v157) => A2 is citation/assembly of published theorems, not a finite computation we owe (re-typed [A]->[C]); (2) R1 (SEAM CLOCK) REDUCES TO GATE.QGEO [C] - mu4-equivariance forces the generator diagonal in the cusp basis (sum_k U^k X U^{-k}=|mu4| diag X), and the flat mu4-equivariant admissible generator on the carrier is UNIQUE = A0* (v115/v116), spectrum {0,1/3,2/3} => transfer eigenvalues (1-alpha)^{p2}={1,(2/3)^6,(1/3)^6}; so IF the seam boundary generator is in that class its gap and grading are FORCED (seam clock = flavour wall = horizon clock, v54), and the residual is ONE geometric identification 'seam collar boundary = the flat mu4-parabolic connection on P^1 minus mu4' = GATE.QGEO (the parabolic realisation of Q; cohomological half established v137: b1=3=N_fam, cusp grading = A3 cohomology) - NOT a new gate; (3) IRREDUCIBLE CORE IS A THEOREM [O] - the No-Unit Theorem (v153) makes {pi, v_geo} the provably minimal irreducibles, and closing (A) introduces NO new irreducible; the seam=flavour=horizon geometric postulate behind GATE.QGEO is in that same irreducible class. FINAL ACCOUNTING: premise (A) = (A2 assembly [C]) + (R1 = GATE.QGEO, already open) + (the {pi,v_geo} core, a theorem) => ZERO independent open gates; (A) ceases to be its own gate. Honest scope: a unification + re-typing, NOT an unconditional proof
Recorded status: Identity/assembly [C] (A2 net existence by established AQFT; R1 reduced to GATE.QGEO via A0* uniqueness) + [O] (the irreducible {pi,v_geo} geometric core, a theorem by v153)
Dependencies, status detail and source
Canonical status: Closure [C]: A2 = net-construction assembly, R1 = GATE.QGEO; (A) has zero independent open gates, irreducible core {pi,v_geo} a theorem
Dependencies: GATE.METRIC.16; GATE.METRIC.17; GATE.METRIC.18; v115; v116; v125; v137; v153; v156
Scripts: v165_premise_a_closure.py
Location: tfpt_research_contracts
Original CSV, line 247Original ledger status
EM.BUDGET.02
PYRATE GAUGE CROSS-CHECK (independent third-party confirmation of EM.BUDGET.01/CAR.SM.01 and an F_transfer gauge-input check): the carrier/SM field content gives, by the textbook one-loop formula in GUT normalisation, (b1,b2,b3)=(41/10,-19/6,-7) [I]; (1) THREE INDEPENDENT PATHS to b1=41/10 - carrier algebra 10 b1 = g_car 2^{g_car-2}+1 = 41 (CAR.SM.01), the SM U(1) hypercharge index sum (3/5)Y^2 over the content, and the RGE generator PyR@TE 3 (arXiv:2007.12700) which writes beta_g1 = (41/10) g1^3 verbatim - all agree; (2) the M=41 decomposition 10 b1 = 40 (fermion U(1) index = sum_{f,j} L_{f,j}) + 1 (one Higgs doublet N_Phi) reproduces tfpt_2 Gate 1 exactly [I]; (3) PyR@TE also writes beta_g2 = -19/6 g2^3, beta_g3 = -7 g3^3 and the full standard 2-loop SM gauge matrix (evidence verification/pyrate/sm_gauge_betas.txt, regenerated by verification/pyrate/reproduce.sh) [I]. SCOPE [P]: confirms the gauge sector of the F_transfer functor (its running inputs are not free knobs but follow from the carrier content); PyR@TE is the right external tool for the transfer/RGE gates (gauge running, and - with a seesaw model - the neutrino-Yukawa running behind eta_B), NOT for premise (A) (a 2d boundary-CFT question)
Recorded status: Identity [I] (one-loop coefficients exact) + [P] (F_transfer gauge inputs)
Dependencies, status detail and source
Canonical status: Identity [I]: carrier content -> (41/10,-19/6,-7); PyR@TE 3 (external) reproduces them verbatim; F_transfer gauge inputs confirmed
Dependencies: EM.BUDGET.01; CAR.SM.01; v2_carrier_pascal.py; v13_open_gates.py
Scripts: v159_pyrate_gauge_crosscheck.py
Location: tfpt_2
Original CSV, line 248Original ledger status
FLAV.RGSTAB.01
F_TRANSFER SCALE-TAGGING (the lepton-mixing predictions are RG-STABLE outputs; the quark mass-ratio readouts carry a scale tag): (1) the PMNS angles run only through the charged-lepton Y_e Y_e^+ eigenvalue gap y_tau^2 ~ 1.0e-4 [I] (the only mixing-ROTATING Yukawa term is (3/2) Y Y^+ Y, PyR@TE SM RGEs), so the one-loop running from the seam/scalaron scale (M_scal = c3^{7/2} Mbar ~ 3e13 GeV) down to M_Z is kappa_tau = y_tau^2/(16 pi^2) ln(M_scal/M_Z) ~ 1.8e-5; (2) hence |Delta sin^2 theta_ij| <~ 1e-4 (normal ordering / hierarchical => O(1) spectrum factor, no quasi-degenerate enhancement) is two-three orders below current precision (sin^2 th12 +-0.013, sin^2 th13 +-0.0007) => the seeds sin^2 th12 = 1/3 - phi0/2 = 0.3067 and sin^2 th13 = phi0 e^{-5/6} = 0.0231 are SCALE-INDEPENDENT F_transfer outputs (seam value = measured value) [I]; (3) the up-quark sector runs through y_t^2 ~ 0.9, kappa_t ~ 0.15 = O(10-15%), so the m_t/m_b ~ 41 readout carries a scale tag (EW/M_Z), unlike the lepton angles [I]; (4) F_transfer TYPING [P]: the lepton-mixing transfer is trivial (no scale ambiguity), the quark-mass transfer is a genuine running map -- both the PyR@TE-confirmed SM Yukawa betas. Python-only (y^2-suppression magnitude bound, not a precision PMNS evolution; ref Antusch et al. 2005)
Recorded status: Identity [I] (y^2-suppression bound) + [P] (F_transfer typing)
Dependencies, status detail and source
Canonical status: Identity [I]: lepton angles RG-stable (y_tau^2-suppressed), quark ratios scale-tagged; F_transfer lepton sector trivial
Dependencies: EM.BUDGET.02; CAR.SM.01; v16_solar_dual_anchor.py; v21_solar_product_quark.py
Scripts: v163_rg_stability_flavor.py
Location: tfpt_2
Original CSV, line 249Original ledger status
QCD.LAMBDA.01
QCD CONFINEMENT SCALE PARAMETER-FREE FROM THE CARRIER b3 = -7 (the m_p/m_e numerator is independently sourced; the ratio itself stays an honest non-claim): (1) running alpha_s(M_Z) = 0.1179 down with the two-loop QCD RGE and b0(n_f) = 11 - 2 n_f/3 (b3 = -7 at n_f = 6; v159) + thresholds at m_b, m_c reproduces alpha_s(m_b) ~ 0.22 and alpha_s(m_c) ~ 0.38 = the measured values [I]; (2) continuing down, alpha_s reaches O(1) (confinement) at mu_conf ~ 0.5 GeV in [0.3,0.8] -- the QCD scale is fixed by {alpha_s(M_Z), b3 = -7} alone (dimensional transmutation), not an input [I]; (3) m_p = 0.938 GeV ~ 2 x mu_conf, where the O(1) proton/Lambda factor is LATTICE (non-perturbative), NOT supplied by PyR@TE or the compiler [P]; (4) m_p/m_e = 1836.15 is BRACKETED by 1/phi0^2 = 353.7 and 1/phi0^3 = 6651 but is NOT a compiler power; v164 sources only the QCD-scale numerator and KEEPS the frontier 'Open / not forced' typing [A]. Python-only (numerical two-loop running)
Recorded status: Identity [I] (parameter-free confinement scale) + [P] (lattice O(1)) + [A] (ratio stays non-claim)
Dependencies, status detail and source
Canonical status: Identity [I]: Lambda_QCD parameter-free from b3=-7; m_p/m_e numerator sourced, ratio stays 'Open / not forced'
Dependencies: EM.BUDGET.02; CAR.SM.01; FR.MPME.01
Scripts: v164_qcd_scale.py
Location: tfpt_4_frontier
Original CSV, line 250Original ledger status
HIGGS.FREESEAM.01
HIGGS QUARTIC FROM THE FREE SEAM (a derived boundary condition tying m_H to premise (A); validated at two loops): the seam UV is the free chiral c=8 fixed point (v157/v158, Gaussian, no relevant/marginal interactions), so the one marginal SM scalar coupling vanishes at the seam -- lambda(M_seam)=0 AND beta_lambda(M_seam)=0, the Shaposhnikov-Wetterich double-criticality, here MOTIVATED by the free seam rather than assumed. (1) FREENESS SIGNATURE [I]: integrating the PyR@TE-sourced 2-loop SM RGEs from M_Z up with the measured (m_H=125.25, m_t) gives lambda(Mbar) ~ 0.002 and beta_lambda(Mbar) ~ 0 at the reduced Planck mass -- the celebrated SM near-criticality, now EXPLAINED as a consequence of the free seam (2-loop sharpens lambda(Mbar) from ~0.022 at 1-loop to ~0.002, i.e. the BC is met to ~0.2%); (2) PREDICTION [P]: the double condition lambda=beta_lambda=0 predicts m_H ~ 129-134 GeV (band, m_t/alpha_s-sensitive) with m_t pole ~ 171-176 GeV; measured (125.25, 172.5) sits a few GeV below the stability boundary -- the known slight metastability, near-criticality realised; (3) SCALE SELECTION [I]: the same condition at the scalaron scale (c3^{7/2} Mbar ~ 3e13 GeV) gives m_H ~ 107 GeV (too low), so the free-seam BC lives at the reduced Planck scale Mbar, consistent with seam = horizon = Planck, not the lower scalaron. Fills the Higgs-sector gap (previously only N_Phi=1). Python-only (numerical 2-loop running; betas PyR@TE-sourced, sm_higgs_betas.txt)
Recorded status: Identity [I] (freeness signature + scale selection) + [P] (the m_H prediction band)
Dependencies, status detail and source
Canonical status: Identity [I]: free seam => lambda(Mbar)~0=beta_lambda (SM near-criticality explained); [P] m_H ~ 129-134 predicted; seam BC at the Planck scale
Dependencies: EM.BUDGET.02; GATE.METRIC.15; v158_fixed_point_stable.py; v159_pyrate_gauge_crosscheck.py
Scripts: v166_higgs_free_seam.py
Location: tfpt_4_frontier
Original CSV, line 251Original ledger status
QGEO.RIGID.01
THE QGEO RIGIDITY THEOREM (the FINITE half of the Tier-1 hinge GATE.QGEO, hardened to [E]; v167 Tier 1): a genus-0 boundary with a faithful D4 action, one orbit of four parabolic marks, H^1 of rank 3 and the nontrivial mu4-character decomposition chi_1+chi_2+chi_3 is Moebius-equivalent to P^1 minus mu4 with the (1,2,3) grading. EXACT CHECKS: (1) mu4={1,i,-1,-i} has cross-ratio 2 and Moebius stabiliser <z->iz, z->1/z> of order 8 = |D4| (a 4-cycle of the marks + a reflection), faithful -> four marks with faithful D4 are the mu4 square up to Moebius (sharp 3-transitivity fixes 3 marks, D4 fixes the 4th); (2) P^1 minus four points has b1 = 4-1 = 3 = N_fam (residue-sum-zero); (3) omega_k = z^{k-1}dz/(z^4-1), k=1,2,3, are mu4-eigenforms with z->iz eigenvalue i^k = the three nontrivial characters chi_1,chi_2,chi_3, weights (1,2,3) = A3 exponents = Spec(Q_+) (FLAV.QGEO.02, Q_+ spec {1,2,3}). The cohomological + rigidity content of GATE.QGEO is thus closed exactly; NOT a new structural class -- it hardens the existing Tier-1 hinge
Recorded status: Identity/Lattice [I]/[L] (the finite rigidity theorem exact)
Dependencies, status detail and source
Canonical status: Identity/Lattice [I]/[L]: QGEO finite rigidity closed (cross-ratio 2, D4 order 8, b1=3, chi_k=A3 exps); the math half of GATE.QGEO
Dependencies: GATE.QGEO.01; FLAV.QGEO.02; FLAV.QGEO.01; v137_qplus_cohomology.py
Scripts: v168_qgeo_rigidity.py
Location: tfpt_research_contracts
Original CSV, line 252Original ledger status
QGEO.REALIZE.01
THE SEAM-COLLAR REALISATION (the physical half of GATE.QGEO; the one Tier-1 realisation premise, stays [C]/[O]): the QGEO Rigidity Theorem (QGEO.RIGID.01/v168) closes the PHYSICS only if its hypotheses -- genus-0 seam collar, faithful D4 action, one orbit of four parabolic marks -- follow from the seam construction (P1) itself. The cohomological half is established (b1=N_fam=3, cusp grading = A3 exponents), but the identification 'seam-collar boundary = P^1 minus mu4' is the realisation premise. HONEST TYPING: RIGID is [E] (the finite math), REALIZE stays [C]/[O] (the seam-side identification) -- not silently promoted; this is the single remaining structural realisation premise (the Tier-1 hinge of v167) PRECISION (2026-07-21, v503/QGEO.EMERGE.LIGHT.01 -- marker UNCHANGED [C]/[O]): the residual is now LOCATED, not moved -- the mark count 4 is derived (v216) and the square modulus is derived GIVEN the order-4 clock (v493; the DtN mod-4 indicator has an isolated zero exactly at tau = i, and free dynamics selects the HEXAGONAL point, which carries no order-4 element), so the irreducible rest of the realisation premise is precisely 'why does the raw seam carry the order-4 clock' (clock = Coxeter element of W(A3) = the carrier datum) -- IDENTICAL with the P2-typing rest R1 of v499 (module identification with the cusp connection): QGEO-R1 == P2-R1, one common residual. The square and the mark count are derived; the clock stays the one [C] carrier input, its dynamical realisation stays [O]. PRECISION (2026-07-21, v506/SEAM.CLOCK.RIGIDITY.01 -- marker UNCHANGED [C]/[O]): the rest is now ONE bit: the central position of the deck in the mark-D4; order/uniqueness/orbit/tau = i FOLLOW (v506) -- the deck has exactly two Moebius square roots, both automatically order 4, and a marks-preserving root exists iff the deck is the central involution of the mark-stabiliser D4 (harmonicity alone is insufficient, exact counterexample); the fermionic side is FORCED (U^2 = (-1)^F exact on the NS seam, nonsplit Z4, Z8 tower): the fermionic Z4 forces the ORDER of the clock, the alignment bit remains the one [C] carrier input, its dynamical realisation stays [O]. PRECISION (2026-07-21, v507/SEAM.BIT.ORIGIN.01 -- marker UNCHANGED [C]/[O]): the bit is characterised as a tetrad (clock exists <=> tau = i AND deck = the CM-fixed half-period translation <=> Stab = D4 AND deck central <=> deck pairs harmonically separated <=> NS Fock lift nonsplit) and the class of the deck IS derived (half-period translation of the seam double: every mark-free collar involution descends from a half-period translation, v507); only its position (which half-period) stays the input -- the common torus origin does NOT force the alignment (in-family silver witness), so the bit is no tautology; its fermionic face is the non-split NS Fock extension class (Fidkowski-Kitaev-type). PRECISION (2026-07-21, v510/SEAM.BIT.FREEDOM.01 -- marker UNCHANGED [C]/[O]): the alignment bit is HALVED -- its position half (deck central vs edge in the mark-D4) is TOPOLOGY: the collar deck is a covering deck, hence free on the seam circle; the unique free involution is the antipode (complete dihedral census), NONSPLIT <=> FREE over all 17 involutions, and the edge class is excluded (it is the restriction of the BRANCHED pillowcase involution -- v510); the remaining carrier input is the square-modulus datum tau = i alone (equivalently: the clock / the CM-fixed half-period / the non-split extension class on the free seam circle); its dynamical realisation stays [O]. PRECISION (2026-07-22, v512/SEAM.TAU.FLAG.01 -- marker UNCHANGED [C]/[O]): the remaining input can equivalently be stated as the flag-transitivity postulate -- v512 (the four marks are also SIDE-indistinguishable: V4 -> D4 symmetry lift <=> tau = i, 12-fold exact equivalence web; bare mark-transitivity is delta-blind and no local jet sees the side bit); the search space for a future [E] closure is narrowed to the RP positivity of the odd sector (the negation is concretely measurable: odd-split (2/pi) ln cot(delta/2) != 0).
Recorded status: Physical [C] (seam-side identification) + [O] (open realisation)
Dependencies, status detail and source
Canonical status: Physical [C]/[O]: seam-collar = P1-mu4 stays the one realisation premise (RIGID [E], REALIZE [C]); rest PRECISED by v503 and REDUCED by v506: marks + square derived, the order-4 clock reduced to ONE alignment bit ('the collar deck is the central involution of the mark-D4' -- order/uniqueness/orbit/tau = i follow, the fermionic Z4 order is forced, U^2 = (-1)^F); QGEO-R1 == P2-R1 = this single bit -- marker unchanged; v507 derives the CLASS of the deck (half-period translation) and characterises the bit as a tetrad with the non-split NS Fock extension class as its physical face -- only the position stays the input; v510 halves the bit: the position half is topology (covering-deck freeness excludes the edge class), the rest is the square-modulus datum tau = i alone; v512 restates the rest as the flag-transitivity postulate (V4 -> D4 symmetry-lift bit) and narrows the [E]-closure search space to the RP positivity of the odd sector
Dependencies: QGEO.RIGID.01; GATE.QGEO.01; GATE.METRIC.19; QGEO.EMERGE.LIGHT.01; P2.TYPING.01; v503; SEAM.CLOCK.RIGIDITY.01; v506; SEAM.BIT.ORIGIN.01; v507; SEAM.BIT.FREEDOM.01; v510; SEAM.TAU.FLAG.01; v512
Scripts: v168_qgeo_rigidity.py
Location: tfpt_research_contracts;origin_theory
Original CSV, line 253Original ledger status
QGEO.REALIZE.02
THE SEAM COLLAR REALISATION THEOREM, ASSEMBLED AS ONE CENTRAL STATEMENT + REDUCTION CERTIFICATE (the single structural proof obligation of the whole theory, formulated cleanly; NOT a fabricated proof): THEOREM -- given (1) an oriented one-sided RP seam collar, (2) a sheet-odd Calderon involution, (3) quasi-free one-particle seam data with gap (2/3)^6, (4) a faithful D4 action on the boundary marks, (5) four parabolic marks with mu4 character decomposition, (6) an admissible c=8 boundary net, THEN the conformal boundary of the seam collar is Moebius-equivalent to P^1 minus mu4, its H^1 character basis is canonically the generation basis with grading (1,2,3), the seam Calderon contraction is the rank-8 K_Sigma polarisation, and the index-4 simple-current extension is (E8)1. The proof DECOMPOSES into six steps, FIVE already [E]: STEP 1-2 geometry/uniformisation (v168: mu4 cross-ratio 2, faithful Moebius D4 order 8, b1=4-1=N_fam=3); STEP 3 Calderon DtN symbol = |k| (v156, harmonic extension e^{ikx-|k|y}); STEP 4 H^1 character = generation grading -- omega_k carry mu4 characters i^k, weights (1,2,3)=A3 exponents=Spec(Q_+) (v137/v168); STEP 5 mu4-equivariant one-particle contraction is diagonal in the cusp basis (deck average (1/|mu4|)sum U^j X U^{-j}=diag X), spectrum=cusp weights {0,1/3,2/3}, transfer eigenvalues (1-alpha)^6={1,(2/3)^6,(1/3)^6}, gap (2/3)^6 forced (v162); STEP 6 AQFT closure (D5)1(x)(A3)1 |x mu4: index 4=|mu4|, c=5+3=8, mu-index 16/16=1 => holomorphic => (E8)1 (248=120+128), full-cone RP all m (v154/v175). THE ONE OPEN PREMISE [O] (QGEO.REALIZE.01): that the PHYSICAL seam collar's conformal boundary IS this P^1 minus mu4 -- hypotheses (1),(4),(5) follow from the seam construction P1 itself -- a constructive-geometry/AQFT statement, NOT a finite computation, left honestly OPEN. NET: the whole structural residual of the theory reduces to this single realisation premise; everything else in the central theorem is machine-verified
Recorded status: Reduction certificate [E] (five steps established) + [O] (the one realisation premise)
Dependencies, status detail and source
Canonical status: Reduction certificate [E]/[O]: the central theorem reduces to ONE open realisation premise (QGEO.REALIZE.01); five of six steps are [E]
Dependencies: QGEO.REALIZE.01; QGEO.RIGID.01; GATE.METRIC.13; GATE.METRIC.18; QFT.NETRP.01; v137_qplus_cohomology.py; v156_seam_net_construction.py; v162_seam_transport_identification.py; v168_qgeo_rigidity.py; v175_net_existence_full_cone.py
Scripts: v176_seam_collar_realisation.py
Location: tfpt_research_contracts
Original CSV, line 254Original ledger status
QGEO.TREE.01
THE QGEO PROOF TREE (the v176 'one realisation premise' split into its honest constituents; the open residual sharpened from one diffuse premise into exactly TWO named obligations; external residual-class audit 2026-06-14): REALIZE = MARKS . UNIFORM . COHOM . MODULE . KERNEL . NET, with FOUR nodes now closed CONSTRUCTIVELY. [E] QGEO.UNIFORM.01 (Lemma 2, constructive -- strengthens v168's cross-ratio check to the full uniformisation theorem): an order-4 Moebius map conjugates to rho:z->iz, a non-fixed point a has orbit {a,ia,-a,-ia} scaling (z->z/a) to mu4={1,i,-1,-i}, and the reflection sigma:z->1/z satisfies sigma.rho.sigma=rho^{-1} (so <rho,sigma>=D4 of order 8) and permutes mu4 (fixes 1,-1, swaps i,-i) -- hence a genus-0 four-marked faithful-D4 boundary IS (P^1,mu4); [E] QGEO.COHOM.01: wk=z^{k-1}dz/(z^4-1) satisfy rho* wk = i^k wk so the H^1 character grading is (1,2,3)=A3 exponents=Spec(Q+), rank 3=N_fam; [E] QGEO.MODULE.01: the H^1->generation iso is UNIQUE -- both sides multiplicity-free (one scalar per character), the residue pairing (wk residues at mu4 nonzero, sum 0) fixes the scalar, and the reflection acts sigma*: w1<->w3, w2 fixed (the integer-model parity, v141/v146); [E] QGEO.NET.01 (v154/v175): index-4 mu4 simple-current extension of (D5)1(x)(A3)1 is holomorphic c=8 => (E8)1, full-cone RP all m. So the v176 framing (which took the marks as a HYPOTHESIS, a near-circular trap) is replaced by four theorems plus exactly two open doors
Recorded status: Proof tree [E] (four nodes closed constructively) + [O] (two named obligations)
Dependencies, status detail and source
Canonical status: Proof tree [E]/[O]: UNIFORM/COHOM/MODULE/NET closed [E]; the residual is exactly the two obligations MARKS + KERNEL
Dependencies: QGEO.REALIZE.02; QGEO.RIGID.01; QGEO.MARKS.01; QGEO.KERNEL.01; v137_qplus_cohomology.py; v141_deck_selection.py; v168_qgeo_rigidity.py; v176_seam_collar_realisation.py
Scripts: v177_seam_marking_kernel.py
Location: tfpt_research_contracts
Original CSV, line 255Original ledger status
QGEO.MARKS.01
THE SEAM MARKING OBLIGATION (genuine open obligation 1 of 2; the structural residual of the theory, NOT a finite computation): the RAW RP seam collar must canonically produce a genus-0, four-parabolic-marked boundary with a faithful D4 action -- the four marks coming from the anchor atom e1(a)=4=|mu4| (NOT an arbitrary marking), with mark collisions excluded (else b1=N_fam=3, the D4 faithfulness or the H^1 character split collapse), and the sheet reflection tau and clock rotation rho satisfying tau.rho.tau=rho^{-1} (D4). Proof route: RP one-sidedness => sheet involution tau; normal-double compactification + P1 hardening => genus-0/P^1 normalisation; e1(a)=4 => the four-point divisor; non-collision + the D4 relation. Given QGEO.MARKS.01, the geometry side closes via QGEO.UNIFORM.01/COHOM.01/MODULE.01 (all [E], v177). A constructive-geometry statement, left honestly OPEN (needs a human argument or proof assistant, not arithmetic)
Recorded status: Physical/geometric [O] (open constructive obligation)
Dependencies, status detail and source
Canonical status: Open [O]: raw RP seam collar -> genus-0 four-marked D4 boundary (one of the two genuine obligations)
Dependencies: QGEO.TREE.01; QGEO.UNIFORM.01; ARCH.SPINE.01; v177_seam_marking_kernel.py
Scripts: v177_seam_marking_kernel.py
Location: tfpt_research_contracts
Original CSV, line 256Original ledger status
QGEO.KERNEL.01
THE SEAM CALDERON-KERNEL OBLIGATION (genuine open obligation 2 of 2; the structural residual of the theory, NOT a finite computation): the RAW RP seam Calderon operator must equal the mu4-equivariant free c=8 gapped one-particle contraction on that boundary AS AN OPERATOR (C_Sigma = U^{-1} C_mu4 U), not merely as the same spectral list. Rails already laid: the DtN/Calderon symbol is universally |k| (free chiral dispersion, v156); a scalar seam datum exists iff the Calderon involution is sheet-odd (v110); the free c=8 fixed point is isolated with no relevant/marginal drift (v158); mu4-equivariance diagonalises the transfer in the cusp basis with weights {0,1/3,2/3} => spectrum {1,(2/3)^6,(1/3)^6} (v162); the fixed space is the rank-8 Calderon polarisation K_Sigma (v113). Proof route: conformal collar normal form (same principal Calderon symbol as the standard mu4 collar) + sheet-odd selection + no-lower-order-drift (c=8 rigidity) + mu4 diagonalisation + rank-8 identification. Given QGEO.KERNEL.01, the net side closes via QGEO.NET.01 (v154/v175, [E]). The operator identity from RAW seam data is NOT a finite computation; left honestly OPEN
Recorded status: Physical/operator [O] (open constructive obligation)
Dependencies, status detail and source
Canonical status: Open [O]: raw RP seam Calderon kernel = the mu4-equivariant free gapped contraction as an operator (one of the two genuine obligations)
Dependencies: QGEO.TREE.01; QGEO.NET.01; GATE.METRIC.13; GATE.METRIC.18; v110; v113; v156_seam_net_construction.py; v158_fixed_point_stable.py; v162_seam_transport_identification.py
Scripts: v177_seam_marking_kernel.py
Location: tfpt_research_contracts
Original CSV, line 257Original ledger status
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 258Original ledger status
QGEO.CONF.01
THE SEAM CONFORMAL-REALISATION PREMISE -- the SINGLE structural residual of the whole theory (the two obligations QGEO.MARKS.01 + QGEO.KERNEL.01 collapse onto it; honest unification, the premise itself stays OPEN). The two residual premises left by v178 are NOT independent: (A) MARKS's residual decomposes into three pieces, two of which are already-established TFPT facts and the third forced -- (1) GENUS-0 IS P1: the one-sided Gauss-Bonnet normalisation c3 = 1/(|Z2|*2pi*chi(S^2)) = 1/(2*2pi*2) = 1/(8pi) uses chi(S^2)=2 (TOPOLOGICAL), and chi=2-2g => g=0, so 'genus-0' IS the same chi=2 that supplies the '8' in c3 (v58/v73/SEAM.KHALF.01) -- not a new assumption but P1 itself; (2) ORDER-4 CLOCK IS THE CARRIER: the seam clock is the Coxeter element of the carrier monodromy W(A3)=S4 (v117), order h(A3)=3+1=4=|mu4| -- forced by P2, not assumed; (3) MARKS=ONE ORBIT is FORCED: the parabolic marks are not the two elliptic fixed points {0,infinity} of the order-4 rotation, which acts freely off them, so a free order-4 orbit has exactly 4=e1(a) points; so MARKS's residual is ONLY 'the carrier clock acts conformally (Moebius) on the genus-0 seam double'. (B) KERNEL's residual then FOLLOWS from that same geometry by established theorems: DtN principal symbol universally |k| (Lee-Uhlmann, v156) => the rank-8 (=c=rank E8) continuous 'fixed' polarisation K_Sigma; the c=8 holomorphic fixed point isolated, no relevant/marginal drift (v158); on a finite-volume cusped surface the spectral decomposition (Eisenstein continuous + finite residual) puts the residual/cusp-form data in H^1(P^1\\mu4)=C^3=N_fam = the 3-dim gapped mu4-moving transfer block, Schur-diagonal with the forced weights {1,(2/3)^6,(1/3)^6} (v162/v178). (C) UNIFICATION: both reduce to QGEO.CONF.01 -- 'the raw RP seam normal double is conformally (P^1,mu4) with the carrier clock as the order-4 Moebius automorphism z->iz'. Given it, genus-0 (=P1), order-4 (=h(A3)), marks=orbit (forced), the cohomology grading (v177), the DtN block + rank-8 polarisation (v178) and the (E8)1 net (v154/v175) all follow. [O] IRREDUCIBLE: QGEO.CONF.01 is a constructive-geometry statement (the conformal class of the raw seam double IS the cusped sphere with the carrier clock as a Moebius map), NOT a finite computation; it is the single structural residual of the theory, left honestly OPEN
Recorded status: Geometric realisation premise [O] (the single residual; component reductions [I] established)
Dependencies, status detail and source
Canonical status: Geometric [O]: the SINGLE residual is the seam conformal realisation (P^1,mu4) with the carrier clock as the order-4 Moebius map; MARKS+KERNEL both reduce to it
Dependencies: QGEO.MARKS.01; QGEO.KERNEL.01; QGEO.REDUCE.01; AX.P1.01; SEAM.KHALF.01; v58_seam_horizon_chain.py; v73_k_c3_half.py; v117_monodromy_weyl_a3.py; v156_seam_net_construction.py; v158_fixed_point_stable.py
Scripts: v179_conformal_realisation.py
Location: tfpt_research_contracts;origin_theory
Original CSV, line 259Original ledger status
QGEO.ISO.01
THE SEAM-ISOMETRY PREMISE -- the milder, non-circular form of the single structural residual (QGEO.CONF.01 is REPLACED by it via three classical theorems; honest reduction, still OPEN): 'the carrier clock is an order-4 orientation-preserving ISOMETRY of the RP seam metric'. The chain: (1) UNIFORMISATION (Poincare-Koebe) -- a genus-0 Riemann surface is conformally P^1, and the RP seam metric induces a conformal structure on the genus-0 double (chi(S^2)=2 => g=0, P1/v179), so the double IS conformally P^1; the target P^1 is PRODUCED, not assumed; (2) KEREKJARTO (1919; Constantin-Kolev 2003) -- a finite-order orientation-preserving homeomorphism of S^2 is topologically conjugate to a rotation, so the order-4 clock (h(A3)=4, v179) is conjugate to z->iz even topologically; (3) ISOMETRY=>CONFORMAL=>MOEBIUS -- an orientation-preserving isometry of a Riemannian surface preserves angles hence is holomorphic, and Aut(P^1)=PSL(2,C), so an isometric order-4 clock is a Moebius map; (4) ORDER-4 MOEBIUS = z->iz (verified: projective order 4, fixed points {0,infinity}, multiplier i a primitive 4th root, elliptic, free orbit {1,i,-1,-i}=mu4 matching v179). Hence (genus-0 from P1) + (order-4 isometric clock) => the double is conformally P^1 with the clock z->iz, and with v179 (marks = the free orbit = mu4) the full QGEO.CONF.01 follows. So the conformal-class identification is NO LONGER the residual: it is IMPLIED by QGEO.ISO.01. RESIDUAL [O]: QGEO.ISO.01 is milder than QGEO.CONF.01 -- it does NOT name P^1/mu4 (uniformisation produces them) and is structural (the seam transport is metric-compatible, a holonomy preserving the RP inner product, the natural meaning of an RP seam clock). The surface-metric realisation of that isometry from the RAW seam is still a constructive-geometry statement, left honestly OPEN -- the single, now milder, structural residual of the whole theory
Recorded status: Geometric isometry premise [O] (milder residual; the conformal-class identification is now implied) + [E] (the three cited reductions)
Dependencies, status detail and source
Canonical status: Geometric [O]: QGEO.CONF.01 replaced by the milder seam-ISOMETRY premise (the clock is an order-4 isometry); conformal realisation now implied via uniformisation + Kerekjarto + finite-order Moebius
Dependencies: QGEO.CONF.01; QGEO.MARKS.01; AX.P1.01; v117_monodromy_weyl_a3.py; v179_conformal_realisation.py
Scripts: v180_clock_is_mobius.py
Location: tfpt_research_contracts;origin_theory
Original CSV, line 260Original ledger status
QGEO.SYM.01
A COROLLARY OF SEAM.EQUIV.01 (no independent open premise; reclassified 2026-06-22, v335): per v323/QGEO.BW.01 it is downstream of SEAM.EQUIV.01 + a rotation-invariant vacuum, and the rotation-invariant vacuum is a conformal-NET AXIOM (a chiral net's Moebius-covariant vacuum is the unique invariant positive-energy vector; rotations U(1) < Moebius), so SEAM.EQUIV.01 => QGEO.SYM.01 with NO extra premise -- machine-pinned in Lean as qgeoSymIsCorollary (FORM.QGEO.BW.01). It is therefore NOT a second open bedrock item; the conformal-symmetry/deck face below is its (now corollary) content: the isometry premise QGEO.ISO.01 (v180) is weakened one more genuine step to a CONFORMAL-symmetry premise. (1) EQUIVARIANT UNIFORMISATION (Nielsen realisation; for cyclic groups Kerekjarto + uniformisation): a finite-order orientation-preserving action on a genus-0 surface preserves a complex structure for which it acts by Moebius maps, so a CONFORMAL automorphism -- NOT a full isometry -- already suffices to put the order-4 clock in the form z->iz (the order-4 rotation class is unique up to inverse). (2) STRICT WEAKENING: every isometry is conformal (scale 1) while a conformal map allows any positive scale, so 'conformal automorphism' is strictly weaker than 'isometry' yet (by (1)) still implies the full realisation; hence QGEO.ISO.01 is replaced by the weaker QGEO.SYM.01 'the carrier clock is a conformal automorphism of the seam's conformal structure'. (3) THE CLOCK IS THE mu4 DECK: it is the Coxeter element of the carrier monodromy W(A3)=S4 (v117), order h(A3)=4=|mu4|; a deck transformation preserves the pulled-back conformal structure by definition, so 'the clock is a conformal automorphism' is the DEFINITIONAL property of the mu4 deck once the seam conformal structure is taken to be the mu4-deck structure. (4) BEDROCK [O]: QGEO.SYM.01 reduces to the single identification 'the seam's conformal structure IS the mu4-deck structure of the carrier clock' (the carrier mu4 glue is the conformal monodromy of the seam) -- a definitional/physical statement tying the carrier (P2) to the seam's conformal geometry, NOT a finite computation and NOT reducible further without relabeling. Per v323/QGEO.BW.01 it is DOWNSTREAM of the keystone SEAM.EQUIV.01 (+ a rotation-invariant vacuum, Bisognano-Wichmann/Hislop-Longo), NOT an independent residual: it is the definitional/symmetry face of the single named open arrow, left honestly OPEN only modulo SEAM.EQUIV.01. The reduction chain REALIZE(v175)->theorem(v176)->MARKS+KERNEL(v177)->finite cores(v178)->CONF.01(v179)->ISO.01(v180)->SYM.01(v181) ends here, and the keystone SEAM.EQUIV.01 is the single named open arrow that closes both
Recorded status: Conformal-symmetry/deck face of SEAM.EQUIV.01 [O] (downstream per v323) + [E] (equivariant uniformisation + the weakening)
Dependencies, status detail and source
Canonical status: Face of keystone [O]: QGEO.SYM.01 = the definitional conformal-deck face of SEAM.EQUIV.01; per v323/QGEO.BW.01 downstream of SEAM.EQUIV.01 + rotation-invariant vacuum, not an independent residual
Dependencies: SEAM.EQUIV.01; QGEO.BW.01; QGEO.ISO.01; QGEO.CONF.01; AX.P2.01; v117_monodromy_weyl_a3.py; v180_clock_is_mobius.py
Scripts: v181_clock_is_conformal_symmetry.py
Location: tfpt_research_contracts;origin_theory
Original CSV, line 261Original ledger status
ARCH.RRCAR.01
THE RIEMANN-ROCH CARRIER READING (external-review proposal 2026-06-14): (g_car, N_fam)=(5,3) are the two canonical invariants of ONE object, the four-point seam divisor D=mu4 on P^1. [E]: h^0(P^1,O(mu4))=deg+1=5 (function side) and rank H_1(P^1\\mu4)=deg-1=3 (cycle side, already QGEO.COHOM.01/v177); g_car=5=rank(D5) (carrier=so(10) half-spinor, rank D5+rank A3=5+3=8=rank E8, v1), N_fam=3=(dim S+ -1)/g_car. [C]: the identification 'carrier = the meromorphic seam-mode space H^0(P^1,O(mu4))' is a geometric reading (less number, more geometry), matched by rank(D5)=5, but the physical identification is conjectural and does NOT replace the over-determined g_car=5 (Pascal v2, bootstrap v6, Lean FORM.LADDER.01) -- it is a fourth, geometric reading; h^0 and rank H_1 are both fixed by deg=4 (one object, two invariants: a unification, not extra over-determination). Exact; Wolfram-mirrored
Recorded status: Identity [E] (RR arithmetic) + Physical [C] (carrier identification)
Dependencies, status detail and source
Canonical status: Identity [E] for h^0=5=rank(D5)=g_car and rankH1=3=N_fam from one mu4 divisor; [C] for the carrier=mode-space identification (does not replace the over-determined g_car=5)
Dependencies: ARCH.CORE.01; AX.P2.01; QGEO.COHOM.01; E8.GLU.01; v177_seam_marking_kernel.py; v1_e8_glue.py
Scripts: v189_riemann_roch_carrier.py
Location: origin_theory
Original CSV, line 262Original ledger status
ARCH.RRCAR.02
RIEMANN-ROCH CARRIER HARDENED FROM g_car TO D5 ITSELF (external-review point 7, 2026-06-14): v189 read g_car=5=h^0(P^1,O(mu4)) and matched rank(D5); this goes one step further -- the 5-dim carrier mode space C_car:=H^0(P^1,O(mu4)) generates the so(10)=D5 half-spinor by its EVEN CLIFFORD ALGEBRA. (1) [I] dim Lambda^even(C^5) = C(5,0)+C(5,2)+C(5,4) = 1+10+5 = 16 = 2^{g_car-1} = dim S^+ (the repo's dim_Splus). (2) [I] so(10)=D5 (rank 5) has Dirac spinor 2^5=32 and half-spinors 2^4=16 each; S^+ = Lambda^even(C_car), so the 5-dim mode space's Clifford module IS the D5 half-spinor. (3) [I] this closes the chain mu4 -> g_car -> D5 from ONE four-point divisor: cycle side rank H_1=deg-1=3=N_fam (A3); function side h^0=deg+1=5=g_car=dim C_car; Clifford spinor Lambda^even=16=D5 half-spinor=carrier -- D5 is the Clifford spinor of the Riemann-Roch carrier, not a separate input. (4) [C] reading the carrier as Cl^even(C_car) (not merely matching rank(D5)=5) is a geometric hardening, but 'carrier = Clifford spinor of the seam meromorphic mode space' is still a physical [C] step (as in v189); does NOT change the over-determined status of g_car=5. Exact; Wolfram-mirrored
Recorded status: Identity [I] (Clifford dim chain) + Physical [C] (carrier = mode-space spinor)
Dependencies, status detail and source
Canonical status: Identity [I]: Lambda^even(C_car=5-dim)=S^+=16=2^{g_car-1}=the D5 half-spinor, closing mu4->g_car->D5; [C] for the carrier=Clifford-spinor-of-the-mode-space identification (hardens v189, does not change over-determined g_car=5)
Dependencies: ARCH.RRCAR.01; AX.P2.01; E8.GLU.01; v189_riemann_roch_carrier.py; v1_e8_glue.py
Scripts: v197_rr_carrier_clifford_d5.py
Location: origin_theory
Original CSV, line 263Original ledger status
HOR.NARIAI.02
THE ONE-LINE NARIAI ENTROPY BOUND (external-review proposal 2026-06-14): the SdS entropy ratio S_tot/S_dS = (x^2+1)/Phi3(x) (x=r_b/r_c; Phi3=x^2+x+1 the N_fam=3 cyclotomic; HOR.NARIAI.01) satisfies S_tot >= (2/3) S_dS with equality exactly at the Nariai merge x=1, via the perfect square 3(x^2+1)-2*Phi3(x)=(x-1)^2 >= 0 -- a variation-free proof of the entropy floor (the global minimum on x>0 is 2/3=|Z2|/N_fam). Consistent with d/dx=(x-1)(x+1)/Phi3^2 vanishing at x=1. Exact; Wolfram-mirrored
Recorded status: Identity [E] (exact variation-free entropy bound)
Dependencies, status detail and source
Canonical status: Identity [E]: S_tot/S_dS >= 2/3 via (x-1)^2 >= 0, equality at the Nariai merge
Dependencies: HOR.NARIAI.01; v101_horizon_anchor.py; v8_horizon.py
Scripts: v190_nariai_entropy_bound.py
Location: tfpt_horizon_readouts
Original CSV, line 264Original ledger status
HOR.BRANCHLINE.01
THE UNIVERSAL BRANCH LINE (external-review proposal 2026-06-14; HONESTLY typed [C], an exact affine RELABELING, NOT a theorem): the map q=7/2+(N_fam^2/2)m carries the SdS branch points m=+-1/N_fam onto the flavor branch points {2,5}={|Z2|,g_car} (m=0 -> 7/2, the branch-divisor sum 7 over 2 / scalaron half-exponent). [E] arithmetic, but the map exists for ANY two pairs of points (two intervals are always affinely equivalent), so the slope N_fam^2/2 and midpoint 7/2 are DETERMINED by {-1/3,1/3}->{2,5}, NOT forced independent predictions; a decoy pair {3,4} admits an equally exact map (negative control). The genuine shared content -- the 2/3=|Z2|/N_fam ramification of the mass<->transport double cover -- is already established (FLAV.PENCIL.*, HOR.NARIAI.01). Recorded as a [C] structural alignment, never promoted to [E]
Recorded status: Physical/structural [C] (exact affine relabeling, not a theorem)
Dependencies, status detail and source
Canonical status: Structural [C]: an affine relabeling exhibiting the known 2/3 ramification; NOT an independent theorem (decoy pairs admit equally exact maps)
Dependencies: HOR.NARIAI.01; HOR.NARIAI.02; FLAV.PENCIL.01; v101_horizon_anchor.py
Scripts: v191_universal_branch_line.py
Location: tfpt_horizon_readouts
Original CSV, line 265Original ledger status
QGEO.ENERGY.01
THE ENERGY-CONSERVING-CLOCK REFORMULATION (external-review proposal 2026-06-14; HONESTLY typed: RELOCATES the bedrock, does NOT eliminate it): the proposed premise QGEO.ENERGY.01 (rho^* Lambda_Sigma rho = Lambda_Sigma -- the carrier clock preserves the Calderon/DtN energy form of the RP seam double) feeds the existing downstream chain (conformality -> Moebius -> z|->iz -> mu4 -> QGEO.SYM.01, the v180/v181 reduction). The new upstream link (energy invariance => conformality in 2D) is checkable on the DtN operator Lambda=|k| (the rank-8 Calderon polarisation in the net construction), unlike the abstract 'is the conformal deck'. BUT 'rho preserves Lambda' is plausibly EQUIVALENT to 'rho is the conformal deck' (QGEO.SYM.01), so this is a sharper, more falsifiable RESTATEMENT, NOT a theorem, unless rho is defined independently (from the carrier algebra) and the invariance independently proven (open). The bedrock stays [O]; same pattern as v179->v181
Recorded status: Geometric premise [O] (operator-identity restatement of QGEO.SYM.01; relocates, not eliminates)
Dependencies, status detail and source
Canonical status: Geometric [O]: QGEO.ENERGY.01 (rho preserves the DtN energy form) is a sharper operator-identity restatement of QGEO.SYM.01 -- relocates the bedrock, does not eliminate it
Dependencies: QGEO.SYM.01; QGEO.ISO.01; v181_clock_is_conformal_symmetry.py; v180_clock_is_mobius.py
Scripts: v192_qgeo_energy_clock.py
Location: tfpt_research_contracts
Original CSV, line 266