Original ledger status
HOR.NARIAI.01
THE MAXIMAL BLACK HOLE IS THE ANCHOR (carrier-in-the-bulk surface; Schwarzschild-de Sitter in seam units): (1) NARIAI = ANCHOR - at M_N = 1/(N_fam sqrt(L)) the horizon cubic is t^3-3t+2 = (t-1)^2(t+2), roots (1,1,-2) = the traceless projection of the anchor a=(1,1,2) (coefficients (-3,2) = (-N_fam,|Z2|); cf chi_a = (t-1)^2(t-2), ARCH.CORE.01). (2) the Koide 2/3 IS the Nariai entropy bound: S/horizon = S_dS/N_fam, total = (|Z2|/N_fam) S_dS, deficit S_dS/3; interpolation S_tot/S_dS = (x^2+1)/Phi_3(x), monotone, min at the merge. (3) three-sheet conservation pi sum r_i^2 = |Z2| S_dS for every M. (4) Koide-form quotient of the three roots ranges [3/8,1/2] = the two nonzero SU(4)_1 weights (pure dS -> 1/2 = delta; Nariai -> 3/8 = p2(a)/e1(a)^2). (5) mass-line double cover disc ~ (1-3m)(1+3m): branch +-1/N_fam, separation 2/3; deck = horizon swap (gravitational twin of the sheet Z2). (6) temperature lemma |kappa_b/kappa_c| = (2x+1)/(x(x+2)) > 1: evaporation flows AWAY from the merge - anchor point = repeller, democratic endpoint = attractor (same orientation as the flavor flow, FR.KOIDE.04) [audit]. (7) seam-unit mechanics: dM = c3 kappa dA, Smarr 2c3, Bekenstein 1/(4c3), P_H = c3/(1920 M^2) (=|W(D5)|, HOR.01), lifetime 5120 pi M^3 = 128 g_car M^3/c3 (128 = 2^7 = dS prefactor), Kerr A_ext = M^2/c3 (ratio 1/2 = 1/|Z2|, S_ext: 1/4 = 1/|mu4|), area quantum 4 ln3 = ln(N_fam^4) = ln(disc of the flavor cover) [P as HOR.QNM]. Six independent landings on already-load-bearing atoms, zero free parameters; lifetime/power normalisations are standard photon/geometric-optics conventions (external); carrier-in-the-bulk reading [P]; structure surface, not a measurement surface (M_N today ~1e22 M_sun)
Recorded status: Identity [I] (exact GR arithmetic on compiler atoms) + Physical [P] (bulk reading)
Dependencies, status detail and source
Canonical status: Identity: six atom landings in SdS mechanics; bulk reading [P]
Dependencies: AX.P1.01; ARCH.CORE.01 (anchor); FLAV.PENCIL.03 (cover); FR.KOIDE.04 (orientation); HOR.01; GATE.METRIC.07 (SU(4)_1 weights)
Scripts: v101_horizon_anchor.py
Location: tfpt_horizon_readouts;origin_theory;tfpt_2
Original CSV, line 184Original ledger status
HOR.TRISECT.01
TRISECTION NORMAL FORM (the canonical coordinate of the SdS moduli line; answers the HOR.ORIENT.01 curvature-matching question at the geometric level): the horizon cubic is uniformized by ANGLE TRISECTION - r = 2cos(theta) gives r^3-3r = 2cos(3theta) exactly, cubic <=> cos(3theta) = -3m; centered angle psi: m = cos(psi)/N_fam, Nariai psi=0, pure dS psi=pi/2; deck involution psi->-psi (= the x->1/x deck of HOR.NARIAI.01), Z3 trisection rotation = the triality deck (GATE.QGEOM.03/v72 cross-ref). NORMAL FORM [I]: sigma(psi) = S_tot/S_dS = 4/3 - (2/3)cos(2psi/3) - mean |mu4|/N_fam, amplitude |Z2|/N_fam, frequency |Z2|/N_fam: one cosine, every constant a glue atom. CANONICAL CURVATURE [I]: sigma''(0) = 8/27 = (2/3)^3 = (|Z2|/N_fam)^N_fam - the Koide constant to the family power. INVARIANT BASE SLOPE [I]: dsigma/dm|_Nariai = -8/9 = -rank(E8)/N_fam^2 (coordinate-invariant, cross-checked in both coordinates; generally -(4/3)sin(2psi/3)/sin(psi)); dimensionful dS_tot/dM|_N = -r_N/(N_fam c3). BRIDGE [P]: flavor multiplier (2/3)^{2N_fam} is a RATE, gravity curvature (2/3)^{N_fam} is a CURVATURE - same base 2/3 = |Z2|/N_fam, exponent ratio |Z2|; the full identification needs the gravity-side CLOCK (near-Nariai evaporation generator), the same missing-object class as P2's continuous transfer generator: one clock, two known geometries. No open gate closed; figure trisection.pdf
Recorded status: Identity [I] (uniformization, normal form, curvature, slope) + Physical [P] (clock bridge)
Dependencies, status detail and source
Canonical status: Identity: one cosine of glue atoms; canonical curvature (2/3)^N_fam; clock [P]
Dependencies: HOR.NARIAI.01; HOR.ORIENT.01; FR.KOIDE.04 (rate); GATE.QGEOM.02 (triality)
Scripts: v103_trisection_normal_form.py
Location: tfpt_horizon_readouts
Original CSV, line 186Original ledger status
HOR.CLOCK.01
THE CLASSICAL NARIAI CLOCK IS THE ANCHOR (third appearance) + honest (2/3)-test (executes the HOR.TRISECT.01 clock question at the classical level): STATIC PIN [I] - phi(rho) = rho solves d/drho[(1-L rho^2)phi'] = -2L phi EXACTLY on the dS2 static patch, so the exact SdS family itself pins the S^2-radius modulus mass m^2 = -2L = -|Z2|L (the Laplace-type form of the Nariai linearization is standard GR - Ginsparg-Perry 1983 / Bousso-Hawking 1997 - typed external; the VALUE is pinned internally). Horizon split linear in the canonical angle, coefficient 1/sqrt(N_fam) [I]. GINSPARG-PERRY TOWER [I]: (l(l+1)-2)L has exactly ONE negative mode -|Z2|L (l=0), zero modes l=1. THE CLOCK [I]: in Hubble units chi_clock(lambda) = lambda^2+lambda-2 = (lambda-1)(lambda+2) = THE ANCHOR QUADRATIC; eigenvalues {1,-2} = the distinct anchor roots; Nariai cubic = (t-1) x chi_clock - the anchor appears as configuration roots (HOR.NARIAI.01), curvature base (HOR.TRISECT.01) and clock spectrum; entropy-deviation rate = 2H = |Z2| x Hubble exactly [I]. HONEST (2/3)-TEST NEGATIVE for the classical clock: eigenvalues are integers (anchor roots), not (2/3)-powers; the 2/3-powers stay in the functional; the one-loop conversion curvature -> rate (quantum (anti-)evaporation) remains external [P] - the flavor-rate bridge is NOT closed; the seam variational principle now has exactly one missing object: the QUANTUM clock
Recorded status: Identity [I] (static pin, tower, clock spectrum, rate) + Physical [P] (quantum clock)
Dependencies, status detail and source
Canonical status: Identity: clock spectrum = anchor roots; quantum clock = the one [P]
Dependencies: HOR.TRISECT.01; HOR.ORIENT.01; HOR.NARIAI.01; ARCH.CORE.01 (anchor)
Scripts: v104_nariai_clock.py
Location: tfpt_horizon_readouts
Original CSV, line 187Original ledger status
HOR.CLOCK.06
THE CLOCK IS AN ENTROPY POWER LAW (the transfer eigenvalues are the Nariai entropy fractions to the hexagon power; the ring coupling is the fractional entropy deficit): (1) THE THREE ENTROPY LEVELS [I]: the established Nariai bookkeeping (HOR.NARIAI.01) has S/S_dS in {1, 2/3, 1/3} (pure dS; two-horizon total; single horizon - deficit S_dS/3 per step) - EXACTLY the complementary cusp weights 1 - n/N_fam. (2) THE CLOCK IS AN ENTROPY POWER LAW [I]: lambda_n = (S_n/S_dS)^{p2} = the frozen transfer spectrum {1, (2/3)^6, (1/3)^6}; rate(n) = p2 ln(S_dS/S_n) = {0, Delta, 6 ln 3} - hexagon-weighted log-entropy deficits; audit: exponent p2 = 6 = 2h reads as the two-point form of a weight h = 3 = N_fam operator (recorded, not claimed). (3) THE COUPLING IS THE ENTROPY DEFICIT [I] (triple identity): alpha = n/N_fam = the Mehta-Seshadri parabolic weight (GATE.UWALL.07/HOR.CLOCK.04) = 1 - S_n/S_dS = DeltaS_n/S_dS - the RPA insertion strength is the fractional entropy deficit of the SdS configuration: the coupling is not a free parameter in ANY of its three readings. (4) ORIENTATION CONSISTENCY [I]: weight 0 <-> pure dS (max entropy, rate 0: the stationary attractor); weight 2 <-> single horizon (lowest level, fastest decay) - monotone, the established repeller -> attractor orientation (FR.KOIDE.05/HOR.NARIAI.01/HOR.ORIENT.01). (5) R1 THERMODYNAMIC FORM [P] (recorded, not claimed): derive Gamma_n ~ (S_n/S_dS)^{p2} from the near-Nariai one-loop - a Gibbons-Hawking-type entropy power law with exponent = the hexagon size; the exponent (weight h = N_fam) is the remaining quantum content
Recorded status: Identity [I] (entropy-level + power-law + triple-coupling identities) + Physical [P] (derivation)
Dependencies, status detail and source
Canonical status: Identity: lambda = (S/S_dS)^p2; rate = p2 ln(S_dS/S); alpha = entropy-deficit fraction = parabolic weight; orientation consistent; R1 = Gibbons-Hawking power law
Dependencies: HOR.CLOCK.05; HOR.CLOCK.04; HOR.NARIAI.01; HOR.ORIENT.01; GATE.UWALL.07
Scripts: v129_entropy_power_law.py
Location: tfpt_horizon_readouts
Original CSV, line 214Original ledger status
HOR.CLOCK.07
THE BORN SQUARE (the amplitude weight is h = N_fam = half the zero-mode count; the clock exponent p2 = 2h is its Born square - the HOR.CLOCK.05 multiplicity and the HOR.CLOCK.06 weight are ONE object): (1) EXPONENT BOOKKEEPING [I]: in the standard collective-coordinate treatment each zero mode trades a Gaussian integral for a moduli factor ~ S^{1/2}; with n_zero = 6 the transition AMPLITUDE scales as A ~ (S/S_dS)^{n_zero/2} = (S/S_dS)^3 and the PROBABILITY is its Born square Gamma = |A|^2 = (S/S_dS)^6 = the HOR.CLOCK.06 entropy power law => h = n_zero/2 = 3 = N_fam and p2 = 2h: the weight audit is DERIVED from mode counting; the factor 2 between weight and exponent is the Born rule, nothing else. (2) THE THREE ARE THE SPHERE'S CONFORMAL DIRECTIONS [I]: the l = 1 scalar eigenspace on S^2 has dimension 2l+1 = 3 = the number of proper conformal Killing vectors of the sphere (gradients of the l = 1 harmonics; the classic zero modes of near-Nariai physics, Ginsparg-Perry/Bousso-Hawking class, external standard); the doubling x2 is the HORIZON PAIR = the SdS mass-line deck (HOR.NARIAI.01): n_zero = |Z2| x 3 = 6 = p2 - every factor an established object. (3) CONSISTENCY [I]: multiplicity (E8.GRADE.01) = exponent (HOR.CLOCK.06) = Born square of the amplitude weight; h = N_fam ties the clock's conformal weight to the family count - the same 3 counts generations and the sphere's conformal directions. (4) RESIDUE [P] (recorded, not claimed): justify the per-zero-mode S^{1/2} collective-coordinate normalisation on the Nariai instanton for exactly these six modes - a textbook-class computation; no exotic object remains in R1 (log = ring sum, power law = entropy fractions, exponent = Born-squared mode count)
Recorded status: Identity [I] (exponent bookkeeping + mode-count identities) + Physical [P] (measure normalisation)
Dependencies, status detail and source
Canonical status: Identity: h = n_zero/2 = N_fam; p2 = 2h (Born rule); 3 = proper CKVs of S^2; x2 = horizon pair; R1 residue = standard zero-mode measure
Dependencies: HOR.CLOCK.06; HOR.CLOCK.05; E8.GRADE.01; HOR.NARIAI.01
Scripts: v130_born_square.py
Location: tfpt_horizon_readouts
Original CSV, line 215Original ledger status
HOR.CLOCK.10
THE ZETA BUDGET, BOTH ROUTES COMPUTED EXACTLY (the reduced seam route carries pure anchor-ratio anomalies; the naive 4d route does not - the budget computation structurally selects the reduced seam reading): Euclidean Nariai = S^2 x S^2, so the temporal dS2 sector continues to the SAME unit sphere and both candidate routes are exactly computable. (1) THE REDUCED ROUTE [I]: each 2d sector carries the HOR.CLOCK.09 operator with zeta(0)|det' = -2/3; two sectors give budget = -4/3 = -e1/p0 = MINUS THE SEED GAIN (the second ARCH.TRIAD.01 ratio; the first, -2/3, is the per-sector share); the six zero modes split 3 + 3 across the two spheres - the sheet doubling of E8.GRADE.01/HOR.CLOCK.07 IS the two-sphere structure of Euclidean Nariai (= the horizon pair, HOR.NARIAI.01). (2) THE NAIVE 4D ROUTE [I]: with the standard unit-S2 heat expansion 1/t + 1/3 + t/15 (verified numerically) and the symmetric split L4 = (-Delta1 - 1) + (-Delta2 - 1): per-factor trace 1/t + 4/3 + (9/10)t => a2(4d) = (4/3)^2 + 2(9/10) = 161/45; zero modes (1,0)+(0,1) = 6; zeta(0)|det'4d = 161/45 - 6 = -109/45 (numerical continuation ~1e-8) - NO anchor-atom reading. (3) ROUTE DISCRIMINATION [I arithmetic + P reading]: reduced-route anomalies = pure anchor ratios (-2/3, -4/3: two of the three triad values); 4d-route anomaly = -109/45, not an atom => the zeta budget structurally favours the REDUCED seam reading, consistent with the theory's 2d-seam architecture throughout; typed as route-selection evidence, not proof. (4) REMAINING [P] (recorded): the graviton/ghost shares on S^2 x S^2 (Volkov-Wipf-class computation, external standard) complete the budget; both scalar-sector shares pinned exactly - the remaining work is a finite list of known heat coefficients
Recorded status: Identity [I] (exact heat-kernel arithmetic both routes + numerics) + Physical [P] (route reading + remaining shares)
Dependencies, status detail and source
Canonical status: Identity: reduced budget = -4/3 = -seed gain (per sector -2/3); 4d route = -109/45 no atom; zero modes 3+3 = horizon pair; route selection -> reduced seam reading
Dependencies: HOR.CLOCK.09; ARCH.TRIAD.01 (triad); E8.GRADE.01; HOR.NARIAI.01
Scripts: v133_zeta_budget.py
Location: tfpt_horizon_readouts
Original CSV, line 218Original ledger status
FLAV.DUAL.01
THE DUAL ANCHOR LEMMA (the inverse flavor response of the anchor IS the Nariai root; the third purely algebraic leg of the flavor-horizon bridge; external review 2026-06-12, validated): (1) THE DUAL ANCHOR [I]: d := a^T R^-1 = a^T L^-1 = (-1/2, -1/2, 1) with d.1 = 0, d.a = 1 and d = (3/2)(a - (4/3)1)^T - the normalised TRACELESS anchor - and (1,1,-2) = -2d: the inverse flavor response stores EXACTLY the Nariai double-root structure (HOR.NARIAI.01) up to sign and scale; the horizon is not glued on afterwards - it sits inside the flavor compiler as a dual invariant. (2) WHY INVARIANT [I] (Sherman-Morrison, exact): L = R + 6*1 e1^T gives v^T L^-1 = v^T R^-1 <=> v^T R^-1 1 = 0; R^-1 1 = (1,1,-1)/4 (denominator 5/2); a.(R^-1 1) = 0 - the anchor lies on the 2-plane of invariant covectors: the winding deformation lives in the democratic direction 1, which d annihilates. (3) CONTROL [I]: 1, e1 and n = (5,-9,6) do NOT lie on the invariance plane (1/4, 1/4, -5/2) - the membership is special, not generic. (4) THE DUAL NORMAL PAIR [I]: d (sheet normal: kills 1, dual to a, proportional to the Nariai root) and n (torsion normal: n^T R = (8,0,0), n^T L = (20,0,0), n.a = 8, n.1 = 2 = |Z2| cf. FLAV.DIAMOND.02) form the dual basis of the flavor boundary. (5) CONSEQUENCE [P] (recorded): third algebraic bridge leg (besides the shared spectrum HOR.CLOCK.04 and the entropy power law HOR.CLOCK.06); supports the reduced seam reading (HOR.CLOCK.10); the R4' selector programme (FLAV.H2.05) acquires a geometric target: derive the PAIR (d, n), not n alone
Recorded status: Identity [I] (exact dual-vector + Sherman-Morrison + controls) + Physical [P] (bridge reading)
Dependencies, status detail and source
Canonical status: Identity: a^T R^-1 = a^T L^-1 = Nariai root/(-2); invariance <=> orthogonality to R^-1 1; dual normal pair (d n); R4' target = the pair
Dependencies: HOR.NARIAI.01; FLAV.DIAMOND.02; FLAV.H2.05 (selectors); HOR.CLOCK.04; HOR.CLOCK.06
Scripts: v134_dual_anchor.py
Location: tfpt_2; tfpt_horizon_readouts
Original CSV, line 219Original ledger status
GATE.UWALL.10
THE DUAL-NORMAL SELECTOR ((d,n) pins R columnwise; the R4' residue is bounded; external review 2026-06-12, validated and sharpened): (1) COLUMN NORMAL FORM [I]: d.c_j = a_j and n.c_j = 8 delta_1j for the columns of R; the common kernel of (d,n) is the primitive vector (6,8,7) (audit: p_2, rank E8, scalaron-7), so within the address box {0..5}^3 each line contains at most one lattice point; brute-force census (216 per column): c_1 = (1,1,2) = a, c_2 = (3,5,5), c_3 = (0,2,3) are each the UNIQUE solution - R4' shrinks from a 6^9 matrix census (FLAV.H2.04) to three 1-of-216 column problems: (d,n) => R. (2) HONESTY [I]: K is NOT pinned directly (d^T K = (1,1/2,1), n^T K = (14,1,-6)); det K = 4 follows from R via the diamond (mu_4 wall, FLAV.SURF.01). (3) SPECTRAL NORMAL [I]: the zero mode of the exact anchor residue A0* (GATE.UWALL.07) is v = (-sqrt2,3,-sqrt5)/3 with signed squares = -(2,-9,5) = -(|Z2|, -N_fam^2, g_car); NEW ATOMS: ||v||^2 = 16/9 (numerator 16 = dim S+) and adj(A0*) = (2/9) P_v with 2/9 = |Z2|/N_fam^2 = the SdS entropy curvature (HOR.NARIAI.01). (4) SIGMA RELATIONS [I]: sigma.1 = -|Z2|, sigma.a = N_fam, n.sigma = 121 = ||Pl(K)||_1^2 (the v119 audit constant). (5) ORBIT CONTROL [I]: exact enumeration |W(A3)| = 24 (GATE.UWALL.09); the only real orbit images of sigma are its signed copies; NO image is proportional to n - the naive cofactor/orbit lift FAILS as the review predicted; the step sigma -> n is a genuine mechanism beyond the monodromy group. (6) R4' RESTATED [P] (recorded): derive the PAIR (d,n); then R is forced columnwise; d is structural (FLAV.DUAL.01), the residue is the derivation of n - bounded by the sigma relations and the negative orbit control
Recorded status: Identity [I] (column census + spectral normal + orbit control) + Physical [P] (restated programme)
Dependencies, status detail and source
Canonical status: Identity: (d n) => R columnwise (each column 1-of-216); A0* zero mode = -(2 -9 5) signed squares; n.sigma = 121; W(A3) orbit excludes the naive lift
Dependencies: FLAV.DUAL.01; GATE.UWALL.07; GATE.UWALL.09; FLAV.H2.04 (superseded census); FLAV.SURF.01; HOR.NARIAI.01
Scripts: v136_dual_normal_selector.py
Location: tfpt_research_contracts; tfpt_2
Original CSV, line 221Original ledger status
HOR.CLOCK.11
THE VOLKOV-WIPF FIREWALL (R1 typed closure: the external full-4d graviton/ghost value is pinned and the edge part is exactly two copies of the reduced seam budget; external values verified against arXiv:2506.02142 Table 4.1 which states agreement with Volkov-Wipf Nucl. Phys. B582 (2000) 313 = hep-th/0003081): (1) EXTERNAL DATUM [I typed external]: alpha_bulk = 22/45, alpha_edge = -8/3, alpha_PI = -98/45 for d = 3 (S^2 x S^2, 4d); arithmetic 22/45 - 8/3 = -98/45 exact; the review's arXiv citation 0204021 corrected to 0003081. (2) THE EDGE MATCH [I]: alpha_edge = -8/3 = 2 x (-4/3) - the external edge factor consists of TWO IDENTICAL COPIES (one per horizon) and the per-copy magnitude 4/3 = e_1/p_0 is EXACTLY the reduced seam budget of HOR.CLOCK.10 (= the seed gain; -2/3 per sector); the TFPT reduced route lands on the EDGE sector of the external bulk/edge split; the bulk 22/45 is the ideal graviton gas which the seam clock does not contain; two copies = the horizon pair = the sheet doubling (HOR.NARIAI.01; HOR.CLOCK.10's 3+3 zero-mode split). (3) FIREWALL ARITHMETIC [I]: -98/45 + 60/45 = -38/45 with 38 = 2*19; neither -98/45 nor -38/45 nor 22/45 is an anchor atom (census) - consistent with HOR.CLOCK.10 where the naive scalar 4d route (-109/45) was already non-atomic (different operator content: scalar split vs full graviton + ghosts + isometries, recorded). (4) TYPING DECISION [P] (recorded): R1 = the reduced zero-mode/RPA seam clock = an EDGE-sector object; the full 4d Volkov-Wipf determinant is the GRAVITY FIREWALL (its -98/45 absorbed in the mu_0/(Lambda G)^3 normalisation), not a TFPT atom; per-copy sign/orientation (the edge factor enters inverted) and the Lorentzian edge-mode reading stay [P]
Recorded status: Identity [I] (exact arithmetic vs external values) + Physical [P] (typing decision) + External (VW hep-th/0003081; arXiv:2506.02142)
Dependencies, status detail and source
Canonical status: Identity: -98/45 = 22/45 - 8/3 external; edge = 2 x reduced budget (-4/3); diff -38/45 no atom; typing: seam clock = edge object full 4d determinant = firewall
Dependencies: HOR.CLOCK.10; HOR.NARIAI.01; HOR.CLOCK.03-09 (the clock chain)
Scripts: v138_vw_firewall.py
Location: tfpt_horizon_readouts
Original CSV, line 223Original 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
REVIEW.MAP.01
THE FOUR EXTERNAL-REVIEW CONCERNS REDUCE TO THE TWO ALREADY-NAMED RESIDUALS + ONE DATA-ONLY ITEM (a careful 2026-06-14 review raised A mapping 2D->4D, B UV-gravity abstractness, C grammar-tuning/meta-look-elsewhere, D Koide Mobius flow; this maps them honestly): three reduce by the same discipline as v175-v181 onto {QGEO.SYM.01 (the seam realisation), F_transfer (the continuous transfer functor / missing dynamical principle)}, and the fourth is experiment-only. (A) MAPPING [I]/[C]: the readout integer is exact -- the Plucker norm 11 = sum_{k<=2}C(4,k) = 1+4+6 = dim S+ - g_car = 16-5 (the QBL-protected boundary state count, v174); the 2D->4D step is the holographic reduction (bulk measure -> seam-boundary measure, gap-decoupled G5, Delta_eff>0); so A = QGEO.SYM.01 + F_transfer, NOT a new gate. (B) UV GRAVITY [I]: the TFPT answer 'gravity is the geometric readout of the boundary' IS QGEO.SYM.01 (the seam conformal deck); B is the bedrock postulate itself, an identity not a new premise. (C) GRAMMAR TUNING [N]/[C]: the strongest honest defence -- the grammar is FROZEN pre-data (v84/REG.FREEZE.01), minimal (anchor a + pi), and OVER-DETERMINED (the same anchor a=(1,1,2) lands in >=6 mutually-independent not-selected-for structures: Nariai roots (1,1,-2) HOR.NARIAI.01; Coxeter-30=|Z2|N_fam g_car SEAM.CYCLE.01; spine tetrahedron {2,3,4,5} ARCH.SPINE.01; EM budget 41=a^T K a; seed 4/3=|mu4|/N_fam; c3=1/(2 e1(a) pi)); a look-elsewhere-resistant signature, but -- the review is correct -- the residual meta-risk falls only to out-of-sample data (JUNO/CMB-S4), never to argument. (D) KOIDE MOBIUS FLOW [I]/[C]: the Mobius nature is not arbitrary -- Aut(P^1)=PSL(2,C) is the Mobius group and the Koide/cusp flow lives on the deck P^1 minus mu4, so its generator is Mobius BY THE GEOMETRY; the non-integer flow time t~2.84 (FR.KOIDE.06) only locates the physical point; the missing QFT RG generator (the beta-function realising the orbit) IS F_transfer; so D = QGEO.SYM.01 + F_transfer, not a new gate. NET: A/B/D collapse onto {QGEO.SYM.01, F_transfer}; C is the single experiment-only meta-question. A unification of the concern structure, NOT a closure of the underlying premises (which stay [O]/[C], honestly)
Recorded status: Reduction map [I]/[C] (A/B/D reduce to the two named residuals; C is experiment-only)
Dependencies, status detail and source
Canonical status: Reduction [I]/[C]: external-review concerns A/B/D reduce to {QGEO.SYM.01; F_transfer}; C is data-only (JUNO/CMB-S4)
Dependencies: QGEO.SYM.01; FR.KOIDE.06; FR.ETAB.02; AUDIT.NULLMC.01; REG.FREEZE.01; QFT.FOCK.01; HOR.NARIAI.01; SEAM.CYCLE.01
Scripts: v182_reviewer_residual_map.py
Location: tfpt_5_redteam
Original CSV, line 281Open questions preserve their achieved subresults
Each research problem has its own scope. A resolved task does not close its whole physical parent. Historical tasks remain explicitly historical in the source record.
Future quotient and positive GNS reconstruction
What is determined by complete future behavior, and what additional positive word-kernel source is needed to reconstruct a cyclic operator realization?
- Resolved in scope: Future quotient from complete rRead result
- Resolved in scope: Conditional GNS reconstruction from supplied KRead result
- open: Select complete K from the original source
Historical: common source, state and event selection
Outside the active mathematical research program since the user's23Oct2026 decision. Historical question: Do the original principles derive a common physical source together with its state, dynamical events, and physically observed fields?
Seam connection and family action
Does the joint discrete theorem determine a concrete connection and a family coupling compatible with the determinant seam action?
- Resolved in scope: Separate classes from actual transportRead result
- open: Derive the common connection from the original source
Physical time and complete transfer
Do the original reflection/projector structures determine the full physical time generator and required field transfer?
- Resolved in scope: Reuse the sign-projector counterexampleRead result
- Resolved in scope: Reuse conditional full-transfer reconstructionRead result
- open: Identify the physical complete TFPT transfer
- Resolved in scope: Reuse complete collar reconstructionRead result
- Resolved in scope: Classify homogeneous GKLS embedding of the shared register familyRead result
- Resolved in scope: Decide every homogeneous GKSL logarithm of the fixed M4 channelRead result
Flavor ratio and absolute amplitude scale
Which flavor quantity is fixed on the derived discrete stratum, and which requires the continuous holonomy anchor?
- Resolved in scope: Reuse the derived flavor ratioRead result
- open: Determine the absolute holonomy amplitude
Alpha closure for fixed inputs
Which closure equation follows for a fixed seam projector, and which inputs still need justification?
- Resolved in scope: Separate root calculation from source selectionRead result
- open: Derive alpha inputs and Thomson transfer
- Resolved in scope: Establish the unique global positive rootRead result
Geometric flow and gravity normalization
Do common matter-only observations derive geometric horizon flow and the area response from the original gravity source?
- Resolved in scope: Record scope of fixed original functionalRead result
- open: Derive geometric modular response and area coefficient
Clocks and complete neutral source response
Which complete quadratic response can the actual clock images reconstruct?
- Resolved in scope: Reconstruct all neutral quadratic matrix directionsRead result
- open: Derive physically admissible probe access
Clock action on charge, time and quarter transition
How does the actual Gaussian J act on the complete marked source?
- Resolved in scope: Construct original J lift with complete time/charge actionRead result
- open: Derive physical meaning of the frame orbit
Which responses distinguish charged time action?
Which data separate sources with identical complete neutral vacuum response?
- Resolved in scope: Determine twist blindness completelyRead result
- Resolved in scope: Reconstruct twist from charged responsesRead result
- open: Derive actual charged source probes
Which seam action distinguishes native opposite charges?
Can existing native charge fields produce the quarter-twist time response of the seam?
- Resolved in scope: Check native fields and response discriminatorRead result
- open: Derive actual marked seam/state action
Constructive seam search: operators, state and source compatibility
What does the complete phase search decide, and which additional state information prevents a false source solution?
- Resolved in scope: Finite search closed, actual winding and parity equivalenceRead result
- Resolved in scope: Positive finite-word state extensionRead result
- Resolved in scope: E8 current group conditionally determines the P signRead result
- Resolved in scope: The same shift functional hides distinct ground statesRead result
- Resolved in scope: No phase hit realizes the unchanged sourceRead result
Which partner actually belongs to the original seam?
Which charge, state type and time action belong to the root partner and original sheet pairing?
- Resolved in scope: Concrete pair operator; source neutrality is not hypercharge neutralityRead result
- Resolved in scope: Fixed quarter time splits the color/weak multipletRead result
- Resolved in scope: Explicit conjugation for the existing sheet pairingRead result
- Resolved in scope: Actual partner map between quarter domainsRead result
- Resolved in scope: Bilinear sheet pairing is not Hermitian kernel selectionRead result
- Resolved in scope: Actual quarter conjugation transports the supplied markingRead result
- Resolved in scope: No time-stabilizing orthogonal repair of the fixed markingRead result
- Resolved in scope: Spinor16 is a state sector, not a 16-real one-particle fieldRead result
Automated construction of operator maps and sources
Which tools generate operator maps, learn counterexamples, and can search for the full positive source?
- Resolved in scope: Calibrate new search without supplying the target mapRead result
- open: Synthesize a joint field, marking and transfer dictionary
- open: Search for the positive common source kernel itself
- Resolved in scope: Automatically construct, certify and distinguish finite kernelsRead result
- Resolved in scope: Repair search conditions against source types and collar controlsRead result
- Resolved in scope: Reconstruct multi-field sewing of the canonically identified boundary sourceRead result
- Resolved in scope: Retain absolute reference amplitude in searchRead result
- Resolved in scope: Integrate supplied free source including boundary response and scalarRead result
- Resolved in scope: Convert the full finite CAR kernel into a link functionalRead result
- Resolved in scope: Close original recursive word reconstruction with memoryRead resultRead result
- Resolved in scope: Retain whole original caller through scale and readoutRead resultRead result
- Resolved in scope: Execute actual shared Higgs source with full matter words and local RPRead resultRead result
- Resolved in scope: Reduce whole constant original Higgs spectral fiberRead result
- open: Resolve original geometric Higgs residue sign and field map
- Resolved in scope: Evaluate local original Higgs heat identification and whole finite consumerRead resultRead result
- Resolved in scope: Execute whole variable bound Higgs reference and original scale mapRead resultRead result
- Resolved in scope: Execute whole inner Higgs scale/source and normal kernel transportRead resultRead result
- Resolved in scope: Execute given whole superconnection and normal spectral readerRead resultRead result
- Resolved in scope: Determine own-admissibility and whole total-chiral spectral readersRead resultRead result
- Resolved in scope: Derive whole scale-energy map,normal profile and relative flowRead resultRead result
- Resolved in scope: Execute original Green energy producer and mixed scale readoutRead resultRead result
- Resolved in scope: Match current action argument and common Higgs/gravity weightsRead resultRead result
- Resolved in scope: Execute whole original curvature consumers and Higgs radial sourceRead resultRead resultRead result
- Resolved in scope: Execute original whole four-ghost source and geometric type testRead resultRead result
- Resolved in scope: Execute original moving normal kernel derivative and whole source responseRead result
- Resolved in scope: Decide fixed original O1 source and normal operator placementRead result
- Resolved in scope: Compare whole Higgs mixture and covariance reader on invariant four-field witnessRead result
- Resolved in scope: Test exact bounded cutoff on whole ordinary Higgs volumeRead result
- Resolved in scope: Test whole original circle joint mode and IR Higgs normalizationRead result
- Resolved in scope: Test original O1 mode covariance against whole Higgs-law classRead result
- open: Reconstruct original localization from the whole process
- Resolved in scope: Test bare native-code word compression against actual localityRead result
- Resolved in scope: Decide original geometric local-time class and execute actual interval readerRead resultRead result
- Resolved in scope: Execute actual regional two-face partner and supported charged wordRead resultRead result
- Resolved in scope: Execute original color marginal, modular field law and complete class readerRead resultRead resultRead result
- Resolved in scope: Reconstruct common Higgs law from whole original quarter source towerRead resultRead resultRead result
- Resolved in scope: Execute original record action on Doily and ordered whole source responseRead resultRead resultRead resultRead result
- Resolved in scope: Locally implement original record process and test unchanged exterior sourceRead resultRead resultRead result
- Resolved in scope: Execute original elliptic insertion,whole source and causal responseRead resultRead resultRead result
- Resolved in scope: Evaluate actual joint Higgs and color group sourceRead resultRead result
- Resolved in scope: Execute whole original graph color reader with typed original center selectorRead resultRead result
- Resolved in scope: Execute original color fixed source and first inherited grading testRead resultRead result
- Resolved in scope: Execute actual original color-spinor CAR four-word and complete spin-sector sewingRead resultRead result
- Resolved in scope: Decide actual color admissibility of density operations and coordinate regionsRead resultRead result
- Resolved in scope: Execute actual whole seam-operation class and two-face responseRead resultRead result
- Resolved in scope: Execute entire original C6 word expansion with source amplitudeRead resultRead result
- Resolved in scope: Execute original collective Higgs force source and entire mean dualRead resultRead resultRead result
- Resolved in scope: Execute original all-mode force with actual time and whole sourceRead resultRead result
- Resolved in scope: Execute original local space/time force source and causal liftRead resultRead result
Origin reverse selection, field dictionary and original P1 kernel
What does reverse selection of P1/P2 give for concrete local fields and multi-field responses, and which identification with the original P1 kernel has actually been proved?
Observable reality: minimal conditions and counterworlds
Which operational conditions are independently required, which inequivalent models satisfy them, and which observable distinctions remain for selection?
Formal carrier core: unbounded Pascal uniqueness and finite glue
Which carrier and glue statements are already present in the papers and Lean sources, and which physical selection does not follow?
- Resolved in scope: Classify the unbounded Pascal proofRead result
- Resolved in scope: Classify the formal finite glue scopeRead result
Active mathematical program: marked seam monodromies and lattice lifts
Which marked seam/lattice transport geometries, lift classes and local-coefficient invariants arise from existing clock/reflection/quartic data? First complete case: sign lifts of fourJ representation on CP1 minusμ4.
- Resolved in scope: Define marked seam category and factor formulaRead result
- Resolved in scope: Completely classify quarter-clock four-puncture liftsRead result
- Resolved in scope: Determine central class and all subgroup restrictionsRead result
- Resolved in scope: Determine full G0 cocycle and classRead result
- Resolved in scope: Determine native4/5/6local cohomologyRead result
- Resolved in scope: Classify unrestricted G31 reflection monodromiesRead resultRead result
- Resolved in scope: Determine lift class beyond G0Read result
- open: Classify additional reflection/clock equivariance and mapping-class quotients
- Resolved in scope: Equivariant lifting and divisibility by eightRead result
- Resolved in scope: All62clock obstructions and central transport variantsRead result
- Resolved in scope: Actual group comparison and central pushout exclusionRead result
- Resolved in scope: Complete invariants and explicit collisionsRead result
- Resolved in scope: Compare E6 and E7 slices with the actual quarter clockRead resultRead resultRead resultRead result
- Resolved in scope: Classify original character-valued G31monodromy liftsRead resultRead result
- Resolved in scope: Determine E7-pair action on all original lattice fieldsRead result
- Resolved in scope: Completely connect E6/E7 cuts to the original compilerRead result
- Resolved in scope: Compare common covers and actual clock carriersRead result
- Resolved in scope: Prove shared representation consequence for48,4/3 and5/4Read result
- Resolved in scope: Completely decide joint compiler-field-cover constructionRead resultRead resultRead resultRead result
- Resolved in scope: Reconstruct canonical local compiler field source from C4Read resultRead result
- Resolved in scope: Eliminate redundant sector and multiplicity assumptionsRead result
- Resolved in scope: Classify native equivariant markingsRead result
- Resolved in scope: Classify pure quarter clock mapping class quotientRead result
- Resolved in scope: Determine complete cut algebra and lossless tetrahedron transformRead resultRead resultRead resultRead result
- Resolved in scope: Completely compare scalar glue and actual native compiler classRead resultRead resultRead resultRead result
Common clock sectors, quartic geometry and operational reconstruction
Which previously separate data of the original TFPT core follow from a common clock and representation geometry, and which complete finite measurement classification follows without asserting physical source selection?
Automatic response search with original-source decision
Which additional joint response actually follows from original source equations, and which entire finite process family remains undecided without it?