# TWIST-J Canon v166 CONSOLIDATED: THE GRAVITATIONAL WAVE ARC **Author.** A. M. Thorn. **ORCID.** 0009-0008-5463-278X. **Hub.** twistj.com. **Date.** 8 July 2026. **Status.** Consolidated fold of the strong-field and gravitational-wave arc of 8 July 2026 (nine commits, b9bfa92c through 286856ed). Predecessor consolidated in this repository: TWIST_J_Canon_v163_CONSOLIDATED.md (7 July 2026). Version number per the architect. Zero new free parameters (cumulative still 1, the m_e SI anchor). No axiom change. No prior LOCK retracted. Two falsifiers FIRED first-class; both purchased constructions. **Conventions.** No em dashes. No decimals unless justified (all decimals below are computed or measured witnesses). Integers and ratios primary. If it cannot be calculated in integers, it is not physics. Plenum, not vacuum. Two forces = two J-projections: modulus to gravity / scale, argument to EM / phase. Time is a counter; space is a commutator. Official SEO name: TWIST-J. Hub: twistj.com. **Status taxonomy.** T-LOCK immutable; T theorem; D derived; D-survivor fixed by preregistered elimination against data (identikit sense); C computed; H hypothesis with falsifier; O open; F falsified; R remark. No summary stronger than the label it summarizes. --- ## The fold One day, one arc, one question driven to the end: does the strong-field and radiative sector of the rank-1 gravity survive contact with GW250114, and if not, what does the theory have to build. The answer: the minimal exponential reading is falsified in the GW channel on every dynamical branch [F]; the half-angle reading of the kernel TT plane is falsified [F]; and each falsification produced its successor exactly. The chain now runs end to end: kernel vector doublet, bilinear (squaring) decoder, slaved-metric attachment, lambda = -1 kinetics, gauge-natural propagation, ringdown inside GW250114 on a data-bounded background corridor, with one leftover prediction for ngEHT and two named residues. --- ## Part I. The strong-field confrontation (O-METRIC-O3) Exact static structure of the isotropic exponential metric (m = 1): photon sphere rho_ph = 2, critical impact parameter b_c = 2e (ratio to Schwarzschild kappa = 2 sqrt(3) e / 9), ISCO at rho = 3 + sqrt(5) = 2 phi^2 (polynomial rho^2 - 6 rho + 4, discriminant 20 = 4p), throat R = e m, no horizon. [T/D] Confrontations: EHT shadow, spin-marginalized via the NJ / Azreg-Ainou Delta-form (Delta = rho^2 + a^2 exact, horizonless at every spin), maximum tension 2.05 sigma: F-SHADOW NOT FIRED. Solar-system channels cannot reach the O(Phi^3) coefficient (F-SOLAR-NEGATIVE registered; over-claim barred). GW250114 ringdown (pSEOBNR delta-f_220 = 0.02 +- 0.02 at 90 pct) against the WKB3 axial line delta_f = -0.0744: F-RINGDOWN-IMR FIRED [F, WKB3 grade, 7.8 sigma]. The eikonal theorem lambda = 1 / (2 e m) = 1 / b_c ties the QNM spectrum to the light ring exactly; the exponential potential is a single barrier (minimum 2 sqrt(2) - 2 at rho = 1/sqrt(2)), so the echo cavity is half discharged. Commits b9bfa92c, 3c372d78, 0777fa6c, 71f49fcd. ## Part II. O-QNM-DYNAMICS closed negative The rank-1 perturbation equations, derived exactly (9/9): sqrt(-g) g^{mn} d chi d chi = e^{4 chi} chidot^2 - (grad chi)^2 The spatial kinetic term is EXACTLY FLAT (the plenum shows through). The DeWitt lambda = -1 trace action on the slaved metric equals 12 e^{4 chi} chidot^2 identically: the time sector is Canon-forced. Linear perturbations obey Box_g deltachi = 0 exactly (no induced potential); the breathing potential is IDENTICALLY the S = 0 line; the breathing mode surfs the photon light ring exactly. The TT projection of the slaved perturbation is IDENTICALLY ZERO: the rank-1 sector radiates breathing only, completion independent. Branch verdict: B1 tensor-RW frequency-dead (7.8 sigma); B2 covariant composed polarization-dead; B3 flat-plenum polarization-dead and modeless. O-QNM-DYNAMICS CLOSED NEGATIVE. The minimal exponential reading is falsified in the GW channel on every dynamical branch [F]. GATE-0 is forced to the new-decoder-component branch (PART_XXII horn 1 mandatory; horn 2 dead). Commit 7d37d2b8. ## Part III. O-GW-TT-LIFT: kinematics, protection, corridor Kinematics [D]: dim P_TT = 2, eps^2 = -I; helicity dichotomy by exact Z_4 congruences; S^2|_TT = -I is the exact spin-2 phase of the plaquette quarter-turn. DeWitt protection [D]: G(lambda)[K_TT, K_TT] = 2(a^2 + b^2), lambda-INDEPENDENT and positive; G(lambda)[K_TT, K_trace] = 0 identically (F-CHI5-NOT-STANDALONE structurally safe). The pincer: GW170817 forces any TT lift onto the slaved optical metric; the mu-family A_mu = A_exp^{1-mu} A_Schw^mu satisfies log A_mu = -2/rho - (mu/6)/rho^3 EXACTLY: the dial mu IS the O(Phi^3) coefficient, deviation from Schwarzschild (1 - mu)/6, beta = gamma = 1 for all mu. GW250114 cuts the corridor: mu >= 0.804 (3 sigma); the registered +1/6 = 0.167 squeezed five-fold to <= 0.033; the 90 pct edge wants mu >= 1. Surviving prediction: shadow excess in [0, +0.93 pct]. ngEHT decides the whole corridor. Commit 7f3e09ec. ## Part IV. The discriminator: F-TT-HALF-ANGLE fired; the bilinear target Anchor [D, T-LOCK anchored]: T-SPIN-BISECTOR gives R = t^-1 S; a global phase changes no conjugation, hence no implemented rotation; R conjugates the axes by the physical quarter-turn. ONE KERNEL C_4 STEP = PHYSICAL pi/2, representation independent. Consequence: P_TT is the m = +-1 VECTOR doublet (D-TT-VECTOR-DOUBLET); a helicity +-2 doublet cannot live in scalar C_4 functions (the m = 2 class is one-dimensional; +-2 alias). F-TT-HALF-ANGLE FIRED [F]. H-TT-HALF-ANGLE falsified, first-class. SS8B.6 GW Remark requalified. The falsification bought the target: Sym0^2(P_TT) = span{H_plus, H_cross} is the helicity +-2 doublet (induced quarter-turn = -I, the exact spin-2 phase; G_a induces diag(-1, +1); trace-orthogonal). The TT carrier is the QUADRATIC read of the vector doublet: T-LQ-READING-SPLIT placement (D-TT-BILINEAR-TARGET). Commit a9ca2fda. ## Part V. O-TT-DECODER constructed; O-TT-ACTION time sector closed D-TT-DECODER-MAP [D]: the bilinear decoder component is the complex SQUARING map, h_plus + i h_cross = (v_1 + i v_2)^2. Norm squares (the Born square), phase doubles, and the exact kernel of the map is {+-1}: the spin double cover realized as squaring. D_4-equivariant (quarter-turn and swap, dihedral relations verified). Attaches as g_ij = e^{2 chi}(delta + h^TT). D-TT-VOLUME-NEUTRAL [D]: det(I + H^TT) = 1 - |h|^2 exactly, no linear term: the scalar source is untouched at O(h). D-TT-KINETIC-TIME [D]: the SAME lambda = -1 trace action on slaved + TT, exactly to second order: O(eps^0) = 12 e^{4 chi} chidot^2; O(eps^1) = 0 IDENTICALLY (linear source decoupling at the action level); O(eps^2) static = (1/2) e^{4 chi} (hdot_plus^2 + hdot_cross^2): same lapse weight, no new normalization freedom. D-TT-BACKREACTION [D]: exact quadratic channel e^{4 chi}[-6 |h|^2 chidot^2 - 8 (h . hdot) chidot]. Gradient sector FORCED by GW170817 onto the light cone of g. Commit 3ae77522. ## Part VI. The propagation identikit: D-TT-WAVE-SURVIVOR Candidates (all light-cone-correct, two-derivative): (i) component-scalar (Lfac = l(l+1), c = +1); (ii) minimal spin-weighted (Lfac = l(l+1) - s^2, c = +1); (iii) gauge-natural (Lfac = l(l+1), c = 1 - s^2). Leaver triple regressions in one probe (mu = 1): axial 0.373672, scalar 0.483644, EM 0.457596, all within 0.15 pct. Strikes: (i) DEAD at +0.295 / +0.284; (ii) DEAD at -0.220 / -0.225; (iii) SURVIVES, the GW250114 3 sigma edge falling in (4/5, 9/10), reproducing the corridor pin. D-TT-WAVE-SURVIVOR [D-survivor]: the unique surviving propagation law is gauge-natural, c = 1 - s^2 with full l(l+1). One law, three in-theory instances, none fitted: s = 0 rank-1 breathing c = +1 s = 1 the photon c = 0 s = 2 the TT square c = -3 The two J-projections and their quadratic read share ONE propagation law. Commit 286856ed. --- ## Falsification registry (v166) ```text F-RINGDOWN-IMR FIRED [F, WKB3 grade, 7.8 sigma]. The minimal exponential reading is dead in the GW channel on every dynamical branch (Parts I, II). F-TT-HALF-ANGLE FIRED [F]. One kernel C_4 step = physical pi/2; P_TT is a vector doublet (Part IV). F-SHADOW NOT FIRED (max 2.05 sigma spin-marginalized). F-SOLAR-NEGATIVE registered: solar-system channels cannot test the O(Phi^3) coefficient; over-claim barred. F-TT-LIFT-ABSENT DID NOT FIRE: the bilinear lift exists (Parts IV, V). F-TT-SCALAR-PROPAGATION ARMED (~30 pct) against O-TT-GAUGE-DERIVATION. F-CHI5-NOT-STANDALONE INTACT: protected at the supermetric level (GB2), at the metric level (volume neutrality), and at the action level (O(eps^1) = 0 identically). ``` ## Obligation movements (v166) ```text O-METRIC-O3 minimal reading CLOSED at F; the strong-field background reduced to the mu corridor (mu >= 0.804 at 3 sigma; +1/6 -> <= 0.033; shadow excess [0, +0.93 pct], ngEHT decides). O-QNM-DYNAMICS CLOSED NEGATIVE (Part II). O-GW-TT-LIFT kinematics CLOSED at D (Parts III, IV). O-TT-DECODER CONSTRUCTED [D]: the D_4-equivariant squaring map. O-TT-ACTION time sector CLOSED [D]; gradient forced by GW170817; propagation law fixed by identikit [D-survivor]. O-TT-WAVE-POTENTIAL CLOSED by identikit (Part VI). NEW O-TT-GAUGE-DERIVATION derive c = -3 from the covariant TT action (F-TT-SCALAR-PROPAGATION armed against it). NEW O-TT-SOURCE the emission map, anchored on SS8A.11 LOCK. NEW O-QNM-LEAVER-MU Leaver-grade corridor edges on the mu-family. NEW O-POL-READ pin the LVK polarization Bayes factors. FLAG SS-FRW.11 r = 0 was derived under 0 independent tensor DOF; after the bilinear lift it must be RE-DERIVED, not assumed. ``` ## Verifier index (two-platform SHA256, byte-identical stdout) Blocks 1 to 8 of CROSSPLATFORM_LOCK_RECORD.md carry the full pin set of the arc. The five construction probes, pinned verbatim: ```text o_qnm_dynamics_probe.py (9/9) file b9279bd8784c065d4b4a8f9834bad26d22ca2d154b30d45ccc89984764b7d981 stdout eba0c1c01fb74f548dfcee7dc8ebdaf0ad600614ed19d4c097d34e6f3655f191 o_gw_tt_lift_probe.py (8/8) file 187a4cbc761c8f78e9db845b1e5c34a7de11591b920e9fa094b2e99668b6f589 stdout 763ef5f8a671535f710ec49d4e72edb72c4f92c851529c8c2f874a96be5b74fb o_tt_discriminator_probe.py (13/13) file b7285adaaf3abaa9d888584170a7b4d00a9252c7c0078030cc291c3379329510 stdout b0fcb13ed7202e7f97819413a6d62602e712e112f619645c18892faf0212167b o_tt_decoder_probe.py (12/12) file ec4665dc6b48c94661ce729d4e96b14e5ff76bda834a647f0c8a4d5f4197159f stdout 9ee197376549ab6af8280f2f339b52e98e368ea638569a7ad37d97697197a5ba o_tt_wave_identikit_probe.py (6/6) file 07b463c7dbdce513b7666aa3bf862cead1fa965036fd1f68087d0a50ddb4d8ff stdout 1a698e0f9efd44e543bd1f9c2b4b156af2c31fcd99bb2642c68765aadced6bb3 ``` Platforms: JAS 2 aarch64 py3.12.3 and TWISTER x86_64 py3.13.5 (sympy 1.14.0, mpmath 1.3.0); the discriminator ran JAS 4 aarch64 + TWISTER during a fleet tunnel outage (cross-architecture requirement satisfied; all transfers hash-verified before run). --- ## Closing Two falsifiers fired and neither wasted a shot: the death of the exponential reading bought a data-bounded corridor with an ngEHT prediction, and the death of the half-angle hypothesis bought the squaring decoder with the spin double cover as its kernel. The gravitational wave now has a place in the theory: the modulus projection carries it as a square, on one propagation law shared with the photon. What remains is named, gated, and armed.