# THE EQUATION LEDGER — every equation, every parameter, every bracket # Companion: CONSTANTS.md — every fundamental constant interrogated # (includes the sweep's wound: the second-order CC problem, up to 1e89) # (2026-07-10; the framework's full quantitative state in one file) # Classes: [T] theorem [A] exact within the model [B] measured shape x data # [C] conditional on order-unity coupling [R] reading (interpretive) ===================================================================== I. THE EQUATIONS ===================================================================== E1. SUBSTRATE H = 1/2 Σ p_i^2 + 1/2 Σ_e k_e (x_i - x_j)^2 + (mu^2/2) Σ x_i^2 ; k_e = 1 + dk_e status: postulate (the lattice, its dimension, mu are assumed) E2. CONSTRAINT (A dk)_i = - c_i status: postulate (the axiom: conserved budget) consequence [A]: Gauss law; exact zero mode of W at q* (1e-32) E3. THE PRICE G_ef = 1/8 Tr[ Om^-1 (d_e Om) Om^-1 (d_f Om) ], Om = sqrt(K) status: canonical choice (uniqueness NOT claimed — n85-F1); energy excluded as price by [T] concavity (Lowner) E4. STATICS E(c) = 1/2 c^T W^+ c , W = A G^-1 A^T status [A]: exact; Coulomb measured at 3e-6 (1D), IR-quadratic dispersion 0.24%/0.36% (2D/3D) E5. MONITOR rho' = -i[H,rho] + gamma Σ_e (L rho L† - 1/2{L†L, rho}), L_e = constraint residuals (violations ONLY) status: postulate (the second axiom); consequence [A]: dark states = zero rest decoherence; [R]: charge superselection E6. THE KNEE Gamma_dec(omega) ∝ (dT00/dt)^2 / (gamma^2 + omega^2) status [A]: exact Lorentzian measured at 0.3%; THE EXISTENCE GATE E7. INDUCED GRAVITY Omega_eff = - g^2 Delta / (Delta^2 + kappa^2/4); U_AB ∝ - lambda^2 h_A L^+ h_B status [A] within the n33 model family (passivity scope: n85-F6); attraction requires Delta < 0 [T within family] E8. REDSHIFT omega(x) = E(x)/hbar = (m/hbar)(1 + Phi(x)) status [A]: linear+universal, residual ∝ 1/N -> exact (0.19% at N=96); companion [T]: classical drift rates see only nabla^2 Phi E9. INERTIA M_ad = 2hbar^2 Σ ||^2/(E_n - E_0) ∝ k^(-5/2) status [A]: verified 9e-7; independently re-derived (hostile review) E10. THE Q LOCK gamma_knee / Omega_grav = kappa/|Delta| = Q status [A]: exact, verified 4 digits across parameter space E11. PPN gamma_PPN = (1 - 2a)/(1 + 2a) status [A] under 6 named assumptions (A1-A6) + strong-monitoring regime gamma*F >~ 7; optical ingredient verified only at 10% E12. ANHARMONIC LAYER Delta-beta = (+543 per unit xi, toy norm); Delta-P(pump bill) = +232 * xi^2 status [A]: exact 1st/2nd-order perturbation theory; the chain Mercury -> xi > 0 -> bill > 0 -> Lambda > 0 closes in sign [R] ===================================================================== II. THE PARAMETERS AND THEIR BRACKETS ===================================================================== a audit state-dependence (fixes gamma_PPN) BRACKET: -5.8e-6 < a < +5.8e-6 [Cassini | A*] (*with the 10%-grade optical-ingredient caveat, n85-F2) theory's expectation: a = 0 exactly (minimality argument) l_s substrate scale BRACKET: 0 (Planck allowed) < l_s < 4.3e-27 m [GRB photon-dispersion limits x the lattice form | B, n92; supersedes Coulomb 2.5e-15 m by twelve orders; substrate energy scale > 4.6e10 GeV] gamma audit rate = the knee BRACKET: 5.2e14 s^-1 < gamma < ~1.2e23 s^-1 [floor: PSR J0737-3039 decay, class C at c_drag=0.02; ceiling: c/l_s from the Coulomb bound on l_s] weaker same-side floors: LLR 4.3e9, flybys 1e6 [C] ceiling updated by n92: c/l_s ~ 7e34 s^-1 PREDICTED WINDOW [C', n89]: 1e19 - 1e22 s^-1 (UV to X-ray) — the hierarchy demand (Q from observed G/alpha) lands inside the independent band; three disjoint constraint sources converge on two decades EXACT SIMPLIFICATION [n93]: gamma_knee = alpha*m*c^2/hbar — G cancels; the window's width IS m_p/m_e = 1836, and a measured knee picks which mass the vacuum counts in. Sharpened bet: the extremal-dressing anchor -> knee ~ 5.7e18 s^-1 (soft X-ray) Delta monitor detuning BRACKET (sign only): Delta < 0 [passivity theorem within the n33 family; active vacuum required; stability measured] Q kappa/|Delta| — the vacuum's quality factor BRACKET: Q >> 1 (unquantified until the knee); carries the RATE-half of the gravity/EM hierarchy [A for the lock itself] S_inf continuum coupling 1/e^2 (the audited sector) VALUES: S_inf(2D) = 202.588 +- 0.010 ; S_inf(3D) = 493.83 +- 0.30 [finite-size 1/L^2 fits, residuals ~3 digits | A in the toy] alpha^-1 ballpark {494 - 6205 by convention} vs nature's 137.036 [R — characterization only; numerology risk flagged n85-F10] xi substrate anharmonicity SIGN: xi > 0 [Mercury stage A, geometry-robust | A(pert)] IN-SITU VALUE: fixed by Delta-beta = +0.5000 +- 0.0001 [Mercury + LLR Nordtvedt | B] — the four-digit target the tensor junction must DERIVE (theorem) or the framework tunes Delta-beta the anharmonic beta contribution BRACKET: +0.4999 < Delta-beta < +0.5001 [sky data | B] linear sector contributes exactly 1/2 [A: E2 = 0 machine] Delta-P pump bill (Lambda direction) VALUE: +232 * xi^2 (N=6 baseline; per-site 38.7 -> 50.5 at N=6 -> 8: extensivity scaling OWED) ; SIGN: positive, even in xi, branch-independent [A(pert)] -> Lambda > 0 [R] pump inversion stability BRACKET: |d ln(inversion)/dt| < 1e-14 / yr [LLR Gdot/G | B] substrate constancy (S_inf, extremal-dressing cost) BRACKET: |d ln/dt| < ~1e-19 / yr [alpha-dot atomic clocks; mu-dot quasar bounds 6e-17 | B, n93] — the sharpest stability entry on the card lambda consumption-per-energy universality BRACKET: composition dependence < 1e-15 [MICROSCOPE | B] m_gamma photon mass (the audited sector's collective mode) VALUE: 0 by theorem (exact Gauss zero mode at every mu, 1e-32) [T] — satisfies m_gamma < 1e-18 eV structurally; converts "light = the Gauss mode" from assumption to requirement c_drag friction conversion factor TOY VALUE: 0.02 at kappa_read = 1 [C] — the single number all class-C brackets await; THE UNITS BRIDGE, still unbuilt mu substrate regulator TOY VALUE: mu^2 = 1e-6; physical value unconstrained for the phonon sector; irrelevant to the photon [T above] g, kappa monitor couplings toy values (0.05-0.2, 1-4); only RATIOS are physical (E10); absolute values await the units bridge ===================================================================== III. THE STANCES (parameters the framework has bet on) ===================================================================== - alpha discrepancy (5.4 sigma, Cs vs Rb): SYSTEMATICS [falsifiable] - CODATA G spread (~5e-4): SYSTEMATICS [falsifiable] - any clock-EP violation without a force-EP violation: IMPOSSIBLE - DP rest floor: WILL NEVER BE FOUND - c_GW = c: FOREVER - charged particles below the line m >= |q/e|*m_e: DO NOT EXIST [the charge<=mass inequality, n90 — live vs millicharge searches] - photon vacuum dispersion, if ever seen: QUADRATIC and SUBLUMINAL only [the lattice form, n92 — superluminal or linear kills] - if constant drift is ever confirmed: alpha moves, mu = m_p/m_e FROZEN (d ln mu/d ln alpha = 0 — anti-GUT, from the conformal weight) [n94 — |dmu| >= |dalpha| kills the uniform-substrate reading] Settled so far: F9 (screening) — against us, 11 days after signing. ===================================================================== IV. WHAT NO EQUATION HERE HAS ===================================================================== Physical units (everything above is lattice-normalized or bounded from outside); a matter sector; a dynamical/tensor sector (its target: Delta-beta = +0.5000(1)); external verification. Twenty-eight headstones guarantee the sincerity, not the truth. Everything rides on E6.