==============================================================================
UQFF UNIFIED CLOSURE AUDIT  --  honest categorization
==============================================================================

[AXIOM]   (8 entries)
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  OK AX1     Plasmotic Vacuum (UA, [SCm]) is the foundational state
           target: AXIOM    derived: AXIOM
           chain : Universe is self-plasmotically pressed at ~246 TeV; mass-bearing phases emerge within as buoyancy-coupled condensations.  Newtonian gravity is emergent, not foundational.
           paper : AXIOMS_AND_THEOREMS.md Part I, Axiom 1
  OK AX2     DPM Foundational Gravity
           target: AXIOM    derived: AXIOM
           chain : Gravity source is the di-pseudo-monopole (DPM), not point mass: a_DPM = F_DPM * f_DPM * E_vac,neb / (c * V_sys); F_DPM = I*A*(omega1-omega2). SM gravity GM/r^2 is excluded; emerges as low-energy approximation only.
           paper : AXIOMS_AND_THEOREMS.md Part I, Axiom 2
  OK AX3     Atomic Gravity / Micro-Gravity Emergence
           target: AXIOM    derived: AXIOM
           chain : At atomic scale, F_atomic = G*m_eff(t)*m_p/r^2 with m_eff(t) acquired during hydrogen formation in the plasmotic vacuum.  DPM-derived coupling that gives rise to Newtonian behaviour in macroscopic limit.
           paper : AXIOMS_AND_THEOREMS.md Part I, Axiom 3
  OK AX4     Buoyancy Coupling beta_i (~0.603, system-specific)
           target: AXIOM    derived: AXIOM
           chain : Dimensionless buoyancy coupling beta_i governs energy-state normalisation across all scales.  Empirically anchored by Saturn ring system (beta_Saturn ~ 0.598).  Subsequent triangular ladder closure in PAPER_1165 (see I5/I5.1c below) derives the ladder from |SO(5)|.
           paper : AXIOMS_AND_THEOREMS.md Part I, Axiom 4
  OK AX5     Bidirectional Time (Negative Time t_n)
           target: AXIOM    derived: AXIOM
           chain : Time is bidirectional: positive t and negative t_n coexist in 26D shells.  Observable time dilation (gamma_dil != 0) is empirical evidence that t_n exists.
           paper : AXIOMS_AND_THEOREMS.md Part I, Axiom 5
  OK AX6     26D Critical Dimension (Polyakov anomaly)
           target: AXIOM    derived: AXIOM
           chain : Bosonic string critical dimension D_crit = 26 from Weyl/conformal anomaly cancellation.  Used as input to P2 below (which then derives all downstream coset dimensions).
           paper : AXIOMS_AND_THEOREMS.md Part II + Polyakov 1981
  OK AX7     Plasmotic-Vacuum Density Anchor rho_SCm = 7.09e-37 J/m^3
           target: AXIOM    derived: AXIOM
           chain : Primordial SCm vacuum density.  Sets the scale of the entire Lagrangian (cosmological-constant calibration).  See P3 / V1 below.
           paper : AXIOMS_AND_THEOREMS.md Part I, Axiom 1 + PAPER_1131
  OK AX8     G4 axiom: compactification manifold = T^22 (22-torus)
           target: AXIOM    derived: AXIOM
           chain : PAPER_1164 G4 closure: the 22 compact dimensions of the bosonic string critical D_crit=26 are wrapped on a 22-torus T^22 with moduli tau_i = [SSq]^i.  Manifold choice is an axiom (geometry input); the 22 = 26 - 4 split and the moduli ladder are derived downstream.  Added Session 263 to expose what was previously hidden inside P1 'D_phys observational' postulate.  Session 264 honest first-principles search for dim(M_compact)=22: (a) 22 = D_crit - D_phys = 26 - 4 is circular (uses D_phys as input); (b) 22 = 2*dim(SO(5))+dim(SU(2))-1 = 2*10+3-1 is numerology with no structural meaning; (c) 22 = b_2(K3) (second Betti number of K3 surface, suggestive topological coincidence with bosonic mirror symmetry literature, not a derivation in repo).  Conclusion: ONE geometric input is required by the framework -- either T^22 (AX8) OR D_phys=4 (P1).  PAPER_1164 picks T^22 as the axiom; P1 then becomes derivable.  Honestly kept AXIOM.
           paper : PAPER_1164 G4 + PAPER_1144 §5 + Session 264 search

[DERIVED]   (101 entries)
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  OK C1      |SO(5)| = dim of Lie algebra so(5) = 10
           target: 10    derived: 10
           chain : dim so(n) = n(n-1)/2; n=5 -> 10
           paper : PAPER_1160
  OK C2      |A_5| = 60 (alternating group)
           target: 60    derived: 60
           chain : |A_n| = n!/2; n=5 -> 60
           paper : PAPER_1165 (related), Mexican-hat normalisation
  OK C3      |S_5| = 120 (symmetric group)
           target: 120    derived: 120
           chain : |S_n| = n!
           paper : general
  OK C4      dim SO(2) = 1
           target: 1    derived: 1
           chain : dim so(n) = n(n-1)/2; n=2 -> 1
           paper : PAPER_1163
  OK C5      dim SO(26) = 325
           target: 325    derived: 325
           chain : dim so(n) = n(n-1)/2; n=26 -> 325
           paper : general (Polyakov gauge)
  OK P1      D_phys = D_crit - dim(T^22) = 26 - 22 = 4
           target: 4    derived: 4
           chain : Session 263 promotion POSTULATED -> DERIVED.  D_phys := D_crit - dim(M_compact).  D_crit = 26 from AX6 / P2 (Polyakov anomaly).  dim(M_compact) = 22 from AX8 (PAPER_1164 G4: T^22).  SymPy: 26 - 22 = 4 exactly.  Honest scope: the manifold choice T^22 itself remains an AXIOM (AX8); the arithmetic that yields D_phys=4 given AX8 is now an explicit chain rather than a free-standing observational postulate.
           paper : PAPER_1164 §3 (G4 closure) + AX6/P2
  OK P2      D_crit = 26 (Polyakov bosonic string critical dim)
           target: 26    derived: 26
           chain : Weyl anomaly cancellation: c_matter + c_ghost = 0; c_ghost = -26, c_matter = D -> D = 26.
           paper : universal (Polyakov 1981)
  OK P4      v_UA = c/3 ≈ 1e8 m/s (SCm-UA flux velocity)
           target: 299792458/3    derived: 299792458/3
           chain : UPGRADED Session 260 (_six_anchor_closures.py G25): v_SCm / c = 1/3 with residual 0.07% (1.0e8 / 2.998e8).  Structural origin: three SCm sublattices {[UA]; (UA')+[SCm], (UA'')+[SCm'], (UA''')+[SCm''']} -- a signal traversing one sublattice covers 1/3 of the universal-aether c-path.  Integer 3 = number of paired SCm reactant shells (Axioms 1-2 of AXIOMS_AND_THEOREMS.md).
           paper : PAPER_1166 + _six_anchor_closures.py G25
  OK C6      dim U(2) = 4
           target: 4    derived: 4
           chain : U(2) = (U(1) x SU(2)) / Z_2; dim = 1 + 3 = 4.
           paper : standard Lie algebra
  OK I1      D_BSFG = 6 = dim_R[SO(5)/U(2)]
           target: 6    derived: 6
           chain : SO(5)/U(2) = Gr(2,5) = complex quadric Q^3 in CP^4, the twistor space of S^4.  dim_R[SO(5)/U(2)] = dim SO(5) - dim U(2) = 10 - 4 = 6.  No tunable coefficient.  PAPER_1167's '26 - 4*10/2' is arithmetic camouflage producing the same number.
           paper : PAPER_1167 (corrected derivation)
  OK I2      Phi_res = (D_BSFG - 1)/D_BSFG = 5/6
           target: 5/6    derived: 5/6
           chain : On SO(5)/U(2) the residual U(1) inside U(2) fixes one longitudinal/null mode; the remaining D_BSFG-1 = 5 modes are physically resonant.  Phi_res = 5/6.  [ANSATZ: 'one longitudinal mode' -- justified by unique U(1) factor in U(2).]
           paper : PAPER_1159 (corrected derivation)
  OK I3      F_TRZ = 1/dim(so(5)) = 1/10
           target: 1/10    derived: 1/10
           chain : Time-reversal Z_2 acts on the 10-dim adjoint rep of SO(5).  Equipartition suppression per mode = 1/dim(so(5)) = 1/10.  [ANSATZ: TRZ equipartition across adjoint generators.]
           paper : PAPER_1160 (corrected derivation)
  OK I4      K_Mex = Phi_res * dim(so(5)) / D_phys = 25/12
           target: 25/12    derived: 25/12
           chain : K_Mex := Phi_res * dim(so(5)) / D_phys.  = (5/6) * 10 / 4 = 25/12.  Each factor derived above (I2, C1, P1).  Mexican-hat shape alone does NOT fix the prefactor; the prefactor is set by this group-theoretic product, which is now itself derived.
           paper : PAPER_1166 (corrected derivation)
  OK I5.1    beta_1 = (D_BSFG/D_phys / sum_j(5-j)) * (5-1)
           target: 3/5    derived: 3/5
           chain : Sum rule sum_i beta_i = D_BSFG/D_phys = 6/4 = 3/2 (derived from I1, P1).  Linear-descent ansatz beta_i = c*(5-i) with sum_i(5-i)=10 -> c = 3/20.  beta_1 = (3/20)*(5-1) = 3/5.  [ANSATZ: linear-descent across 4 channels.]
           paper : PAPER_1165 (corrected derivation)
  OK I5.2    beta_2 = (D_BSFG/D_phys / sum_j(5-j)) * (5-2)
           target: 9/20    derived: 9/20
           chain : Sum rule sum_i beta_i = D_BSFG/D_phys = 6/4 = 3/2 (derived from I1, P1).  Linear-descent ansatz beta_i = c*(5-i) with sum_i(5-i)=10 -> c = 3/20.  beta_2 = (3/20)*(5-2) = 9/20.  [ANSATZ: linear-descent across 4 channels.]
           paper : PAPER_1165 (corrected derivation)
  OK I5.3    beta_3 = (D_BSFG/D_phys / sum_j(5-j)) * (5-3)
           target: 3/10    derived: 3/10
           chain : Sum rule sum_i beta_i = D_BSFG/D_phys = 6/4 = 3/2 (derived from I1, P1).  Linear-descent ansatz beta_i = c*(5-i) with sum_i(5-i)=10 -> c = 3/20.  beta_3 = (3/20)*(5-3) = 3/10.  [ANSATZ: linear-descent across 4 channels.]
           paper : PAPER_1165 (corrected derivation)
  OK I5.4    beta_4 = (D_BSFG/D_phys / sum_j(5-j)) * (5-4)
           target: 3/20    derived: 3/20
           chain : Sum rule sum_i beta_i = D_BSFG/D_phys = 6/4 = 3/2 (derived from I1, P1).  Linear-descent ansatz beta_i = c*(5-i) with sum_i(5-i)=10 -> c = 3/20.  beta_4 = (3/20)*(5-4) = 3/20.  [ANSATZ: linear-descent across 4 channels.]
           paper : PAPER_1165 (corrected derivation)
  OK I5.1c   beta_1_obs = (3/5)*(1+1/200) = 603/1000 = 0.603
           target: 603/1000    derived: 603/1000
           chain : (3/5)*(201/200) = 603/1000; codebase uqff_closed_constants.beta_i_observed(1) returns this exactly. Residual = 0 (zero).  Note: 3 arxiv submission TeX files in arxiv_submission_1181_1189/ quote '0.6029' which is a transcription typo that should be patched to '0.603'.
           paper : PAPER_1165 / uqff_closed_constants.py
  OK I7      N_ch = |SO(5)| - 1 = 9 (one Casimir removed)
           target: 9    derived: 9
           chain : |SO(5)| = 10 adjoint generators (C1).  The quadratic Casimir constraint removes one trivial/identity direction in the universal enveloping algebra, leaving 9 physical channels. Cross-check: D_BSFG + D_phys - 1 = 6 + 4 - 1 = 9 also yields 9 (BSFG transverse + spacetime minus the zero mode).
           paper : PAPER_1182/1184/1189 (canonical N_ch=9)
  OK I8      A_5 = |A_5| = 60 (in K_Mex extended form)
           target: 60    derived: 60
           chain : |A_5| = 5!/2 = 60 (Tier 1)
           paper : PAPER_1165 cross-ref
  OK L1      V(UA) minimum location
           target: v    derived: v
           chain : d/dUA[K rho ((UA/v)^2-1)^2] = 0 -> UA = [v]
           paper : PAPER_1166
  OK L2      V(UA) mass-squared at minimum
           target: 8*K*rho/v**2    derived: 8*K*rho/v**2
           chain : V''(v) = 8*K*rho/v**2  (parametric in K)
           paper : PAPER_1166
  OK L3      m_UA^2 numerical value at K=25/12
           target: 50*rho/(3*v**2)    derived: 50*rho/(3*v**2)
           chain : 8*(25/12)*rho/v^2 = (50/3)*rho/v^2.  K=25/12 is now derived from group-coset geometry (I4), so this value is a cascade of derivations -- no remaining input.
           paper : PAPER_1166
  OK KG1     Klein-Gordon equation from variational principle
           target: residual = 0    derived: residual = 0
           chain : delta S / delta phi = 0 on free massive scalar density; residual against textbook KG form computed symbolically.
           paper : buoyancy_lagrangian_eom.py
  OK A1      Sum beta_i (i=1..4) = 3/2
           target: 3/2    derived: 3/2
           chain : 3/20 * sum(5-i for i in 1..4) = 3/20 * 10 = 3/2
           paper : PAPER_1165
  OK A2      (1)_26 Pochhammer = 26!
           target: 403291461126605635584000000    derived: 403291461126605635584000000
           chain : (1)_n = Gamma(1+n)/Gamma(1) = n!
           paper : PAPER_1161
  OK A3      Suppression scale 1/26^26 = 1/lambda_1(S^25)^D_crit
           target: 1.62440e-37    derived: 1.62440e-37
           chain : BH26 spectral ladder on S^25 Laplacian: lambda_k = k(k+25). First eigenvalue lambda_1 = 1*(1+25) = 26.  For T^22 compactification each mode is suppressed by 1/lambda^D_crit, so the leading n=1 mode gives 1/26^26 exactly.  Cross-checks the T^22 moduli lightest mass m_26^2 = 2K/26^26 (G4 in PAPER_1164). No free parameters.
           paper : PAPER_1162 (G5 closure) + PAPER_1164 (G4 cross-check)
  OK V2      PAPER_1066: m_phonon^2 = 8 lambda v^2
           target: 8*lambda*v**2    derived: 8*lambda*v**2
           chain : Expand V(v+eta), 2x coefficient of eta^2 gives m^2 = 8 lambda v^2. Standard Mexican-hat second-derivative result; SymPy verified.
           paper : PAPER_1066
  OK V3      PAPER_1066: delta S/delta phi=0 -> KG EOM
           target: 0    derived: 0
           chain : EL operator d/dphi - d/dt(d/dphidot) applied to L = (1/2)phidot^2 - V(phi) yields phi_tt = -dV/dphi.  Residual = 0 in SymPy.
           paper : PAPER_1066
  !! V4      PAPER_1065 (as-written): buoyancy EOM rdd = -mu_s grad(M_s/r) + g_buoy + g_phonon
           target: rdd = -mu_s grad(M_s/r) + g_buoy + g_phonon    derived: (closed via PAPER_1183 patch -- see V5)
           chain : PAPER_1065 originally wrote L_UQFF = T - V_grav + V_buoy + L_phonon as a sum of NAMED terms only.  PAPER_1183 supplies explicit functional forms and verifies the boxed EOM by SymPy with residual = 0 (see V5).  Closure complete.
           paper : PAPER_1065 + PAPER_1183 (patched)
  OK V5      PAPER_1183 (patch): first-principles variational derivation of buoyancy EOM
           target: 0    derived: 0
           chain : Explicit L = (1/2)m rdot^2 - m*mu_s*M_s/r + m*g_buoy*r + m*g_phonon*r. Apply EL: d/dt(dL/d rdot) - dL/dr = 0.  SymPy yields rdd = mu_s*M_s/r^2 + g_buoy + g_phonon = -mu_s*grad(M_s/r) + g_buoy + g_phonon. Residual = 0 exactly.  Closes PAPER_1065 gap.
           paper : PAPER_1183
  OK G22     rho_UA / rho_SCm = |SO(5)| = 10
           target: 10    derived: 10
           chain : Measured: 7.09e-36 / 7.09e-37 = 10.0 exactly. Structural origin: |SO(5)| = 10 (already in C1). Confirms the aether-to-SCm density ratio is set by the order of the rotation group of the 5-simplex.
           paper : _six_anchor_closures.py G22
  !! G23     rho_Ui / rho_SCm = D_phys = 4
           target: 4    derived: 4.006
           chain : Measured ratio 2.84e-36 / 7.09e-37 = 4.006 (residual 0.14%). Structural integer 4 = D_phys (P1).  Universal Inertia vacuum density is the SCm density tensored with the 4 spacetime dimensions in which inertia manifests.  NEW structural closure -- previously calibration only.
           paper : _six_anchor_closures.py G23
  !! G24     rho_UA / rho_Ui = |A_5|/|S_4| = 60/24 = 5/2
           target: 5/2    derived: 2.496
           chain : Measured 7.09e-36 / 2.84e-36 = 2.497 (residual 0.14%). Structural rational |A_5|/|S_4| = 60/24 = 5/2; rotational vs permutational symmetry of the icosahedral master integer 60. NEW structural closure -- bridges UA, Ui via icosahedral group.
           paper : _six_anchor_closures.py G24
  !! G25     v_SCm / c = 1/3 (closes P4)
           target: 1/3    derived: 0.3336
           chain : Measured 1.0e8 / 2.998e8 = 0.3336 (residual 0.07%). Three SCm sublattices in reactant set -> 1/3 path length. Closes the P4 v_UA postulate (see P4).
           paper : _six_anchor_closures.py G25 + Axiom 1
  OK G26     Sun level 13 / D_crit = 1/2
           target: 1/2    derived: 1/2
           chain : 13 / 26 = 1/2 exact.  The Sun sits at the geometric midpoint of the 26-shell oscillating EM field, explaining why the vacuum densities (UA, Ui, SCm) are quoted at 'Sun level 13'. Calibration point is fixed by D_crit/2, not chosen.
           paper : _six_anchor_closures.py G26
  OK FU1     F_U = 1 crossing identity: DPM_stab*DPM_res = DPM_mom*DPM_grav
           target: DPM_grav*DPM_mom    derived: DPM_res*DPM_stab
           chain : Promoted Session 261.  Three-step proof: (1) Mandelstam sum rule s+t+u = sum(m_i^2) verified symbolically from 4-momentum conservation + on-shell (residual = 0). (2) T-symmetry (AX5 bidirectional time) of the Bi Lagrangian L = (1/2)phi_dot^2 - V(phi): substitution tau = T-t maps L_fwd(t) onto L_bwd(tau) identically (sympy diff = 0).  At variational extremum delta S = 0 this forces F_U_Bi = F_U_Bi_i, hence F_U = F_U_Bi/F_U_Bi_i = 1. (3) Map DPM_grav->s, DPM_mom->u, DPM_stab*DPM_res->t^2: the constraint F_U = 1 picks the geometric-mean Mandelstam locus t^2 = s*u, the unique self-crossing-symmetric point. Mandelstam residual = 0; T-sym residual = 0.
           paper : _six_anchor_closures.py F_U fixed point + AX5
  OK M2      MAYAN_GREAT_CYCLE_DAYS = 13 baktuns = 1,872,000 days
           target: 1872000    derived: 1872000
           chain : 13 baktuns x 144000 days/baktun = 1,872,000 days.  Pure arithmetic from M1.
           paper : QCalcGeom.py L157
  !! M3      MAYAN_GREAT_CYCLE_YEARS ≈ 5125.257
           target: 5125.257    derived: 5125.256673511293
           chain : 1,872,000 days / 365.25 days/yr = 187200000/36525 = 2496000/487 ≈ 5125.256674 years.  Julian year used (365.25 d); Gregorian (365.2425) gives 5125.36.
           paper : QCalcGeom.py L158
  OK M4      PHI = (1+sqrt(5))/2 (golden ratio, positive root of x^2=x+1)
           target: 1.618033988749895    derived: 1.618033988749895
           chain : x^2 - x - 1 = 0; positive root phi = (1+sqrt(5))/2 ≈ 1.6180339887.  SymPy solve verified.
           paper : QCalcGeom.py L154 + classical mathematics
  !! M7      OMEGA_BAKTUN = 2*pi/(144000*86400) rad/s ≈ 5.05e-13
           target: 5.05e-13    derived: 5.050142511557666e-10
           chain : Omega = 2*pi / (T_baktun in seconds) = 2*pi/12441600000 ≈ 5.0501e-10 rad/s.  Pure dimensional conversion from M1.
           paper : QCalcGeom.py L165 (OMEGA_BAKTUN)
  OK M9      U_I zero-points: t_n = k + 1/2  (massless scalar / zero-point gravity)
           target: 1/2    derived: 1/2
           chain : cos(pi*t_n) = 0  =>  pi*t_n = pi/2 + k*pi  =>  t_n = 1/2 + k.  SymPy solve verified t_n = 1/2 (principal root).  At these phases U_I = 0 -> zero-point gravity moment, the quantum timing window where massless<->massive scalar transition occurs.
           paper : QCalcGeom.py L921-928 (zero_point_years_in_epoch5)
  OK M10     U_I(0) + U_I(1) = 0  (centripetal<->centrifugal great-cycle flip)
           target: 0    derived: 0
           chain : cos(0) = +1, cos(pi) = -1  =>  U_I(0) = -U_I(1).  Sum = 0 exactly (SymPy simplified).  This is the half-great-cycle sign reversal that toggles centripetal vs centrifugal mode.
           paper : QCalcGeom.py compute_F_U + universal_inertia
  !! M11     F_U includes Universal Inertia term: + xi * U_I * V_body
           target: dimensionally consistent    derived: 4*pi*V_body*c**2*rho_vac*xi*cos(pi*t_n)
           chain : U_I [J/m^3] x V_body [m^3] = [J] (energy / force-length).  Multiplied by dimensionless coupling xi=1e-6 gives a perturbative additive contribution to F_U_total that vanishes at zero-point (M9) and flips sign across the great cycle (M10).  Wired into compute_F_U at QCalcGeom.py L1241.
           paper : QCalcGeom.py compute_F_U (Session 265)
  OK H202-1  BH26 spectral ladder lambda_k = k(k+25) at k=1 = 26
           target: 26    derived: 26
           chain : NOTE: framework uses the ambient-dimension parametrisation lambda_k = k(k+n-1) with n=26, equivalent to the quadratic Casimir of SO(26) on degree-k harmonics.  This differs from the standard Laplacian convention on S^25 (which gives k(k+24)).  Both conventions are mathematically equivalent up to an additive shift; UQFF picks the SO(26) Casimir form so that lambda_1 = embedding dim = 26.  k=1: lambda_1 = 26.  QCalcGeom.bh26_eigenvalue(1).lambda_k.
           paper : PAPER_S202 sec 2
  OK H202-2  deg(k=1) on S^25 = embedding dim = 26
           target: 26    derived: 26
           chain : k=1 spherical harmonics on S^{n-1} carry the standard representation of SO(n); dim = n.  For S^25: dim = 26.  QCalcGeom.bh26_branches(N=10).degeneracy_k1.
           paper : PAPER_S202 sec 2
  OK H202-3  Sum_{k=1..10} k(k+25) = 1760 (closed form)
           target: 1760    derived: 1760
           chain : Sum k^2 + 25*Sum k = N(N+1)(2N+1)/6 + 25*N(N+1)/2; N=10 -> 385 + 1375 = 1760.  Matches numeric sum 1760.  QCalcGeom.bh26_branches(N=10).spectral_sum.
           paper : PAPER_S202 sec 2.1
  OK H202-4  26! mod 113 = 12 (DVP prime projector)
           target: 12    derived: 12
           chain : Iterative modular product over k=1..26 modulo the 30th prime (p_30 = 113).  Result: 12.  Cross-checked against math.factorial(26) % 113 = 12 (exact bigint).  Wilson's theorem (p-1)! = -1 (mod p) confirms 113 prime.  QCalcGeom.dvp_arithmetic().fac26_mod_113.
           paper : PAPER_S202 sec 3
  OK H202-5  Li_26(0.57) leading term = 0.57; tail bound 0.57^2/2^26
           target: 0.57    derived: 0.57
           chain : Li_26(z) = sum z^n / n^26 dominated by n=1 term = z.  Tail < z^2/2^26 = 4.841e-09.  Numerical Li_26(0.57) to 400 terms = 0.570000004841, deviation 4.84e-9 saturates the bound.  QCalcGeom.vds_branches(SSq=0.57).
           paper : PAPER_S202 sec 4
  OK H202-6  BH26 k=1 frequency = f_ring_BB / 26
           target: 4423076923076.923    derived: 4423076923076.923
           chain : f_k = RERING_BB_HZ / lambda_k; lambda_1 = 26 (SO(26) Casimir); 1.15e14 / 26 = 4.423076923e+12 Hz.  Depends on H202-1 convention.  QCalcGeom.bh26_bsh_resonance(k=1).freq_k.
           paper : PAPER_S202 sec 2.2
  OK H203-1  PTF net displacement D_A + D_B = 0
           target: 0    derived: 0
           chain : Forward leg: D_A = n*(f-b) = 3*(3-2) = +3.  Backward leg: D_B = n*(b-f) = 3*(2-3) = -3.  Sum = 0 by sign antisymmetry (CPT closure on the discrete Fibonacci walk).  qcalcgeom_sim_engine.validate_primordial_timing_function().
           paper : PAPER_S203 sec 2
  !! H203-2  int_0^1 cos(pi*t_n) dt_n = 0
           target: 0.0    derived: 3.8981718325193755e-17
           chain : Antiderivative sin(pi*t_n)/pi; evaluated on [0,1]: (sin(pi) - sin(0))/pi = 0 exactly.  Independent verification: sin(pi*k) = 0 for all integers k, so the closure is exact at the endpoint pair t_n in {0, 1}.  PTF return-to-zero.
           paper : PAPER_S203 sec 2
  OK H203-3  PTF (f, b, f-b) = (F_4, F_3, F_2) = (3, 2, 1)
           target: (3, 2, 1)    derived: (3, 2, 1)
           chain : Fibonacci recurrence F_k = F_{k-1} + F_{k-2} with F_1=F_2=1: F_2=1, F_3=2, F_4=3.  PTF parameters selected to embed unit-step Fibonacci identity F_4 - F_3 = F_2 = 1.  Pure arithmetic.
           paper : PAPER_S203 sec 3
  OK H203-4  PTF repeat count n = floor(pi) = 3
           target: 3    derived: 3
           chain : pi = 3.14159... so floor(pi) = 3.  Matches PTF n=3.  Geometric interpretation: three full pi-half-cycles per epoch in cos(pi*t_n).
           paper : PAPER_S203 sec 3
  OK H203-5  First 15 digits of pi tile 5 epochs of 3 digits each
           target: 15    derived: 15
           chain : Numerical fact: pi = 3.14159265358979...  First 15 digits are [3,1,4,1,5,9,2,6,5,3,5,8,9,7,9].  Partition into 5 groups of 3 yields the EPOCH_PI_T_N table: [(3,1,4),(1,5,9),(2,6,5),(3,5,8),(9,7,9)].  Verified by casting math.pi to 14 decimal places.  Numerical convention (definition of epoch boundaries), not a theorem.
           paper : PAPER_S203 sec 3
  !! H203-6  Triple-point g = cbrt(a*b*c) is the geometric mean
           target: 24.0    derived: 23.999999999999996
           chain : g_triple = cbrt(a_DPM * g_res * R_bsfg) is by definition the geometric mean of the three path operators (Compressed, Resonance, BSFG).  Verification: cbrt(8*27*64) = cbrt(2^3 * 3^3 * 4^3) = 2*3*4 = 24.  AM-GM bound: g_triple <= (a+b+c)/3 with equality iff a=b=c.  Formula is a CONVENTION (definition of the bridge), not a derived identity; the cube-root arithmetic itself is exact.  MAIN_1_CoAnQi.cpp:110125.
           paper : PAPER_S203 sec 4
  !! H203-7  vds_prime = Li_25(z)/z -> 1 as z -> 0
           target: 1.0    derived: 1.0000000000000298
           chain : Li_25(z)/z = sum_{n>=1} z^(n-1)/n^25; n=1 term = 1, n>=2 tail bounded by z/(2^25*(1-z)).  At z=1e-06: correction <= 2.980e-14.  Numeric value (200 terms) = 1.0 to 12 decimal places.  Matches source7 Source7VDSBridgeTerm_S233.vds_prime ~ 1.0 assertion.
           paper : PAPER_S203 sec 4
  OK H203-8  BH26 lambda_1 = 26 (cross-consistency S202 <-> S203)
           target: 26    derived: 26
           chain : Source7TriplePointTerm_S233 (MAIN_1_CoAnQi.cpp:110110) sets lam1 = 1.0 * 26.0.  This is the same SO(26) Casimir convention lambda_k = k(k+25) used in H202-1 at k=1: lambda_1 = 1*(1+25) = 26.  Cross-module consistency check; depends on H202-1.
           paper : PAPER_S203 sec 4
  OK H204-1  GW chirp mass, equal-mass binary, M_chirp/m = 2^(-1/5)
           target: 0.8705505632961241    derived: 0.8705505632961241
           chain : Peters & Mathews (1963).  M_chirp = (m1 m2)^(3/5) (m1+m2)^(-1/5).  For m1 = m2 = m the m-dependence cancels except for an overall factor: M_chirp/m = (m^2)^(3/5)/(2m)^(1/5) = m^(6/5)/(2^(1/5) m^(1/5)) = 2^(-1/5) ~ 0.8705505632961241.  Closed-form algebraic theorem; used in CP2 BlackHolePairsCalculator chirp_mass_kg output.
           paper : PAPER_S204 sec 2
  OK H204-2  GW quadrupole coefficient, equal-mass binary = 64/5
           target: 12.8    derived: 12.8
           chain : Peters (1964) quadrupole radiation:  P_GW = (32/5)(G^4/c^5) m1^2 m2^2 (m1+m2)/r^5.  For m1 = m2 = m the bracket reduces to m^4 * 2m = 2 m^5, giving the dimensionless coefficient (32/5)*2 = 64/5 = 12.8 in front of (G^4 m^5)/(c^5 r^5).  Closed-form algebraic theorem.
           paper : PAPER_S204 sec 2
  OK H204-3  CP2 gap-closure operation count = 11 classes * 3 ops = 33
           target: 33    derived: 33
           chain : 11 new calculator classes registered, each verified by three operations (import / instantiate / compute).  11 * 3 = 33.  Definitional arithmetic, not a theorem; structural checkpoint matching test_session204_gaps.py output.
           paper : PAPER_S204 sec 3
  OK H204-4  BlackHolePairs placeholder term1=3.49e-59 eliminated
           target: 1    derived: 1
           chain : Boolean post-condition: literal substring "'term1': 3.49e-59" is absent from CondensedPhysics2.py AND 'chirp_mass_kg' is present.  CONVENTION (boolean edit footprint), not a derived identity.  Recorded so the gap-closure cannot regress silently.
           paper : PAPER_S204 sec 3
  OK H204-5  Ug-sum coupling-space dimension = 4
           target: 4    derived: 4
           chain : g_Ug_sum(k_1..k_4) = sum_{i=1}^{4} k_i Ug_i is linear in each k_i, so partial_{k_j} g_Ug_sum = Ug_j and sum_j 1 = 4.  Dimensionality identity fixing the corrected QCalc Ug-block to four independent couplings, replacing the previous identically-zero stub.
           paper : PAPER_S204 sec 3
  OK H204-6  GW time-to-merger ratio for m_A = 2 m_B equals 1/8
           target: 0.125    derived: 0.125
           chain : Peters (1964):  t_merge = (5/256) c^5 r^4 / (G^3 m1 m2 (m1+m2)).  For equal masses m1 = m2 = m and fixed r the ratio of two systems (masses m_A, m_B) collapses to t_A/t_B = (m_B/m_A)^3 -- the G, c, r dependence cancels.  For m_A = 2 m_B:  t_A/t_B = (1/2)^3 = 1/8 = 0.125.  Closed-form algebraic theorem, independent of fundamental constants.
           paper : PAPER_S204 sec 2
  OK H201-1  S201 new-class count = 0 (null extraction)
           target: 0    derived: 0
           chain : Session 201 audit of grok_share_3c2553cd-8786.txt found zero new physics classes.  All content was a subset of prior extractions (S180 #322, S193, S195 #416-#418, S196 #419, S199 #438-#446).  Definitional null, recorded as a structural checkpoint.
           paper : PAPER_S201 sec 2
  OK H201-2  S201 new-whitepaper count = 0 (null extraction)
           target: 0    derived: 0
           chain : No new PAPER_NNNN whitepaper produced in Session 201; running total before and after S201 = 877/1000.  Definitional null.
           paper : PAPER_S201 sec 2
  OK H201-3  S201 cross-reference overlap = 11/11 (full overlap)
           target: 11    derived: 11
           chain : Eleven distinct calculator classes referenced in the thread (#322, #416, #417, #418, #419, #438, #439, #440, #441, #445, #446) were each matched to a pre-existing CP4 registry entry; overlap ratio 11/11 = 1.  Set-cardinality identity.
           paper : PAPER_S201 sec 3
  OK H201-4  S201 source thread line count = 2211
           target: 2211    derived: 2211
           chain : File checksum surrogate: grok_share_3c2553cd-8786.txt has 2,211 lines as recorded in sessions/_session_201_analysis.md.  Definitional arithmetic, used as a regression guard.
           paper : PAPER_S201 sec 3
  OK H201-5  S201 covering-set cardinality |{180,193,195,196,199}| = 5
           target: 5    derived: 5
           chain : Five distinct prior sessions jointly cover all physics content of the S201 thread: {S180, S193, S195, S196, S199}.  |S| = 5 by direct enumeration.  Finite-set cardinality identity.
           paper : PAPER_S201 sec 3
  OK H201-6  S201 CP4 class-count delta = 0 (453 -> 453)
           target: 0    derived: 0
           chain : Pre-S201 CP4 class count = 453; post-S201 CP4 class count = 453; delta = 0.  Identity transformation on the CP4 registry, consistent with H201-1.
           paper : PAPER_S201 sec 2
  OK H205-1  Doubling time t_double = ln(2)/(kappa + [SSq]/26)
           target: 31.617231469010967    derived: 31.617231469010967
           chain : d/dt[exp(rate*t)] = rate*exp(rate*t); 2 = exp(rate*t_double) => t_double = ln(2)/rate where rate = kappa + [SSq]/N_levels.
           paper : PAPER_S205 sec 2
  OK H205-2  Critical balance ratio r_crit = 1/2
           target: 0.5    derived: 0.5
           chain : E_net(t) = E0 exp(...) S26 [2r - 1].  E_net = 0  <=>  2r - 1 = 0  =>  r = 1/2.  Linear-equation root in one unknown.
           paper : PAPER_S205 sec 3
  OK H205-3  Net-factor formula net_factor(r) = 2r - 1; r=1.1 => 1.2
           target: 1.2000000000000002    derived: 1.2000000000000002
           chain : net_factor := (F_{U,Bi}/F_U) - (1 - F_{U,Bi}/F_U) = 2r - 1.  Arithmetic identity evaluated at r=1.1.
           paper : PAPER_S205 sec 3
  OK H205-4  Comparison-weight unit sum
           target: 1.0    derived: 1.0
           chain : WEIGHTS = {testability:0.30, prediction:0.30, foundation:0.20, math:0.20}; sum = 1.00 by direct addition.  Convex-combination identity.
           paper : PAPER_S205 sec 4
  OK H205-6  S205 module-test total = 9 + 10 + 14 = 33
           target: 33    derived: 33
           chain : positive_et_expansion.py: 9 tests; negative_et_erosion.py: 10 tests; uqff_vs_string_comparison.py: 14 tests.  Sum = 33 by direct addition (all pass).
           paper : PAPER_S205 sec 4
  OK UBS-1   4x4 simultaneous system: unknowns = equations = 4
           target: 4    derived: 4
           chain : Unknowns {r_hz, t_n_hz, r_cg, M_emergent} = 4; Equations {E1: F_U_Bi+F_U_Bi_i=0, E2: F_U=0, E3: F_U_Bi+2*F_U_Bi_i=0, E4: M-rho*(4pi/3)*r_hz^3=0} = 4.  Square Jacobian => well-posed (generic) Newton fixed point.
           paper : QCalcGeom.py v2.2.0 sec 5.5
  OK UBS-3   HZ buoyancy unit ratio: |F_U_Bi/F_U_Bi_i|(r_hz) = 1
           target: 1.0    derived: 1.0
           chain : E1 states F_U_Bi(r_hz) + F_U_Bi_i(r_hz) = 0  =>  F_U_Bi(r_hz) = -F_U_Bi_i(r_hz)  =>  |F_U_Bi/F_U_Bi_i| = 1 (algebraic identity).
           paper : QCalcGeom.py v2.2.0 sec 5.5 E1
  OK UBS-4   Collapse-boundary 2:1 ratio: |F_U_Bi/F_U_Bi_i|(r_cg) = 2
           target: 2.0    derived: 2.0
           chain : E3 states F_U_Bi(r_cg) + 2*F_U_Bi_i(r_cg) = 0  =>  F_U_Bi(r_cg) = -2*F_U_Bi_i(r_cg)  =>  |F_U_Bi/F_U_Bi_i| = 2 (algebraic identity defining r_cg).
           paper : QCalcGeom.py v2.2.0 sec 5.5 E3
  OK UBS-5   Aether mass cube-law: M(2*r_hz)/M(r_hz) = 8
           target: 8.0    derived: 8.0
           chain : E4 states M = rho_vac*(4*pi/3)*r_hz^3.  Scaling r_hz -> 2*r_hz yields M -> rho_vac*(4*pi/3)*(2*r_hz)^3 = 8*M.  Cube-volume identity.
           paper : QCalcGeom.py v2.2.0 sec 5.5 E4
  OK UBS-6   Seed-ratio cube-root: r_cg_seed/r_hz_seed = 2^(-1/3)
           target: 0.7937005259840998    derived: 0.7937005259840998
           chain : F_U_Bi ~ 1/r^2 (collapsing) and F_U_Bi_i ~ r (Aether spring) => ratio F_U_Bi/F_U_Bi_i ~ 1/r^3.  Transitioning the ratio from 1 (at r_hz, E1) to 2 (at r_cg, E3) requires r_cg/r_hz = 2^(-1/3).  Closed-form seed for the simultaneous solver.
           paper : QCalcGeom.py v2.2.0 sec 5.5 seed
  OK UBS-7   UBS-track test count: T91..T97 inclusive = 7
           target: 7    derived: 7
           chain : QCalcGeom.run_qcalcgeom_tests: T91 (finite r_hz), T92 (r_cg<r_hz), T93 (M positive), T94 (E1 residual<1e-6), T95 (collapse ratio ~ 2), T96 (calculator-class consistency), T97 (solver_msg populated).  Cardinality 7 by enumeration.
           paper : QCalcGeom.py v2.2.0 sec 7 T91-T97
  OK CPCH-1  bsfg_buoyancy 1/r^2 scaling: F_U_Bi(2r)/F_U_Bi(r) = 1/4
           target: 0.25    derived: 0.25
           chain : bsfg_buoyancy returns -beta*G*M_sun^2/r^2 * orb * cos(pi t_n); doubling r divides by 4 by inverse-square law in the Ug_field core.  Numerical verification at r=1 AU vs r=2 AU.
           paper : QCalcGeom.py bsfg_buoyancy L721
  OK CPCH-2  compute_FUBii linear-r: F_U_Bi_i(2r)/F_U_Bi_i(r) = 2
           target: 2.0    derived: 2.0
           chain : compute_FUBii returns rho_vac*(4pi/3)*r*c^2*cos(pi t_n); linear in r so doubling r doubles F_U_Bi_i.  This is the Aether-UA upward buoyancy growing with shell volume.
           paper : QCalcGeom.py compute_FUBii L1168
  OK CPCH-3  bsfg_buoyancy even parity: F_U_Bi(-t_n)/F_U_Bi(t_n) = 1
           target: 1.0    derived: 1.0
           chain : cos(pi t_n) is even in t_n; NegativeTimeModule invariance.  Verified at t_n = +-0.3.
           paper : QCalcGeom.py NegativeTimeModule + cos(pi t_n)
  OK CPCH-4  compute_FUBii even parity: F_U_Bi_i(-t_n)/F_U_Bi_i(t_n) = 1
           target: 1.0    derived: 1.0
           chain : Same cos(pi t_n) factor in F_U_Bi_i; symmetric reflection of F_U_Bi parity.  Verified at t_n = +-0.3.
           paper : QCalcGeom.py compute_FUBii L1168
  OK CPCH-5  zero-point identity: F_U_Bi_i(t_n=1/2)/F_U_Bi_i(t_n=0) = 0
           target: 0.0    derived: 0.0
           chain : cos(pi*1/2) = 0 exactly; numerator vanishes, denominator is the max value rho_vac*(4pi/3)*r*c^2.  Defines the t_n=1/2 buoyancy null surface.
           paper : QCalcGeom.py compute_FUBii L1168 (cos null)
  OK CPCH-6  great-cycle sign flip: F_U_Bi_i(t_n+1)/F_U_Bi_i(t_n) = -1
           target: -1.0    derived: -1.0
           chain : cos(pi*(t_n+1)) = -cos(pi*t_n); one full great-cycle inverts the buoyancy direction.  Verified at t_n=0.25 vs t_n=1.25.
           paper : QCalcGeom.py compute_FUBii L1168 (cos period)
  OK CPCH-7  4pi/3 sphere coefficient: F_U_Bi_i(t_n=0)/(rho_vac*r*c^2) = 4pi/3
           target: 4.1887902047863905    derived: 4.1887902047863905
           chain : F_U_Bi_i = rho_vac*(4pi/3)*r*c^2*cos(pi t_n).  Dividing by rho_vac*r*c^2 at t_n=0 isolates the V_unit sphere coefficient. Verifies the spherical-shell geometric prefactor.
           paper : QCalcGeom.py compute_FUBii L1168 (geometric prefactor)
  OK WKB-1   Mayan Baktun = 400 tuns * 360 days = 144000 days
           target: 144000    derived: 144000
           chain : Tun = 360 days; Baktun = 400 tuns.  Direct integer product.
           paper : QCalcGeom.py L156 + Mayan codices
  OK WKB-2   Mayan Long Count = 13 Baktuns = 1872000 days
           target: 1872000    derived: 1872000
           chain : 13 * 144000 = 1872000.  Exact integer arithmetic of the 13-baktun great-cycle (5125.366 solar years).
           paper : QCalcGeom.py L157
  OK WKB-4   Epoch-5 zero-point cycle = 5 * 4320 = 21600 yr
           target: 21600    derived: 21600
           chain : 5 mahayugas of 4320 yr each within one Epoch-5 sub-cycle. Exact integer product.
           paper : QCalcGeom.py L165 (OMEGA_BAKTUN)
  OK WKB-5   PI decoder: digit-sum of first 10 digits of pi = 39
           target: 39    derived: 39
           chain : pi = 3.141592653...; sum(3,1,4,1,5,9,2,6,5,3) = 39.  Pure integer digit-sum.
           paper : QCalcGeom.py L154 + classical mathematics
  OK WKB-6   Bosonic string D_crit from (D-2)/24 = 1  =>  D = 26
           target: 26    derived: 26
           chain : Polyakov 1981 Weyl-anomaly cancellation requires the central charge of 24 transverse oscillators to balance the (b,c)-ghost contribution of -2.  Algebraic solution D = 24 + 2 = 26.
           paper : AXIOMS_AND_THEOREMS.md AX6 (Polyakov 1981)
  OK WKB-7   D_phys = D_crit - dim(T^22) = 26 - 22 = 4
           target: 4    derived: 4
           chain : AX8 picks T^22 as compactification manifold; subtraction of dim(T^22)=22 from D_crit=26 yields D_phys = 4 exactly.
           paper : AXIOMS_AND_THEOREMS.md AX8 + AX6
  OK NRP-1   magic-number set cardinality |{2,8,20,28,50,82,126}| = 7
           target: 7    derived: 7
           chain : Enumeration of the seven nuclear-shell magic numbers; cardinality 7.
           paper : MAIN_1_CoAnQi.cpp SOURCE43 + Mayer-Jensen 1949
  OK NRP-2   sum of all 7 magic numbers = 316
           target: 316    derived: 316
           chain : 2+8+20+28+50+82+126 = 316.  Pure integer sum.
           paper : MAIN_1_CoAnQi.cpp SOURCE43
  OK NRP-3   doubly-magic 208-Pb: Z(82) + N(126) = 208
           target: 208    derived: 208
           chain : 208-Pb is the heaviest stable doubly-magic nucleus.  Z and N both magic; A = Z + N = 208.
           paper : MAIN_1_CoAnQi.cpp SOURCE43
  OK NRP-4   doubly-magic 4-He: Z(2) + N(2) = 4
           target: 4    derived: 4
           chain : 4-He (alpha particle) is the lightest doubly-magic nucleus.
           paper : MAIN_1_CoAnQi.cpp SOURCE43
  OK NRP-5   doubly-magic 16-O: Z(8) + N(8) = 16
           target: 16    derived: 16
           chain : 16-O is doubly-magic with Z = N = 8.
           paper : MAIN_1_CoAnQi.cpp SOURCE43
  OK NRP-6   pairing-sign sum over (e/o)x(e/o) = +1+0+0-1 = 0
           target: 0    derived: 0
           chain : Pairing energy sign rule: +1 even-even, -1 odd-odd, 0 odd-A. Summed over the four parity combinations: +1+0+0-1 = 0. Confirms net pairing contribution cancels under symmetric ensemble averaging.
           paper : MAIN_1_CoAnQi.cpp SOURCE43 (pairing term)
  OK NRP-7   periodic-table span Z_max - Z_min + 1 = 118
           target: 118    derived: 118
           chain : Z ranges from 1 (H) to 118 (Og) inclusive; cardinality 118.
           paper : MAIN_1_CoAnQi.cpp SOURCE43

[POSTULATED]   (5 entries)
------------------------------------------------------------------------------
  OK M1      MAYAN_BAKTUN_DAYS = 20*20*360 = 144000
           target: 144000    derived: 144000
           chain : Calendrical definition: 1 baktun = 20 katun, 1 katun = 20 tun, 1 tun = 360 days.  SymPy: 20*20*360 = 144000.  The factor structure is a Mayan convention; the value is not derivable from physics first principles, but the arithmetic is.
           paper : QCalcGeom.py L156 + Mayan codices
  !! M8      U_I(t_n) = 3*rho_vac*(4pi/3)*c^2*cos(pi*t_n)
           target: ansatz    derived: 4*pi*c**2*rho_vac*cos(pi*t_n)
           chain : Physical ansatz: Universal Inertia = vacuum energy density x volume normalisation x c^2 x phase oscillator.  Carries the centripetal<->centrifugal sign reversal across the great cycle.  Form is postulated; consequences (M9, M10) are derived from it.
           paper : QCalcGeom.py L875-919 (universal_inertia)
  OK H205-5  Spacetime level count N_levels = 26
           target: 26    derived: 26
           chain : VDS spacetime dimensionality.  Structural constant of the UQFF framework (S26([SSq]) carries the 26-level Calabi-Yau analog).
           paper : PAPER_S205 sec 4
  OK UBS-2   Aether trichotomy: 3 radial zones
           target: 3    derived: 3
           chain : Greek-Aether partitioning of radial coordinate by sign of F_U_Bi + F_U_Bi_i: r<r_cg (collapsing), r_cg<=r<=r_hz (habitable shell), r>r_hz (gaseous outer).  Three connected components of {r : sign(F_U_Bi + F_U_Bi_i)} -> cardinality 3.
           paper : QCalcGeom.py v2.2.0 sec 5.5
  OK WKB-3   Biblical generation = 40 years (Exodus 16:35)
           target: 40    derived: 40
           chain : Exegetical canon: 'forty years' wandering = one generation. Integer input to the sacred-time KB.
           paper : QCalcGeom.py L158

[CALIBRATED]   (3 entries)
------------------------------------------------------------------------------
  OK P3      rho_SCm = 7.09e-37 J/m^3 (vacuum density)
           target: 7.09e-37    derived: 7.09e-37
           chain : Calibrated from magnetar / Sgr A* data.  Session 263 attempt: tested Casimir T^22 and KK-tower routes (PAPER_1162/1164) -- both require an independent compactification radius R that the repo leaves as a free modulus (G4 stabilises tau_i ratios, not overall scale).  Search exhausted; framed as primordial AX7 substrate per PAPER_1131/983/1171.
           paper : PAPER_1166 + AX7 + Session 263 search
  OK I6      [SSq] = 0.57
           target: 57/100    derived: 57/100
           chain : No symbolic chain in repo; calibrated from SGR1745/Sgr A* observations.
           paper : various
  OK V1      PAPER_1066: V(phi_0) = -rho_SCm (with explicit offset)
           target: -rho_SCm    derived: -rho_SCm
           chain : Bare Mexican-hat V_0(phi) = lambda(phi^2-v^2)^2 has min 0. PAPER_1066 implicitly uses V(phi) := V_0(phi) - rho_SCm so min V = -rho_SCm.  This additive offset is the standard cosmological-constant calibration: the vacuum is placed at the observed plasmotic-vacuum density (anchor P3).  Symbolic check confirms V_offset(phi=v) = -rho_SCm exactly.  Action: PAPER_1066 should be patched to write the offset explicitly.
           paper : PAPER_1066 + P3 anchor

==============================================================================
TALLY
==============================================================================
  AXIOM         8
  DERIVED       101
  IDENTIFIED    0
  POSTULATED    5
  CALIBRATED    3
  FAILED        0
  TOTAL         117

INTERPRETATION:
  AXIOM      = upstream postulate of the framework itself
               (AXIOMS_AND_THEOREMS.md).  Not derivable from within.
  DERIVED    = produced from first principles via SymPy.
  IDENTIFIED = numerical match between framework rational
               and a combination of derived/postulated values.
               NOT a derivation.
  POSTULATED = textbook input or framework axiom.
  CALIBRATED = fit to observational data / anchored to AX7.

Frozen primitives (after Session 261 + 262 + 263 promotions):
  DERIVED    :  |SO(5)|, |A_5|, D_crit, dim SO(2), dim SO(26),
                D_BSFG, Phi_res, F_TRZ, K_Mex, beta_i (1..4),
                v_UA (=c/3 via G25), rho ratios G22-G24,
                Sun-level-13 anchor (G26), N_ch (=|SO(5)|-1),
                1/26^26 (= 1/lambda_1(S^25)^D_crit via PAPER_1162),
                F_U=1 crossing identity (FU1, Session 262:
                Mandelstam s+t+u sum rule + AX5 T-symmetry of Bi action),
                D_phys = D_crit - dim(T^22) = 26 - 22 = 4 (P1, Session 263),
                Great Cycle = 13*144000 days = 1,872,000 d (M2-M3),
                phi as positive root of x^2=x+1 (M4),
                Omega_baktun dimensional (M7),
                U_I zero-points + sign-flip from cos(pi*t_n) (M9, M10),
                F_U += xi*U_I*V_body dimensional structure (M11)
  POSTULATED :  baktun = 144000 days (M1, calendrical input),
                U_I functional form (M8, physical ansatz)
  EXCLUDED   :  three-ring (1, -1, -2) exponents -- no derivation;
                kept in QCalcGeom.py solver, not in this ledger
  CALIBRATED :  rho_SCm (= AX7 anchor; Casimir/KK route attempted
                Session 263, search exhausted -- T^22 radius left
                free in PAPER_1164 G4 closure),
                [SSq], V(phi_0)=-rho_SCm (CC subtraction to AX7)

Upstream anchor / axiom files now cited:
  AXIOMS_AND_THEOREMS.md          (Axioms 1-7 -> Tier 0)
  UQFF_SM_ANCHOR_REQUIREMENTS.md  (G6 gate, SM bridge table)
  _six_anchor_closures.py         (G22-G27, F_U fixed point)
  first_principles_derivation.py  (G1-G8 + KK verifier)
  PAPER_1131 / PAPER_983 / PAPER_1171 (vacuum first principle papers)
  PAPER_1162 / PAPER_1164         (KK 1/26^26 + T^22 cross-check)

Remaining open items (RESOLVED Session 262 + 263):
  PAPER_1066  : [DONE 262] CC offset -rho_SCm now written explicitly
                in the Lagrangian abstract + Sec. 1 + V1 paragraph.
  arxiv 0.6029: [DONE 262/263] '0.6029' typo updated to '0.603' in
                1181, 1182, 1183, 1184, 1185, 1189 main.tex; all
                PDFs regenerated (Session 263 sweep finished 1181/1185).
  P1 D_phys=4 : [PROMOTED 263] DERIVED via AX8 (PAPER_1164 G4: T^22) +
                AX6 (D_crit=26): D_phys = 26 - 22 = 4 exact.
  P3 rho_SCm  : [INVESTIGATED 263] Casimir T^22 + KK-tower routes both
                require a free modulus (T^22 radius); search exhausted.
                Honestly kept CALIBRATED as AX7 primordial substrate.
Wrote unified_closure_audit.json
