Einstein tests: Relativistic Compatibility | G Model Perspective

Complete Einstein Tests audit

G MODEL Einstein Compatibility, Spin-2, and Gravitational Field-Equation Tests Complete Current Audit for the Website Tests Section | Gurbuz Dolu | 12 September 2026 Scope: retained Einstein/GR-compatibility records were reviewed and duplicate manuscript copies or repeated restatements were not counted as new tests. Historical failures remain visible. Later native-action, tensor, conservation, rotation, and wave results are used where they genuinely update an earlier status.

Distinct Einstein-related checks 38

PASS / structural / conditional PASS 27

FAIL / rejected / superseded test routes 6

OPEN major derivations / closures 5

Current controlled Einstein verdict The current G Model has a lossless ten-component branch representation of symmetric spacetime tensors; an exact branch representation of the linearized Einstein/Fierz-Pauli continuum structure; an Einstein-operator coefficient pattern that is unique under explicit continuum symmetry and conservation assumptions; a native spinless area-holonomy action class that structurally yields a torsion-free metric-compatible connection; and a conditional two-function static spherical completion whose exterior is exactly Schwarzschild. These are substantial mathematical/compatibility results. They are not yet a proof that the complete finite-cell G Model derives general relativity from microscopic first principles.

Counting and status rule A PASS means the stated mathematical test closes in its declared domain. CONDITIONAL or STRUCTURAL PASS means an adopted action, continuum symmetry class, or completion is part of the premise. A FAIL means a specific ansatz, operator identification, or incomplete route failed its own requirement. OPEN means the decisive microscopic derivation is still missing. None of these labels is experimental validation.

1. Complete De-duplicated Einstein Test Register The table below counts distinct scientific checks once. Closely related algebraic substeps are grouped rather than inflated into separate tests. # Test Core mathematics Status Current interpretation / re-test

1 Four-null inverse-Gram K G4^-1 K^T = eta PASS Exact supporting identity. Gives the spacetime reconstruction required 1+3 spacetime metric in the branch basis.

2 Flat-background branch (G4^-1)^(ab) D_a D_b = Box PASS Exact for a constant branch frame; d'Alembertian curved/discrete use requires connection terms.

3 Full 4+6 symmetric tensor Q_ab=k_a^mu k_b^nu h_mu_nu; PASS 4 self-branch + 6 pair values = all 10 encoding H_ab=k_a^mu k_b^nu T_mu_nu symmetric tensor components; lossless reconstruction.

4 Trace and trace-reversal h=(G4^-1)^(ab)Q_ab; PASS Exact branch image of the standard reconstruction Qbar_ab=Q_ab-(1/2)G4_ab Q spacetime operations.

5 Harmonic-gauge (G4^-1)^(ac) D_a Qbar_cb = 0 PASS Exact representation of the standard representation harmonic condition in the flat branch frame; gauge origin remains separate.

6 Four-component (G4^-1)^(ac) D_a H_cb = 0 PASS The branch basis can represent all four matter-conservation conservation equations. This does not representation force them dynamically.

# Test Core mathematics Status Current interpretation / re-test

7 Weak scalar metric: static G00^(1)=2 nabla^2 M; PASS Correct static pressureless scalar dust Einstein tensor G0i^(1)=Gij^(1)=0 sector.

8 Weak scalar metric as a single M only FAIL Cannot encode general pressure, shear, complete general source or moving-matter response. description Superseded by the full 10-component tensor extension.

9 Native weak source nabla^2 M=C_Sigma c^3 Tc^2 PASS Conditional native source normalization rho/hbar; kappa_E=2 C_Sigma c normalization; with measured Big G it Tc^2/hbar matches 8 pi G/c^4.

10 Full identity-like 4+6 weak Box Qbar_ab = -kappa H_ab PASS Strong conditional/structural pass. sourced equation Exact equivalence to the continuum tensor wave equation once the gauge structure is adopted.

11 Six-channel P as the spec(P)={1,0,0,0,-1/2,-1/2} FAIL Rank-3 action on the six pair sector complete Einstein would erase three source/shear matter-source operator directions. P remains an internal response/equalization operator.

12 Gauge-consistent source S_mu_nu=a T_mu_nu+b eta_mu_nu T PASS Given massless spin-2 gauge symmetry coupling / independent and source conservation, direct tensor trace admixture coupling is consistent; independent trace coupling is not generic.

# Test Core mathematics Status Current interpretation / re-test

13 Microscopic derivation of delta Q_ab = D_a xi_b + D_b xi_a OPEN Continuum branch representation is linearized diffeomorphism exact, but discrete relational ontology gauge symmetry has not yet proved this gauge redundancy from microscopic dynamics.

14 Pure-gauge linearized Q_ab=D_a xi_b+D_b xi_a => PASS Exact in the flat-background branch curvature cancellation R_abcd[Q]=0 calculus.

15 Linearized Einstein operator E_ab[Q]=(1/2)[-D^2Q_ab + ... + PASS Exact representation of the standard in branch variables G4_ab D^2Q] linearized Einstein tensor; identically conserved.

# Test Core mathematics Status Current interpretation / re-test

16 Uniqueness of linearized A=-B, C=-B, D=-B, E=B PASS Exact under explicit assumptions: Einstein coefficient pattern symmetry, Lorentz covariance, locality, <=2 derivatives, gauge redundancy, identical conservation.

17 Fierz-Pauli kinetic structure L_FP in Q_ab branch variables PASS Exactly representable; not yet representability microscopically generated by finite-cell dynamics.

18 Continuum dim W(k-hat)=2; equivalently PASS Strong continuum structural result transverse-traceless 10-4-4=2 under the massless spin-2 gauge gravitational mode count conditions.

# Test Core mathematics Status Current interpretation / re-test

19 First-order Tc relaxation as Tc dq/dtau = -(I-P)q FAIL Centered modes decay exponentially the complete rather than propagate as a gravitational-wave equation conservative two-way wave. Retained only as local recovery/relaxation.

20 Second-order covariant omega^2 -> c^2 k^2 at long PASS Structural long-wave pass. The exact inter-cell tensor propagation wavelength finite-cell/high-k action-derived propagation theorem remains open.

21 Native area-holonomy D[(J_*+beta I)Sigma]=0 => D PASS Structural pass for a nondegenerate action -> torsion-free Sigma=0 => T^I=0 spinless coframe within the adopted connection native action class.

22 Smooth native action -> e^J wedge *F_IJ = 0 PASS Strong structural pass within the Einstein-form vacuum adopted smooth action class; not yet coframe equation complete discrete matter dynamics.

23 Einstein trace coefficient X_ab=R_ab+alpha gamma_ab R; PASS G Model-native connection/curvature from curvature conservation conservation => alpha=-1/2 variables plus the contracted Bianchi identity select the Einstein-type combination.

24 General moving / pressure / H_ab carries density, momentum, PASS Full tensor source is shear / anisotropic source pressure, shear, anisotropic stress information-complete; this repairs the completeness earlier scalar/P-only limitations.

# Test Core mathematics Status Current interpretation / re-test

25 Full microscopic source C_b=(G4^-1)^(ac) Delta_a H_cb = 0 OPEN The rank-four divergence operator conservation exists, but C_b=0 is not yet an identity of proved finite-cell matter dynamics.

26 H Yazici conservation repair symmetric H-level correction cancels PASS Exact in its proved neutral/commuting admissible divergence defect sector with bounded Continuity-Time inverse; unique curved physical update remains open.

27 Nonlinear time-dependent dynamic A,B,C coframe; nonlinear PASS Kasner-type test supports nonflat anisotropic vacuum omega wedge omega curvature vacuum curvature with vanishing compatibility conserved gravitational tensor in the adopted connection architecture.

28 Historical one-function ds^2=-e^(2M)dt^2+e^(-2M)dx^2 FAIL Exact Ricci test forces the nontrivial reciprocal exponential static static vacuum field away. Retained only vacuum as weak-field parametrization.

29 Conditional two-function psi=-mu/r -> exact isotropic PASS Exact Ricci-flat Schwarzschild exterior static spherical exterior Schwarzschild metric; R_mu_nu=0 within the conditional two-function completion.

30 Generic harmonic psi as an nabla^2 psi=0 alone FAIL Harmonicity is necessary but not automatic exact sufficient; the additional spatial Ricci two-function vacuum tensor condition must also hold. solution

# Test Core mathematics Status Current interpretation / re-test

31 Weak rotating-source frame O(J): R^-3 rotational connection / PASS Structural weak-rotation pass using the dragging Lense-Thirring functional form same coupling pathway; no new fitted force.

32 Pure rotational shift alone at rotation-only second-order ansatz FAIL Residual equations require scalar l=0 O(J^2) plus quadrupolar l=2 backreaction. The failure is of the incomplete ansatz.

33 Second-order rotation O(J): P=0; O(J^2): P=1 plus P=-1/2 PASS Structural closure of momentum + closes the 1+3+2 sector scalar + quadrupolar response under hierarchy rotation.

34 Horizon/asymptotic Q_phys = -J^2/(M c^2) PASS Conditional structural result: regularity selection of second-order and asymptotic flatness remove quadrupole independent quadrupole hair.

35 Third-order current-octupole O(J^3): l=1 plus l=3 PASS Angular selection and homogeneous channel / no free l=3 hair no-hair result pass structurally; the native inhomogeneous coefficient is still not independently calculated.

36 All-orders native Kerr M_l+i S_l ?= M(ia)^l from G Model OPEN Higher-order channel structure is multipole coefficients recursion constrained, but full native inhomogeneous coefficients are unfinished.

# Test Core mathematics Status Current interpretation / re-test

37 Two physical action-derived microscopic OPEN Continuum TT count is two; gravitational-wave modes at propagation with only two tensor finite-cell/high-k action-derived closure finite-cell scale modes is still missing.

38 Complete generic all vacuum/source geometries OPEN Several nonlinear and nonspherical nonlinear/nonspherical compatibility tests pass, but full Einstein equivalence general equivalence has not been derived and is not required to be assumed.

2. Weak-Field Tensor and Linearized Einstein Tests 2.1 Full tensor capacity — the essential representational PASS Q_ab = k_a^mu k_b^nu h_mu_nu H_ab = k_a^mu k_b^nu T_mu_nu 4 diagonal + 6 off-diagonal = 10 independent components h = (K^-1)^T Q K^-1 T = (K^-1)^T H K^-1

This removes a basic obstruction: the four-null/six-pair language does not lose pressure, momentum, shear, or anisotropic stress when the full branch tensor H_ab is used.

2.2 The scalar-only and P-only source failures Two early simplifications were too restrictive. A single scalar weak metric correctly reproduces the static dust 00 sector but cannot carry general pressure, shear, or moving matter. Separately, the six-channel equalizer P has three zero eigenvalues and therefore cannot be the complete matter-to-metric source map. spec(P) = {1, 0, 0, 0, -1/2, -1/2} rank(P) = 3 on the six-pair space

These failures do not remove the full tensor construction. They explain why P must remain an internal spectral/equalization operator inside the complete H_ab source rather than replace the stress-energy tensor.

2.3 Linearized Einstein operator E_ab[Q] = 1/2 [ -D^2 Q_ab + D_a D^c Q_cb + D_b D^c Q_ca - D_a D_b Q - (G4)_ab D^c D^d Q_cd + (G4)_ab D^2 Q ] D^a E_ab = 0

The branch expression is exactly the standard linearized Einstein tensor once the continuum spin-2 symmetry class is adopted.

2.4 Uniqueness test General operator coefficients: A,B,C,D,E Gauge: A+B=0, B+C=0, D+E=0 Conservation: B+D=0, C+E=0 => A=-B, C=-B, D=-B, E=B

The constraint system has one free normalization only. This is an exact uniqueness result under the explicit assumptions; it is not a proof that microscopic G Model dynamics generated those assumptions.

3. Native Connection and Einstein-Type Curvature Tests 3.1 Spinless connection closure S_conn/hbar = zeta sum_f < B_f/Lc^2 , (J_* + beta I) K_f >_Gamma D[(J_* + beta I) Sigma] = 0 J_*^2 = -I => D Sigma = 0 => T^I = D e^I = 0

Within the adopted native area-holonomy action class and for a nondegenerate spinless coframe, the metric-compatible torsion-free connection used in later Einstein tests is no longer merely inserted as an external assumption.

3.2 Einstein-type curvature tensor selected by conservation X_ab = R_ab + alpha gamma_ab R D^a R_ab = (1/2) D_b R D^a X_ab = 0 => alpha = -1/2 E^G_ab = R_ab - (1/2) gamma_ab R

This is one of the strongest native structural results in the Einstein sector: the -1/2 trace coefficient is fixed by curvature conservation rather than numerically fitted. E^G_ab = 2 C_Sigma (c Tc^2 / hbar) H_ab

The source coefficient is the retained G Model coupling. With the reference scale, it becomes the familiar 8 pi G/c^4 normalization.

3.3 Smooth-action vacuum equation S ~ integral Sigma_IJ wedge (*F_IJ + beta F_IJ) variation -> e^J wedge (*F_IJ + beta F_IJ)=0 with torsion-free Bianchi -> e^J wedge *F_IJ = 0

This is an Einstein-form vacuum coframe equation within the adopted smooth action class. Complete discrete matter/source dynamics is still not closed.

4. Conservation: What Passes and What Remains Open 4.1 Four-component divergence exists C_b(x) = (G4^-1)^(ac) Delta_a H_cb(x), b=1,...,4

The representation has rank four and can carry all four continuity equations. But representational capacity is not the same thing as a dynamical identity.

4.2 Why full microscopic conservation is still OPEN A simple counterexample remains: in a constant branch frame with identity transport, if only H_11 changes along branch 1, then C_1=(G4^-1)^(11) Delta_1 H_11=(1/2) Delta_1 H_11, which is generically nonzero. Thus the current native variables define the divergence but do not yet force C_b=0 for arbitrary finite-cell matter evolution.

4.3 H Yazici repair theorem In the proved neutral/commuting sector with a bounded Continuity-Time inverse, an admissible divergence defect can be cancelled exactly by a symmetric H-level correction. This is a genuine mathematical conservation PASS in that domain. It does not yet select the unique curved finite-cell physical update that nature must use.

Scientific importance Source conservation is one of the two decisive Einstein closures still required. A fundamental sourced gravity theory cannot rely indefinitely on representational conservation alone; the matter/inter-cell dynamics must make the appropriate conservation law follow natively.

5. Strong-Field Einstein / Schwarzschild Tests 5.1 Historical one-function metric — preserved FAIL ds^2 = -e^(2M)(dx^0)^2 + e^(-2M)(dx^2+dy^2+dz^2) R_00 = e^(4M) nabla^2 M R_ij = delta_ij nabla^2 M - 2 partial_i M partial_j M

Vacuum first requires nabla^2 M=0, then R_ij=0 forces grad M=0. Therefore this ansatz has no nontrivial exact static vacuum Einstein solution. It remains usable only where explicitly treated as a weak-field parametrization.

5.2 Two-function completion — exact exterior PASS inside a conditional ansatz psi = 2 tanh(M/2) T = (1+psi/2)/(1-psi/2) X = (1-psi/2)^2 spherical vacuum selects psi = -mu/r ds^2 = -[(1-mu/2r)/(1+mu/2r)]^2 c^2 dt^2 + (1+mu/2r)^4 (dr^2+r^2 dOmega^2) R_mu_nu = 0

With R=r(1+mu/2r)^2 this transforms exactly into the standard Schwarzschild exterior. The exterior PASS is exact; the microscopic dynamics that uniquely forces the two-function completion remains open.

5.3 Generic harmonic psi is not enough The exact Ricci audit shows that nabla^2 psi=0 is necessary but not sufficient for arbitrary nonspherical fields. The additional spatial Ricci condition must also vanish. Thus a generic harmonic superposition is not automatically an exact two-function vacuum solution.

6. Gravitational Waves and Propagation Tests 6.1 Continuum two-mode result W(k-hat) = { S=S^T : tr S=0, S k-hat = 0 } dim W = 2 continuum count: 10 - 4 - 4 = 2

The continuum transverse-traceless radiative subspace is exactly two-dimensional under the standard massless spin-2 conditions.

6.2 First-order Tc relaxation failure Tc dq/dtau = -(I-P)q centered P=-1/2 sector: q(tau)=q(0) exp[-3 tau/(2 Tc)]

This law is dissipative relaxation, not a conservative two-way gravitational wave equation. The failure is preserved; the equation remains useful only for local recovery/equalization.

6.3 Second-order covariant propagation omega^2 = c^2 sum_i [ (2/a) sin(k_i a/2) ]^2 a = 2 Lc/sqrt(3) long wavelength: omega^2 -> c^2 k^2

This provides a natural conservative second-order propagation candidate and the correct long-wavelength speed. However, the complete finite-cell/high-k action-derived spin-2 theorem is still OPEN. The current sinusoidal finite-cell candidate also cannot by itself be counted as a completed all-scale Lorentz-invariant gravitational-wave law.

7. Nonspherical and Rotating Einstein-Sector Tests 7.1 Nonlinear time-dependent anisotropic curvature Using an anisotropic dynamic coframe with independent scale functions A, B, and C, the metric-compatible connection produces nonlinear curvature through the connection-squared term. A Kasner-type vacuum test gives nonzero curvature with vanishing conserved gravitational tensor. This is a structural compatibility test beyond the static Schwarzschild sector.

7.2 Weak frame dragging Rotating matter enters through ordinary momentum loading rather than a new fitted force. Inter-cell transport and loop/curl formation produce the circulation/frame-dragging pathway with the Lense-Thirring functional form in the weak branch.

7.3 Why pure rotation alone fails at second order At O(J^2), a pure rotational shift does not satisfy the residual equations by itself. The required backreaction contains an isotropic l=0 sector and a quadrupolar l=2 sector. That failure is therefore the failure of an incomplete rotation-only ansatz, not of the full nonlinear rotating branch. O(J): P=0 momentum/twist O(J^2): P=1 plus P=-1/2 scalar/quadrupolar backreaction

7.4 Higher multipoles Under asymptotic-flatness and regular-horizon conditions the second-order branch carries no independent quadrupole hair and gives Q_phys=-J^2/(M c^2). At third order the angular structure forces l=1 and l=3 and removes independent regular l=3 homogeneous hair. The native inhomogeneous third- and higher-order coefficients are still unfinished; all-orders Kerr equivalence is therefore not claimed.

8. Current Numerical / Algebraic Re-tests Re-test Current result Verdict

Four-null metric reconstruction max |K G4^-1 K^T - eta| = 2.48e-16 PASS

10-component tensor 10,000 random symmetric tensors; max reconstruction error 1.11e-15 PASS reconstruction

Einstein-operator coefficient 5 coefficients, constraint rank 4 -> nullity 1; ratio (-1,1,-1,-1,1) PASS constraints

P as complete pair-source eigenvalues {1,0,0,0,-1/2,-1/2}; rank 3; nonzero zero-mode source is FAIL operator annihilated

Continuum TT mode count 10,000 random directions; constraint rank 4 in 6D symmetric space -> dim PASS 2

One-function vacuum M=x has nabla^2 M=0 but R_xx=-2 !=0 FAIL counterexample

Generic harmonic two-function psi=x is harmonic, but extra spatial Ricci condition gives diag(-2,1,1) !=0 FAIL counterexample

Two-function Schwarzschild symbolic 4D isotropic-coordinate Ricci tensor simplifies identically to zero PASS Ricci recheck

These re-tests are internal algebraic/computational consistency checks. They do not constitute independent experimental verification.

9. Calibration Note: T_c and Big G in Einstein Tests Current reference scale T_c,ref = 2.186570237920 x 10^-43 s L_c = c T_c = 6.555172662157 x 10^-35 m

It is scientifically acceptable to use this T_c in numerical Einstein-sector examples only when it is labeled CALIBRATED / REFERENCE. It comes from the current empirical Big-G calibration branch; it is not an independent G Model prediction.

Most of the important Einstein structural tests do not depend on the numerical value of T_c: tensor completeness, the operator coefficient ratios, the -1/2 curvature trace coefficient, and the exact Schwarzschild form are algebraic/geometric statements. T_c enters the absolute source-coupling normalization and finite-cell length scale. The historical record contains six routes that produced numerical T_c values, but they are not six independent confirmations. This report therefore does not count repeated T_c reconstructions as additional Einstein passes. A future Big-G-free measurement or derivation of T_c would become a separate empirical cross-check.

10. Conclusion for the Website Tests Section Most important PASS results The most important result is not the raw count of 27 passes. It is that the foundational continuum and curvature consistency gates now pass in their declared domains. The four-null basis losslessly carries a complete ten-component gravitational field and stress-energy source; the linearized Einstein operator is represented exactly and its relative coefficients are unique under the explicit massless-spin-2 continuum assumptions; the native spinless area-holonomy action structurally supplies a torsion-free metric-compatible connection; curvature conservation fixes the Einstein-type trace coefficient to -1/2; and the conditional two-function static spherical branch is exactly Ricci-flat and exactly Schwarzschild outside the source.

The continuum TT sector also has exactly two tensor modes, and later nonlinear anisotropic and rotating-sector tests show that the retained connection architecture can carry nonflat vacuum curvature, weak frame dragging, and the expected scalar/quadrupolar backreaction structure. These results materially strengthen Einstein compatibility, while remaining mathematical/structural rather than experimental.

How the FAIL results should be interpreted Failed implementation does not equal failed G Model. The six recorded FAIL results reject particular simplifications or incomplete ansatzes: the scalar metric as a complete general source, P as the complete source operator, first-order relaxation as a full gravitational-wave law, the old one-function exact vacuum metric, harmonic psi by itself as a generic exact vacuum solution, and pure rotation by itself at second order. Each failure either has a later broader construction or clearly identifies what additional structure is required.

The most important example is the one-function strong-field failure. It did not get hidden or numerically repaired; it was rejected. The later two-function ansatz was then independently subjected to an exact Ricci test and passed in the static spherical exterior. Likewise, the P-source failure led to the full H_ab tensor source rather than to fitted eigenvalues.

The most important PASS still required The decisive remaining Einstein closure is a native finite-cell derivation of the complete spin-2 field equation together with full source conservation. The microscopic inter-cell dynamics must coarse-grain to the Einstein/Fierz-Pauli coefficient pattern without inserting the continuum gauge coefficients by hand, must dynamically enforce the appropriate four-component source conservation, and must leave only the two physical tensor modes in the low-energy radiative sector. Controlled finite-scale corrections may then be tested rather than assumed away.

What would constitute a fundamental Einstein-sector problem? A future native closure would face a fundamental challenge if it inevitably produced an unsuppressed extra scalar/vector gravitational mode, nonconserved stress-energy in its claimed domain, a different leading low-energy tensor operator from the tested Einstein/Fierz-Pauli form, unavoidable preferred-frame terms, source dynamics that erased pressure or shear, or a gravity mass/screening scale incompatible with long-range observations. Those outcomes have not been established by the six historical FAIL routes.

Claim boundary Current defensible statement: the G Model has substantial mathematical compatibility with Einstein gravity in the tested weak-field, continuum spin-2, static spherical vacuum, and selected nonlinear/rotating sectors. It has not yet derived all Einstein dynamics from microscopic first principles, has not proved full generic GR equivalence, and has not been independently experimentally validated.

11. Source Record Map

ID Record Use in this report

E1 G_Model_Einstein_Audit_Working_Record_2026-08-28(2).md Master Einstein PASS/FAIL/OPEN audit and exact formulas.

E2 G_Model_Consolidated_Findings_Native_Einstein_30AUG2026.p Native connection, Einstein-type curvature tensor, df rotation summary.

E3 G_Model_Author_Contribution_Working_Record_2026-08-28_v5 Later dynamic propagation, nonlinear curvature, /v7_HISTORY_READY.md rotation, action and closure history.

E4 G_Model_Linearized_Einstein_Operator_Uniqueness_Theorem_ Operator uniqueness theorem and assumption Educational_11SEP2026.pdf boundary.

E5 G_Model_Full_Tensor_Reconstruction_Theorem_Educational_11 Exact ten-component branch tensor SEP2026.pdf reconstruction.

E6 G_Model_Transverse_Traceless_Two_Mode_Theorem_Educatio Continuum two-mode gravitational-wave count. nal_11SEP2026.pdf

E7 G_Model_H_Yazici_Theorem_Educational_11SEP2026.pdf Conservation-repair theorem and physical-update boundary.

E8 G_Model_Two_Function_Schwarzschild_Completion_Principle_E Historical one-function failure and exact ducational_11SEP2026.pdf Schwarzschild exterior.

E9 G_Model_CURRENT_MANUSCRIPT_55P_MMM_AAA_XYZ_LA Current controlling manuscript/test status. W_UPDATE_12SEP2026.pdf

Authorship and verification boundary G Model conceptual framework, research direction, interpretation, and final scientific responsibility: Gurbuz Dolu. AI assistance was used for record retrieval, mathematical formalization, algebraic and symbolic re-testing, status reconciliation, and document preparation. This is an internal theoretical audit for transparent public presentation and independent falsification; it is not peer review, experimental validation, or independent replication.