G Model Schwarzschild Tests | Complete Current Audit

Complete Schwarzschild Tests audit

G MODEL Schwarzschild Exterior, Horizon, and Strong-Field Tests Complete Current Audit for the Website Tests Section | Gurbuz Dolu | 12 September 2026 Scope: all retained Schwarzschild/black-hole strong-field records were reviewed, repeated manuscript copies were de-duplicated, and every previously identified failure was re-tested against the latest retained geometry, horizon analysis, and Xyz update. Historical failures remain visible rather than being overwritten.

Distinct Schwarzschild-related checks 24

PASS / supported / structural or conditional PASS 15

FAIL / rejected test routes or interpretations 5

OPEN derivations / physical continuations 4

Current controlled Schwarzschild verdict The old one-function strong-field metric remains rejected. The later two-function static spherical completion survives every current exterior re-test: the vacuum equations select the 1/r branch, the resulting metric is exactly Ricci-flat, and an exact areal-radius transformation gives the standard Schwarzschild exterior. The horizon is supported as a causal-trapping boundary, but the latest invariant tests continue to reject the stronger statement that the horizon itself destroys the local causal fabric. The 12 September Xyz update strengthens that distinction by placing a separate candidate Gram-degeneracy boundary far deeper than an astrophysical horizon.

Status rule A PASS means the stated mathematical test closes in its declared domain. A CONDITIONAL PASS means the two-function completion or the current Xyz source-to-shape normalization is part of the premise. A FAIL rejects a particular ansatz or interpretation, not the whole G Model. OPEN means the microscopic dynamics or physical continuation is not yet derived.

1. Complete De-duplicated Schwarzschild Test Register The following 24 entries count distinct scientific checks once. Algebraic substeps used only to establish the same result are grouped rather than inflated into extra passes. # Test Core mathematics Status Current interpretation / latest re-test

1 Historical one-function ds^2=-e^(2M)c^2dt^2+e^(-2M)dx FAIL Exact static-vacuum Ricci equations reciprocal exponential ^2 force grad M=0. Latest re-test M=x still metric gives lap M=0 but R_xx=-2.

2 General static Ricci tensor R00=[(1+psi/2)/(1-psi/2)^7] lap psi; PASS Direct differential-geometric formula for the two-function Rij exact nonlinear expression retained and independently rechecked. completion

3 Harmonic psi alone as lap psi=0 by itself FAIL Latest counterexample psi=x is sufficient exact vacuum harmonic but the remaining spatial Ricci condition numerator is diag(-2,1,1), not zero.

4 Spherical harmonic solution lap psi=0 -> psi=A+B/r PASS Exact spherical solution of the first family vacuum equation.

5 Nontrivial tangential psi'=-psi/r -> A=0, psi=B/r PASS Exact selection inside the two-function vacuum equation selects 1/r spherical ansatz.

6 Attractive exterior branch psi=-mu/r; T=(1-mu/2r)/(1+mu/2r); PASS Exact substitution into the conditional X=(1+mu/2r)^2 completion.

# Test Core mathematics Status Current interpretation / latest re-test

7 Full exterior Ricci-flatness R_mu_nu=0 PASS Fresh 4D symbolic re-test: every Ricci component simplifies identically to zero in the regular exterior.

8 Exact transformation to R=r(1+mu/2r)^2 PASS Fresh algebraic re-test gives zero Schwarzschild areal radius residual in the identity relating isotropic and Schwarzschild forms.

9 Horizon coordinate mapping r_h=mu/2 -> R_h=2mu PASS Exact map; dR/dr vanishes at the isotropic-coordinate throat/horizon.

10 Schwarzschild Kretschmann K=48 mu^2/R^6 PASS Coordinate-invariant exterior invariant cross-check inherited from exact Schwarzschild equivalence.

11 Horizon is not a curvature K_H=3/(4 mu^4) PASS Finite for every finite nonzero mu; singularity independently re-evaluated.

12 Local four-null Gram at the det G4=-(256/27)Lc^8 PASS Nonzero for Lc>0; the local four-null horizon basis does not lose rank merely at R=2mu.

# Test Core mathematics Status Current interpretation / latest re-test

13 Invariant outward-support C_F=1-2mu/R; C_F(R_h)=0 PASS Exact in the Schwarzschild exterior scalar at the horizon branch; dC_F/dR at the horizon =1/(2mu), finite.

14 360-degree / all-orientation maximum future-directed outward PASS Supports causal trapping / loss of escape diagnostic areal-radius support -> 0 at R=2mu outward-connected support at the event horizon.

15 Divergence of M proves M=(1/2)ln C_F -> -infinity FAIL Latest findings strengthen the rejection: local fabric destruction at C_F has finite gradient, curvature is the horizon finite, and the local Gram is nondegenerate.

16 Use isotropic-coordinate R=r(1+mu/2r)^2 FAIL Exact map has a minimum R=2mu at r<mu/2 as the black-hole r=mu/2 and returns to R>2mu for interior r<mu/2. This chart cannot simply be read as the interior.

17 Exterior redshift/light-deflection/Shapiro/orbital same Schwarzschild metric for same PASS Exact consequence of metric mass parameter mu equivalence; compatibility result, not a structure separate empirical confirmation.

# Test Core mathematics Status Current interpretation / latest re-test

18 Discrete causal-cut criterion Xi_disc_x=max_(x->y)(R_y-R_x)/Delta tau_xy; PASS Structural/conditional network if all future links <0 no statement. The actual physical path returns outward link-update law remains a separate open problem.

# Test Core mathematics Status Current interpretation / latest re-test

19 Microscopic derivation of finite-cell dynamics -> unique T/X OPEN The strongest missing Schwarzschild the two-function completion completion derivation: current equations do not yet uniquely force the completion from microscopic dynamics.

20 Matter interior, collapse, complete R<2mu physical solution OPEN Exterior compatibility does not and singularity-resolution and formation law determine collapse, interior matter, or dynamics singularity physics.

21 Generic nonspherical exact arbitrary strong-field nonspherical OPEN Static spherical success cannot be nonlinear extension sources promoted to generic nonlinear GR equivalence.

22 Event horizon equals Xyz R_h=2mu versus det gamma=0 Xyz FAIL Latest Xyz results separate the surfaces. Gram degeneracy boundary For astrophysical masses the candidate Xyz radius is enormously deeper than the horizon.

23 Schwarzschild-Xyz r_Xyz^3=(3 beta/2) r_s Lc^2; PASS Conditional algebraic corollary of the strong-field corollary K_Xyz=16/(3 beta^2)Lc^-4 current source-to-shape normalization; beta normalization remains ambiguous.

24 Literal ordinary-fabric post-degeneracy topology/fabric OPEN Xyz exactly marks loss of ordinary absence beyond Xyz phase four-null invertibility in the centered Gram model; the physical continuation beyond it is not derived.

2. Historical Strong-Field Failure and Its Re-test 2.1 One-function metric ds^2 = -e^(2M)c^2dt^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 requires partial_i M partial_j M=0, forcing a constant M for a nontrivial static domain. Therefore the branch cannot be an exact nontrivial static-vacuum Schwarzschild theory.

Latest explicit counterexample Choose M=x. nabla^2 M = 0 R_xx = -2 != 0

Re-test verdict: FAIL remains. None of the later Lorentz, Einstein, Xyz, or calibrated-Tc findings repairs this exact Ricci obstruction, because the failure is intrinsic to the one-function metric ansatz itself.

The correct historical interpretation is that the one-function form may still be used where explicitly labeled as a weak-field parametrization; its old higher-order strong-field deviations are not current Schwarzschild predictions.

3. Two-Function Completion and Exact Vacuum Test 3.1 Conditional completion psi = 2 tanh(M/2) T = e^M = (1+psi/2)/(1-psi/2) X = (1-psi/2)^2 ds^2 = -T^2 c^2dt^2 + X^2(dr^2+r^2 dOmega^2)

The algebra is exact once this completion is adopted, but its microscopic selection remains conditional.

3.2 General static Ricci equations R_00 = [(1+psi/2)/(1-psi/2)^7] nabla^2 psi Vacuum also requires: psi partial_i partial_j psi - 3 partial_i psi partial_j psi + delta_ij |grad psi|^2 = 0

This immediately exposes a useful failure: harmonicity alone is not enough.

Latest harmonic counterexample psi=x => nabla^2 psi=0 remaining spatial Ricci numerator = diag(-2,1,1) != 0

Re-test verdict: the 'harmonic psi alone is sufficient' route remains FAIL. The later spherical success does not convert generic harmonic superpositions into exact nonlinear solutions.

3.3 Spherical vacuum selection nabla^2 psi=0 -> psi=A+B/r nontrivial tangential equation -> psi'=-psi/r => A=0, psi=B/r attractive branch: psi=-mu/r

Thus the nontrivial 1/r radial form is selected by the vacuum equations inside the completion rather than inserted merely because Schwarzschild is known.

4. Exact Schwarzschild Exterior Re-test 4.1 Isotropic exterior metric ds^2 = -[(1-mu/2r)/(1+mu/2r)]^2 c^2dt^2 + (1+mu/2r)^4 (dr^2+r^2dOmega^2)

Fresh symbolic result All sixteen components of the 4D Ricci tensor simplify identically to zero in the regular exterior. This is an exact vacuum result, not a weak-field expansion.

4.2 Areal-radius transformation R = r(1+mu/2r)^2 1-2mu/R = [(1-mu/2r)/(1+mu/2r)]^2 dR/dr = 1 - (mu/2r)^2

Substitution gives exactly ds^2 = -(1-2mu/R)c^2dt^2 + (1-2mu/R)^(-1)dR^2 + R^2dOmega^2

The latest algebraic re-test gives zero residual in the coordinate identity. Therefore the surviving exterior is not merely similar to Schwarzschild; it is coordinate-equivalent to it.

4.3 What follows automatically For the same mass-length parameter mu, all observables determined purely by exterior timelike or null geodesics coincide with Schwarzschild GR: gravitational redshift, light deflection, Shapiro delay, and the standard static-spherical orbital structure. This is compatibility, not a new independent empirical confirmation.

5. Horizon Tests and Rejected Destruction Claims 5.1 Horizon mapping and curvature r_h=mu/2 -> R_h=2mu K=48mu^2/R^6 K_H=3/(4mu^4)

The curvature invariant is finite at the horizon for finite nonzero mu. The event horizon is therefore not a curvature-destruction singularity.

5.2 Local cell nondegeneracy det G4 = -(256/27)Lc^8 != 0 for Lc>0

The local four-null basis does not lose rank merely because the Schwarzschild horizon is reached.

5.3 Outward-support scalar C_F = 1-2mu/R C_F(R_h)=0 dC_F/dR |_(R=2mu) = 1/(2mu)

The support scalar reaches zero at the horizon while its radial derivative remains finite. This supports a causal-boundary interpretation rather than literal local-cell annihilation.

5.4 360-degree escape audit Maximizing future-directed outward areal-radius propagation over the allowed local null orientations gives an outward-support measure that approaches zero at R=2mu. This independently supports the statement that the horizon is a causal trapping boundary in the retained spherical branch.

Latest verdict on the old destruction interpretation REJECTED: 'M diverges at the horizon, therefore the local causal fabric is destroyed there.' The latest data make the rejection stronger, not weaker: curvature is finite, C_F is the smoother invariant, its derivative is finite, and det G4 remains nonzero.

6. Coordinate-Domain Failure Re-tested 6.1 Why r < mu/2 is not automatically the black-hole interior R(r) = r + mu + mu^2/(4r) dR/dr = 1 - mu^2/(4r^2)

R(r) has its minimum R=2mu at r=mu/2. For r<mu/2, R increases again and remains greater than 2mu. Re-test verdict: FAIL remains for the interpretation 'the isotropic-coordinate region r<mu/2 is the Schwarzschild black-hole interior.' The standard isotropic chart does not supply a regular one-chart continuation through the event horizon. Interior physics must be treated separately.

6.2 What this failure does not affect It does not affect the exact exterior PASS. It only prevents the exterior isotropic coordinate parameter from being extended naively and reinterpreted as a derived G Model interior solution.

7. Latest Xyz Update: Horizon Is Not the Deep-Interior Degeneracy 7.1 Current Schwarzschild-Xyz relation r_Xyz^3 = (3 beta/2) r_s Lc^2 K_Xyz = [16/(3 beta^2)] Lc^(-4)

This is a conditional strong-field corollary of the current tidal source-to-shape normalization. The normalization beta remains open between the retained routes beta=2/3 and beta=1/6.

7.2 Numerical separation from an astrophysical horizon Route Mass r_s / horizon scale (m) r_Xyz (m) r_Xyz / r_s

Route A 1 solar mass 2.953339e+03 2.332530e-22 7.898e-26

Route A 10 solar masses 2.953339e+04 5.025283e-22 1.702e-26

Route A Sgr A* ~4.3e6 solar 1.269936e+10 3.793005e-20 2.987e-30

Route B 1 solar mass 2.953339e+03 1.469402e-22 4.975e-26

Route B 10 solar masses 2.953339e+04 3.165730e-22 1.072e-26

Route B Sgr A* ~4.3e6 solar 1.269936e+10 2.389443e-20 1.882e-30

Latest re-test verdict: the event horizon is not the Xyz degeneracy surface for ordinary astrophysical black holes. In the current conditional extension the Xyz scale is tens of orders of magnitude deeper than the horizon.

The formal horizon-Xyz crossover occurs only at about 0.04 micrograms in Route A and 0.02 micrograms in Route B. Those are hypothetical Schwarzschild-radius crossover masses, not ordinary laboratory gravity thresholds.

7.3 Current three-regime interpretation outside horizon: ordinary four-null metric nondegenerate inside horizon but before Xyz: local fabric may remain nondegenerate, outward escape blocked at Xyz: det gamma -> 0; ordinary four-null inverse ceases to exist

This latest result reinforces the distinction: event horizon, local fabric destruction, and Xyz degeneracy are three different statements. The physical continuation beyond Xyz remains OPEN.

8. Current Re-test Summary Re-test Current calculation Verdict

One-function vacuum branch M=x: lap M=0 but R_xx=-2 FAIL remains

Harmonic psi sufficiency psi=x: extra Ricci numerator diag(-2,1,1) FAIL remains

Two-function exterior Ricci fresh symbolic 4D calculation: all components zero PASS tensor

Areal-radius transformation identity residual exactly zero PASS

Horizon curvature K_H=3/(4mu^4), finite PASS

Local four-null Gram at horizon det G4=-(256/27)Lc^8 PASS / non degenerate

M-divergence = destruction finite curvature + finite dC_F/dR + nondegenerate Gram REJECTED claim

Naive isotropic-coordinate R(r) has minimum 2mu and returns to R>2mu for r<mu/2 FAIL interior remains

Horizon = Xyz degeneracy astrophysical r_Xyz/r_s ~10^-26 to 10^-30 REJECTED in current conditional extension

These are internal mathematical and computational re-tests. They are not independent observational verification of the G Model.

9. Calibration Note: T_c, Big G, and Schwarzschild Tests T_c,ref = 2.186570237920 x 10^-43 s L_c = 6.555172662157 x 10^-35 m

The calibrated T_c is scientifically acceptable for numerical cell-scale or Xyz examples when it is explicitly labeled CALIBRATED / REFERENCE. It is not needed to establish the exact Ricci-flat Schwarzschild exterior itself.

The exterior metric equivalence is scale-form geometric: once the mass-length parameter mu is supplied, Ricci-flatness and coordinate equivalence do not require the numerical microscopic T_c. T_c enters the G Model coupling calibration and the microscopic/deep-interior scales such as L_c and the conditional Xyz radius. The six historical numerical T_c routes must not be counted as six Schwarzschild confirmations. The exact exterior PASS is one mathematical compatibility result; repeated calibrations of the same scale do not multiply its evidential weight.

10. Conclusion for the Website Tests Section Most important PASS results The most important Schwarzschild PASS is not an orbital fit. Inside the conditional two-function completion, the static spherical vacuum equations select the nontrivial 1/r branch, the resulting four-dimensional metric is exactly Ricci-flat, and an exact coordinate transformation produces the standard Schwarzschild exterior. This means the entire exterior geometry - not one chosen observable - agrees with Schwarzschild for the same mass parameter.

A second important PASS is the horizon consistency audit. The invariant outward-support scalar reaches zero at R=2mu and the all-orientation escape diagnostic independently supports causal trapping. At the same surface, the Schwarzschild curvature invariant remains finite and the local four-null Gram remains nondegenerate. The model therefore cleanly distinguishes a causal horizon from destruction of the local geometric basis. The latest Xyz analysis strengthens this conclusion: in the current conditional strong-field extension, the candidate Gram-degeneracy boundary is vastly deeper than an astrophysical event horizon. The correct current statement is therefore: event horizon is not fabric destruction, and event horizon is not Xyz degeneracy.

How the FAIL results should be interpreted Failed strong-field ansatz does not equal failed G Model. The principal historical failure is the original one-function reciprocal exponential metric, which cannot satisfy the nontrivial exact static-vacuum Einstein equations. That branch remains rejected. The later two-function completion is a distinct construction and has passed the exact exterior Ricci test. Likewise, harmonic psi alone fails as a generic exact-vacuum rule, naive use of the isotropic coordinate below r=mu/2 fails as an interior derivation, and the claim that the horizon destroys the local fabric remains rejected by the invariant tests.

These failures are scientifically important because they remove incorrect claims rather than being hidden. None of the latest findings reverses those negative results; the 12 September re-tests confirm them.

The most important PASS still required The decisive remaining Schwarzschild test is to derive the surviving two-function strong-field completion from the native finite-cell G Model dynamics rather than adopt it as a conditional continuum completion. A stronger theory must show why microscopic branch/connection dynamics produces this nonlinear spherical metric, then extend consistently through matter interiors and collapse without importing the Schwarzschild solution as an external target.

What would constitute a fundamental Schwarzschild-sector problem? A serious failure would occur if a native microscopic strong-field derivation produced an exterior that could not satisfy R_mu_nu=0 where vacuum is claimed, predicted a horizon inconsistent with the Schwarzschild exterior after using the same calibrated mass coupling, generated an unavoidable curvature or local-rank singularity at the ordinary event horizon contrary to the current branch, or could not reproduce the exact two-function exterior without coefficient fitting. Those outcomes have not been established by the current historical failures.

Current defensible statement The G Model is exactly Schwarzschild-compatible in the tested static spherical vacuum exterior once its conditional two-function completion is adopted. The horizon is supported as a causal-trapping boundary, not as proven local-fabric destruction. The microscopic origin of the completion, matter interior, collapse dynamics, generic nonspherical strong fields, and physical continuation beyond the Xyz boundary remain open.

11. Source Record Map ID Record Use

S1 G_Model_Two_Function_Schwarzschild_Completion_Principle_Edu Compact Schwarzschild completion, exact cational_11SEP2026.pdf exterior and status register.

ID Record Use

S2 SI_G_Model_Lorentz_Einstein_Schwarzschild_Supporting_Evidenc Full exact Ricci, coordinate, domain and e_2026-08-28.pdf falsification audit.

S3 G_Model_Einstein_Audit_Working_Record_2026-08-28.md Original detailed Einstein/Schwarzschild derivation and exact exterior recheck.

S4 G_Model_Integrated_Research_Manuscript_04SEP2026.pdf Black-hole causal-support and discrete causal-cut development.

S5 G_Model_CURRENT_MANUSCRIPT_55P_MMM_AAA_XYZ_LAW Current controlling horizon claim boundary _UPDATE_12SEP2026.pdf and latest Xyz strong-field extension.

S6 G_Model_Einstein_Tests_Complete_Current_Audit_FINAL_WEBSIT Cross-check against the current E_12SEP2026.pdf Einstein-sector audit.

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