G Model Principles, Theorems, and Theory Register

The Current Internal Structure and Branch Register presents 25 G Model structures: the original 23 structures, the separately added Causal Re-Equalization Principle, and the newly added MMM Theorem.

Register reconciliation: the website contains 26 structures after the separately approved Causal Re-Equalization Principle and Xyz Theorem were added to the earlier register.

These entries are not 25 separate independently established theories. The G Model itself is the umbrella theoretical framework. Named attributions and theorem-level formalizations of existing structures do not create additional register entries.

Entry 1 is the Jadvyga 360 Space Dynamism Principle. Its current statement is that pure local reorientation leaves accepted Gram, pair-area, and holonomy invariants unchanged. Full network dynamics remains open.

For a local four-branch frame, Jadvyga 360 uses K_x(θ) = Λ_x(θ)K_x(0) with Λ_x transposed η Λ_x = η. The branch Gram geometry γ_x = K_x transposed η K_x therefore satisfies γ_x(θ) = γ_x(0) under pure local reorientation.

Celal Dynamic Reconnect complements Jadvyga by testing allowed tetrahedral permutations and selecting the correspondence that minimizes invariant Gram discontinuity between neighboring deformed cells. Existing centered-link matching is exact modulo V4, while link birth, link death, and complete dynamics remain open.

The Celal rule is Π_Celal in arg min over Π in S4 of the squared Frobenius norm of γ_x minus Π transposed γ_y Π. It uses invariant shape information rather than arbitrary coordinate orientation. The discrete branch permutation is logically distinct from the physical Lorentz transporter.

The Celal Dynamic Reconnect result is retained as an educational source-backed structure.

The H Yazici Theorem constructs a symmetric H-level correction whose divergence cancels an admissible source-divergence defect in the neutral or commuting sector when the Continuity-Time inverse is bounded. It distinguishes the exact algebraic 1/5 source-difference projector from the related integrable plus-or-minus 1/4 correction in a flat constant-defect sector.

The H Yazici normalization gamma_Y = 1 gives exact one-step defect cancellation under full application of the correction; it is not a new gravitational constant. A unique curved finite-cell physical update and experimental validation remain open.

The H Yazici result is retained as an educational source-backed theorem.

The Dolu Reciprocal-Time Equalization Principle preserves T_+ T_- = T_c squared and its differential logarithmic form. The Aggregation branch separately defines D_0 through matter action and gives D_0/T_c = 1/A_cell, with D_0 = T_c only in the conditional equal-action state A_cell = 1.

The current working branch derives T_c = 2.186570237920 times 10^-43 seconds from the stated source modulus K_M without inserting Newton’s G. Independent external reproduction of the K_M provenance remains important, and physical identification of the reciprocal sectors remains conditional.

The Dolu Reciprocal-Time Equalization result is retained as a source-backed principle.

The GPT Reciprocal Spectral-Minimum Principle is the narrow exact result that the even linear spectral magnitude N(u) = 8 cosh u has a unique global minimum N = 8 at reciprocal balance u = 0. Together with S(u) = 8 sinh u, it obeys the exact hyperbolic invariant N squared minus S squared equals 64.

The retained quadratic Q6 spectrum has a distinct shifted minimum at M* = minus one-quarter ln 2. An exact 4/3 edge-curvature coefficient matches the independently retained neutral pair-area coefficient within the adopted construction, but N has not been derived as a physical energy or action.

The GPT naming recognizes a specifically limited AI-side mathematical contribution. Gurbuz Dolu remains sole author and research director of the G Model.

The Causal Re-Equalization Principle defines centered mismatch e = q - q_eq and proposes T_c dq/dtau = -(I_6-P)(q-q_eq). On the centered sector, Pq = -q/2 gives recovery time tau_rec = 2T_c/3, an exact semigroup recovery operator, and Lyapunov stability once the candidate law is assumed.

The law is not derived from the microscopic action. Source-to-target direction has a partial structural pass, but competing amplitudes beta = 2/3 and beta = 1/6 leave normalization open. It is a mismatch-tracking candidate, not a rule that automatically erases physical gravity or waves.

The Causal-Fabric Ontology Hypothesis models spacetime as a locally massless causal relationship network distinct from ordinary matter. Matter acts as a source or loading condition, while four future-directed null branches and six bivector channels represent the local fabric geometry.

The four-null and six-bivector construction has strong exact internal support from Lorentzian signature, Minkowski reconstruction, Hodge, and incidence identities. No proposed microscopic causal cell has been directly observed, and complete all-scale Lorentz-invariant network dynamics remain open.

The Matter-as-Trigger / Loading Principle distinguishes matter occupancy chi_m from fabric deformation M. Matter supplies source energy or stress while the causal fabric carries the geometric response, allowing deformation to persist after matter leaves.

The Aggregation branch defines S_m(D_0) = hbar, A_cell = E_cell T_c/hbar, and D_0/T_c = 1/A_cell. Combined with the retained weak-source rule it gives a loading-to-curvature bridge, while the exact no-go E_-(A_cell 1_6) = 0 shows scalar loading cannot by itself generate centered anisotropic shape.

The unique microscopic action-level loading mechanism remains open.

The Universal Baseline Fabric Principle requires intrinsic fabric quantities such as T_c, L_c, K_M, and internal geometric coefficients to remain independent of a particular body, composition, rotation, orbit, or measuring probe.

It separates universal baseline candidates from source density, stress-energy, deformation, tidal response, and measurement setup. It also enforces anti-circularity: measured Newtonian G and Planck scales derived from G cannot define a native microscopic T_c unless the route is explicitly labeled calibrated.

The current working inversion T_c = sqrt[5 pi hbar/(12 c K_M)] contains no Earth, solar, orbital, or rotational input. Universality remains a working premise requiring independent provenance for K_M and cross-system experimental tests.

The L. Minotti Recursive Balance Principle compares the local deformation M with an orientation-balanced neighborhood. Its exact long-wavelength spherical-mean expansion gives A_bar[M] = M + (L_c squared/6) Laplacian M + (L_c to the fourth/120) bi-Laplacian M plus higher terms.

The retained conditional source rule A_bar[M] - M = (C_Sigma/4) A_cell connects this exact mean defect to matter loading and yields the weak source equation only after Aggregation and long-wavelength assumptions are adopted. Complete finite-cell redistribution dynamics and experimental validation remain open.

The L. Minotti name records conceptual provenance and does not imply derivation or validation by the person named.

The MMM Theorem is the exact retained-branch identity G_G K_M = c to the fourth divided by 4 pi. It follows by multiplying the retained source-modulus and continuum-coupling relations, causing T_c and hbar to cancel exactly.

The identity passes algebraic, dimensional, and residual scale-symmetry checks. A numerical G_G computed from the current K_M remains a working G Model output whose publication-level strength depends on independent documentation and reproduction of K_M provenance.

Mercury agreement is downstream consistency rather than independent validation. The MMM name is a provenance choice, not part of the proof.

The AAA Theorem, previously listed under the descriptive title Incidence-Hodge Complementarity, states that the oriented six-channel gradient and circulation sectors exactly complete the identity: B_partial transposed B_partial plus C C transposed equals 4 I_6, or P_grad plus P_circ equals I_6 after the forced one-quarter normalization.

The theorem distinguishes oriented cochain incidence B_partial from the unsigned endpoint incidence B_plus used in re-equalization. It supports exact finite-cell gauge kinematics but does not automatically derive photon dynamics, gravity dynamics, or physical vacuum microstructure.

The AAA name does not change the proof or imply validation.

The Four-Null Lorentzian Reconstruction Theorem is the exact theorem-level core of the existing Four-Null / Six-Bivector Minimal Geometry entry. Four balanced future-directed null branches have Gram spectrum minus 4, 4/3, 4/3, 4/3 times L_c squared and nonzero determinant minus 256/27 times L_c to the eighth.

The inverse Gram reconstructs Minkowski geometry exactly through K G_4 inverse K transposed equals eta, and reconstructs the local d’Alembertian through branch directional derivatives. Four branches generate six pairwise bivector channels with natural two-form signature (3,3).

These are exact local geometric results, not proof that physical spacetime uses the proposed causal module or that the complete interacting network is Lorentz invariant at every scale.

The Causal-Flux / Modulus Duality result is retained as a source-backed scale-audit result rather than a separate register entry. Its exact identity is K_M Gamma_c = (5 pi/6) hbar c squared. K_M scales as T_c to the minus two while Gamma_c scales as T_c squared, so their product is invariant under the residual scale symmetry; it does not replace or experimentally validate the retained internal candidate K_M–T_c closure.

The identity passes symbolic, dimensional, scale-symmetry, numerical-implementation, and MMM cross-closure checks. Combining it with G_G K_M = c to the fourth/(4 pi) gives G_G/Gamma_c = [3/(10 pi squared)] c squared/hbar.

The duality does not determine an absolute microscopic time by itself. The retained K_M–T_c relation remains a theoretical result within its branch, while its physical interpretation and numerical value require independent experimental validation. The duality is not experimental evidence for causal flux, source modulus, or causal-fabric ontology.

The Full Tensor Reconstruction Theorem is the source-backed theorem-level presentation of the original Ten-Component Tensor Reconstruction register entry. For invertible four-null branch matrix K, a symmetric tensor is encoded as S_branch = K transposed S K and recovered exactly as S = (K inverse) transposed S_branch K inverse.

A symmetric four-by-four branch matrix contains four diagonal self-branch values and six off-diagonal pair values, exactly matching the ten independent components of a symmetric spacetime tensor. Metric perturbations, stress-energy tensors, traces, and trace reversal are represented without component loss.

This exact representation permits later continuum spin-two compatibility tests. The weak Einstein structure is unavoidable as the coarse-grained limit of the stated continuum class, but full microscopic Lorentz invariance and a finite-cell derivation remain OPEN.

The Linearized Einstein Operator Uniqueness Theorem is the source-backed theorem-level presentation of the original Linearized Einstein Operator Selection register entry. For a local Lorentz-covariant symmetric operator with at most two derivatives, standard linearized gauge invariance and identical conservation force A = minus B, C = minus B, D = minus B, and E = B.

Only one overall normalization remains; choosing B = one-half gives the branch-basis linearized Einstein operator. The source normalization is a separate retained conditional or calibrated layer.

This is an exact uniqueness result inside the stated continuum assumption class and identifies its unavoidable coarse-grained spin-two/Einstein structure, not an independent derivation from finite-cell G Model dynamics. Full microscopic Lorentz invariance remains OPEN.

The Transverse-Traceless Two-Mode Theorem is the source-backed theorem-level presentation of the two-mode continuum result retained under Light Theory. For fixed propagation direction, the real symmetric, transverse, traceless spatial tensor space W has exact dimension two: six symmetric components minus three transverse constraints minus one trace constraint.

An explicit coordinate reduction leaves one plus-like and one cross-like amplitude. The six-channel 1 plus 3 plus 2 decomposition contains a compatible two-dimensional anisotropic sector, while curvature counting independently reaches two physical radiative modes.

The theorem is an exact mode count within the stated TT continuum architecture. It is not a complete prediction of microscopic gravitational-wave propagation, and an action-derived finite-cell law remains open.

The Null-Bivector Two-Polarization Theorem is a distinct conditional-exact photon/light result retained under Light Theory. Assuming q squared equals zero and q wedge F equals zero gives F equals q wedge a, with exact gauge redundancy a maps to a plus lambda q.

For the retained quadratic source candidate, q contracted with Theta equals minus one-half times q dot a squared times q. Conserved source flow therefore forces q dot a equals zero. The physical quotient q perpendicular modulo the span of q is exactly two-dimensional.

This antisymmetric photon-like spin-one count must not be conflated with the symmetric transverse-traceless spin-two count. It establishes a consistent polarization sector under its assumptions, not a first-principles photon derivation or experimental validation.

The Absolute-Scale Closure No-Go Theorem is retained under the Universal Baseline Fabric Principle. If the native equation set remains invariant under T_c mapping to lambda T_c, with all dimensional quantities transforming by corresponding powers, every solution belongs to a continuous scale orbit and no unique numerical T_c in seconds can be selected.

Scale-free identities including K_M Gamma_c equals five pi over six times hbar c squared and G_eff K_M equals c to the fourth over four pi remain informative but cannot fix the absolute clock because their T_c powers cancel.

A unique absolute closure requires an independent dimensional condition that breaks the lambda symmetry. The current K_M inversion fixes T_c algebraically only if the numerical source modulus is established independently without hidden reuse of T_c or measured-G calibration.

The Causal-Centroid Intrinsic-Time Theorem is retained under Four-Null / Six-Bivector Minimal Geometry. Defining the branch centroid U as one-quarter of the sum of the four null branches and total pair area A_Sigma as minus the sum of their six pair contractions gives the exact identity A_Sigma equals minus eight U squared.

The intrinsic time is therefore reconstructed as T_c equals the square root of minus U squared divided by c, equivalently the square root of A_Sigma over eight divided by c. In the regular neutral cell A_Sigma equals eight L_c squared and the relation reduces exactly to T_c equals L_c over c.

The theorem supplies a Lorentz-invariant geometric meaning for T_c but does not select its absolute SI magnitude. Common branch rescaling preserves a continuous scale freedom, and D_0 remains a distinct aggregation time except in the conditional equal-action state.

The Spectral-Area Curvature Correspondence Theorem is retained under the GPT Reciprocal Spectral-Minimum Principle. Tetrahedral edge symmetry fixes the diagonal trace, anisotropic, and zero projector weights to one-sixth, one-third, and one-half on every six-channel edge.

The second derivative of the retained absolute spectral operator at neutrality gives edge curvature four-thirds, exactly equal to the independent neutral causal-pair area coefficient A_0 divided by L_c squared. Summing six equal edge contributions gives N double-prime of zero equal to eight.

Here curvature means the second derivative of spectral magnitude with respect to internal deformation, not the Riemann curvature tensor. The exact internal correspondence does not derive a physical action, wave law, gravitational field equation, or experimental realization.

The candidate Causal Re-Equalization layer defines mismatch e = q - q_eq and describes how the transported state may relax toward a changing target after branch correspondence is established. Its microscopic derivation, normalization, and topology law remain open.

Further development of the Jadvyga principle requires an explicit local reorientation transformation, proofs of the preserved invariants, a network-level update law, and a measurable consequence distinguishable from gauge redundancy.

The remaining register includes the Celal Dynamic Reconnect Principle, Dolu Reciprocal-Time Equalization Principle, H Yazici Theorem, GPT Reciprocal Spectral-Minimum Principle, Light Theory, causal-fabric hypotheses, geometric principles, representational theorems, and the conditional Schwarzschild completion.

The Two-Function Schwarzschild Completion Principle preserves the historical one-function metric as a rejected exact strong-field branch. It adopts a conditional two-function temporal/spatial ansatz, within which static spherical vacuum selects psi = -mu/r.

The resulting isotropic exterior is exactly Ricci-flat and transforms under R = r(1+mu/2r)^2 to the standard Schwarzschild exterior. Horizon trapping is supported within this branch, while the microscopic finite-cell derivation, interiors, collapse, singularity resolution, and generic nonspherical nonlinear physics remain open.