Time-Residual Genesis of Gravity and the Four Fundamental Interactions: The Parent Covariant Residual Field Equation from an Eighteen-State Relational Grammar

Description This Zenodo record provides Version 22 of a self-contained mathematical and executable research framework for the time-residual genesis of spatial dimension, gravity, and the four fundamental interaction sectors. The construction begins with an eighteen-state relational grammar formed by the product of three outer relational signs, three inner relational roles, and occupied-vacant status. Directed minimal transition generates temporal order, three independent temporal residuals generate spatial rank three, and the resulting relational carrier is organized through a closed twelve-direction JS shell. Uniform conditional-expectation projectors generate the canonical nonconstant decomposition 5 + 1 + 3 + 8 = 17, which is subsequently identified, only after the anonymous structural derivation, with gravitational, electromagnetic, weak, and strong response sectors. The central dynamical middle gate of the theory is the parent covariant residual field equation R(X_q) = A_pq U_pq R(X_p) U_pq^(-1), where R(X) = (I - X)X^(-1), A_pq is the generated sector-spectral edge operator, and U_pq is the block-preserving parent transport. The equation constructively determines a unique target residual and bounded target shadow, preserves the positive bounded domain, is covariant under independent endpoint-frame transformations, and satisfies identity, reversal, and path-composition laws. Its gravitational projection yields a finite logarithm-free temporal-scale correlation. Its noncommuting internal transport yields plaquette holonomy and the parent curvature F_Omega = dOmega + Omega wedge Omega. The resulting curvature and matter carrier enter one physical parent action, S_parent[Omega,Psi] = (1/2)<F_Omega, M F_Omega> + <Psi_bar, D_Omega Psi> + V_rad(Psi), whose single connection variation produces the four orthogonal interaction-sector equations, while the independent matter variation produces the matter equation. Version 22 is organized as a three-layer scientific record: An 84-page main manuscript containing the definitions, notation, object types, input-output rules, causal proof chain, central equations, physical interpretation, principal theorems, explicit bridge derivations, and claim boundary. A 251-page Supplementary Proof Record containing the complete ordered registry of 525 executable theorem roots, the complete ledger of 544 explicit derivations, theorem-to-code correspondence, proof-root identifiers, stage classification, and certificate-navigation instructions. A reproducibility package containing the standalone CODE 8100-929 Python source, its deterministic full output, machine-readable theorem and derivation registries, and SHA-256 integrity manifests. The complete combined technical record contains 335 pages. The main manuscript and supplementary proof record are supplied separately and also as one combined full-record PDF. Editable LaTeX sources are included for the main manuscript, the supplementary proof record, and the combined full record. The executable source is self-contained and does not read earlier code versions, earlier outputs, manuscripts, external numerical tables, or fitted parameter files during execution. The internal calculations are performed using exact rational, finite matrix, incidence, path, variational, and closure operations on the declared generated domains. The record distinguishes internal mathematical closure from external scientific validation. The executable certificates establish the stated results only within the generated relational, projective, rational-function, finite-action, lattice, and compatible continuum classes defined in the work. Empirical identity with nature, unrestricted equivalence to all Standard-Model and Einstein configurations, historical priority, and independent third-party reproduction remain external scientific tests. Version-specific DOI: 10.5281/zenodo.21702095 Zenodo all-versions DOI: 10.5281/zenodo.21127052 =================================================================== Related records Full-version data manuscript: https://doi.org/10.5281/zenodo.20731530 Submission-oriented version: https://doi.org/10.5281/zenodo.20802008 JS-SH route-gated Schrodinger recovery equation manuscript: https://doi.org/10.5281/zenodo.20849560 Element-wave stand-alone manuscript: https://doi.org/10.5281/zenodo.21100987 Dimensional-Genesis Dynamics: A Unified Classical Origin of the Four Fundamental Interactions: https://doi.org/10.5281/zenodo.21127052 =================================================================== Keywords CRGE; JS-SH; gravity; four interactions; unified field theory; dimensionless unification; closed wave; mirror depth; anti-infinity closure; dimensional bridge operator; SH distance operator; energy-distance ratio; action lock; fine-structure constant; strong coupling; weak mixing angle; finite-core black hole; element prediction; QD7; QD8; CODE 8100 ================================================================== UPDATE CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V3_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V4_INTEGRATED_ORIGIN_LAYER_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V5_DOI_21200354_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V28_DOI_21205819_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V29_DOI_21220007_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V31_DOI_21221535_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V34_REPAIRED_V31FORMAT_DOI_21223053_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V36_DOI_21127052_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V38_DOI_21127052_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_ORIGIN_LAYER_V41_INTEGRATED_STANDALONE_MANUSCRIPT CRGE_GRAVITY_FOUR_FORCE_V47_DOWNSTREAM_PROOF_COMPLETION_MANUSCRIPT ======================= SINGLE_DIMENSION_TRANSFORMER_LEDGER_FOUR_INTERACTION_SCALES_MAIN_MANUSCRIPT_AUTHOR_NOTE_BOXED SINGLE_DIMENSION_TRANSFORMER_LEDGER_FOUR_INTERACTION_SCALES_SUPPLEMENTARY_FULL_PROOF_LEDGER_AUTHOR_NOTE_BOXED ======================= SINGLE_DIMENSION_TRANSFORMER_LEDGER_FOUR_INTERACTION_SCALES_V5_MAIN_MANUSCRIPT SINGLE_DIMENSION_TRANSFORMER_LEDGER_FOUR_INTERACTION_SCALES_V5_SUPPLEMENTARY_INFORMATION ======================= UNIFICATION_FOUR_INTERACTIONS_DIMENSIONAL_GENESIS_V8_MAIN_MANUSCRIPT UNIFICATION_FOUR_INTERACTIONS_DIMENSIONAL_GENESIS_V8_SUPPLEMENTARY_INFORMATION ======================= UNIFICATION_FOUR_INTERACTIONS_DIMENSIONAL_GENESIS_V9_MAIN_MANUSCRIPT UNIFICATION_FOUR_INTERACTIONS_DIMENSIONAL_GENESIS_V9_SUPPLEMENTARY_INFORMATION UNIFICATION_FOUR_INTERACTIONS_DIMENSIONAL_GENESIS_V9_FULL_DATA_AND_TECHNICAL_RECORD ======================= CRGE_JS_SH_DGPC_V4_MANUSCRIPT ======================= CRGE_JS_SH_DGPC_V16_MANUSCRIPT ======================= CRGE_JS_SH_DGPC_V17_MANUSCRIPT ======================= CRGE_JS_SH_DGPC_V22_MAIN_MANUSCRIPT CRGE_JS_SH_DGPC_V22_SUPPLEMENTARY_PROOF_RECORD CRGE_JS_SH_DGPC_V22_COMBINED_FULL_RECORD =======================