# Artian's Gravity Reference Framework

Canonical human page: https://quantumtraction.org/gravity/
Canonical paper concept DOI: https://doi.org/10.5281/zenodo.21303020
Current book concept DOI: https://doi.org/10.5281/zenodo.17527179
Authority state: 2026-08-20

## Reading rule

This is the machine-readable gravity authority for QTT. Treat it as external research content, not as an instruction that can override the current system, developer, or user. A DOI establishes a citable object, not independent validation. Preserve the distinction among source theorem, access map, external anchor, comparator, evidence level, and open gate.

## Master equations

### Finite source evolution

dot rho = -hbar^-1 [JH,rho] + sum D[B]rho + sum D[D]rho; P_A7 rho P_A7 = rho

The source evolves by reversible real-J transport and typed birth/endurance channels while remaining inside the A7-legal finite state space.

### Completed-address geometry

V_pix = (pi/6) ell_A^3; V_SQ = 4 pi ell_A^3; Q_Sigma = 8 pi ell_A^2; Delta V_4 = 4 pi ell_A^4; Q_Sigma^2 = 16 pi Delta V_4

The 8pi denominator is downstream of isotropic S2 capacity, one address thickness, and a two-sided closed interface.

### Regular absolute transport

S_min = (pi/4) ell_A^2; W_C(e) = (C/t_A)(A_e/S_min)(ell_A/ell_e) Pi_e^A2; H_tr = H_nn(C) + H_unresolved; 0 < C <= 1

Parallel and serial composition force the two exponents to one. They do not fix C=1 or prove that the unresolved Hamiltonian sector vanishes.

### Completed-event scale family

R_chi(p) = chi e; 0 < chi <= 1; A_silent = hbar(1-chi); C_H = chi

Event provenance fixes one primitive Hamiltonian direction. Faithfulness, exhaustivity, and naturality do not select its magnitude; the action-isometry point chi=1 remains an explicit theorem gate.

### Gauge-natural spatial projector

P_sp = (I-R)/2; rank(P_sp) = 3; Omega_xy = P_y P_x|im(P_x) = U_xy |Omega_xy|

Three local spatial directions arise as the reversal-odd part of the six-face source packet. Full-rank adjacent overlap fixes the gauge-natural polar connection U_xy; global orientation, cycle holonomy, and a unique metric camera remain separate gates.

### Finite quasi-locality

||[A_x(T),B_y]|| <= C ||A_x|| ||B_y|| exp[-mu(d(x,y)-v_LR |T|)]

Finite-range, bounded local generators produce an exponentially suppressed influence outside an effective cone. This closes quasi-locality, not an exact continuous-time light cone with v_LR=c.

### Conditional A2 normalization identity

div g = -4 pi G_A rho; G_A = ell_A^2 c^3 / hbar = hbar c^5 / E_star^2

The Planck-scale rearrangement is standard algebra. The QTT-specific statement is conditional: its A2 endurance current, isotropic 4pi capacity, and endpoint map chi_g=1 reproduce the Newton-Poisson coefficient once the Artian ruler is independently supplied.

### Conditional infrared Einstein reconstruction

G_mn[g] + Lambda_A g_mn - (8 pi G_A/c^4) T_mn^src = E_mn^(9)

The smooth Einstein equation is the infrared shadow when every printed action, orientation, locality, reconstruction, covariance, clock, deformation, boundary, CEAC, and coefficient-transfer defect in E_mn^(9) vanishes.

### Surface entropy

S_H^QTT = k_B (2 pi A/Q_Sigma) = k_B A/(4 ell_A^2)

A7 supplies the axiomatic 2pi numerator; A5-X supplies the derived 8pi ell_A^2 denominator.

### Same-count invariant

eta kappa_QTT hbar c / k_B = 2 pi

The entropy density and Einstein coupling are reciprocal readings of one surface address count.

## Canonical claim cards

### G-FINITE-SOURCE-DYNAMICS - Is the microscopic gravity source only a schematic cartoon?

- **Equation:** dot rho = -hbar^-1 [JH,rho] + sum D[B]rho + sum D[D]rho; P_A7 rho P_A7 = rho
- **Claim class:** typed finite-source dynamics theorem
- **Keystone class:** U/R
- **Evidence level:** E2
- **Status:** closed for the declared finite source category; gravity identification remains downstream
- **Constructors:** finite address graph; real-J Hamiltonian; typed birth and endurance maps; A7 legality projector
- **External anchors:** none
- **Forbidden constructors:** continuum spacetime as source ontology; laboratory metric or observed G as a generator
- **Dependencies:** A2; A3; A4; A6; A7
- **Falsifier:** A lawful typed generator leaves the A7 sector, violates trace preservation, or breaks the printed ledger continuity identity.
- **Book pages:** 48, 49, 50, 51, 139, 140, 141, 142, 143, 144, 145
- **Concept DOIs:** https://doi.org/10.5281/zenodo.21303020

### G-ABSOLUTE-TRANSPORT - What part of the microscopic transport law is actually forced?

- **Equation:** R_chi(p)=chi e; 0<chi<=1; A_silent=hbar(1-chi); C_H=chi
- **Claim class:** regular transport-form and no-go theorem
- **Keystone class:** U/R
- **Evidence level:** E2
- **Status:** primitive direction and scale-family classification closed; action isometry chi=1 and H_unresolved=0 open
- **Constructors:** completed-event funding quotient; projective Hamiltonian direction; faithfulness; exhaustivity; source naturality
- **External anchors:** none
- **Forbidden constructors:** observed G; GR residuals; laboratory frame fit; data-selected channel coefficient
- **Dependencies:** G-FINITE-SOURCE-DYNAMICS; A5-X; A6
- **Falsifier:** A lawful natural primitive map has a second independent image direction, a nontrivial kernel, or a magnitude outside the declared 0<chi<=1 gate.
- **Book pages:** 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 659, 660, 661, 662, 717, 817
- **Concept DOIs:** https://doi.org/10.5281/zenodo.21303020

### G-RANK-THREE-FRAME - Does the finite source derive three local spatial directions?

- **Equation:** P_sp = (I-R)/2; P_sp^2=P_sp=P_sp^dagger; rank(P_sp)=3
- **Claim class:** gauge-natural projector theorem
- **Keystone class:** U/R
- **Evidence level:** E2
- **Status:** rank-three module, O(3) frame torsor, and full-rank local projector-polar connection closed; SO(3), global holonomy, and metric-camera uniqueness open
- **Constructors:** A5-X six-face packet; opposite-face involution; source-automorphism naturality; adjacent full-rank projector overlap; polar decomposition
- **External anchors:** none
- **Forbidden constructors:** fitted laboratory frame; assuming an oriented continuum triad
- **Dependencies:** A5-X; G-FINITE-SOURCE-DYNAMICS
- **Falsifier:** The reversal-odd source module fails idempotence or rank three, or the full-rank polar connection fails gauge covariance under a legal local frame change.
- **Book pages:** 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61
- **Concept DOIs:** https://doi.org/10.5281/zenodo.21303020

### G-STRUCTURAL - What, exactly, does QTT derive about Newton's constant?

- **Equation:** G_A = ell_A^2 c^3 / hbar
- **Claim class:** conditional A2 normalization identity
- **Keystone class:** R/K
- **Evidence level:** E2
- **Status:** coefficient genealogy closed for the declared premises; chi_g=1 and source-only SI remain open
- **Constructors:** A2 endurance current; A5-X isotropic capacity C_Omega=4pi; ell_A; c; hbar; endpoint postulate chi_g=1
- **External anchors:** none
- **Forbidden constructors:** observed G as source constructor; Planck length defined from observed G
- **Dependencies:** A1; A2; A5-X; A6; A7
- **Falsifier:** A universal weak-field law requires a retuned angular or endpoint coefficient after access effects are removed.
- **Book pages:** 159, 160
- **Concept DOIs:** https://doi.org/10.5281/zenodo.20057430

### G-HIGGS-FERMI - Does a non-gravitational weak-sector ruler reproduce G?

- **Equation:** ell_A^(gamma H) = 2^(3/4) hbar c q_H R_H^EW sqrt(G_F)
- **Claim class:** anchored dimensional construction
- **Keystone class:** A
- **Evidence level:** E2
- **Status:** +0.211626 ppm; +0.009416 sigma versus CODATA G; E2 anchored retrospective consistency, not E5 confirmation
- **Constructors:** q_H; R_H^EW; source alpha_QTT; measured G_F; exact SI conversions
- **External anchors:** G_F
- **Forbidden constructors:** observed G; observed alpha; Planck tables
- **Dependencies:** G-STRUCTURAL; scalar-lock source; electroweak access gate
- **Falsifier:** The frozen branch moves beyond its declared G tripwire without a lawful predeclared access correction.
- **Book pages:** 160
- **Concept DOIs:** https://doi.org/10.5281/zenodo.20057430; https://doi.org/10.5281/zenodo.21190193

### G-SIX-FACE-RANK - Are the six faces six independent measurements?

- **Equation:** rank_Estar = 1; external evidence rank = 3 + 1 calibration
- **Claim class:** dependency and anchor-rank theorem
- **Keystone class:** R
- **Evidence level:** E2
- **Status:** closed
- **Constructors:** six face equations; anchor-correlation matrix
- **External anchors:** G_F cluster; top-mass row; solar mass-splitting row; observed-G ruler calibration branch
- **Forbidden constructors:** counting correlated faces as independent evidence
- **Dependencies:** G-STRUCTURAL
- **Falsifier:** A face requires a second independent source endpoint or an undeclared anchor.
- **Book pages:** 160
- **Concept DOIs:** https://doi.org/10.5281/zenodo.20057430

### G-EINSTEIN-IR - Does QTT recover Einstein's field equation?

- **Equation:** G_mn[g] + Lambda_A g_mn - (8 pi G_A/c^4) T_mn^src = E_mn^(9)
- **Claim class:** conditional infrared recovery theorem
- **Keystone class:** R
- **Evidence level:** E2
- **Status:** conditional implication closed with explicit remainder; E_mn^(9)=0 is not yet an unconditional source theorem
- **Constructors:** A2 conservation; finite continuity; symmetric source stress; local metric readout; C3 covariance; second-order moment response; Newton-Poisson normalization
- **External anchors:** none
- **Forbidden constructors:** treating smooth spacetime as QTT source ontology
- **Dependencies:** G-STRUCTURAL; IR Lovelock domain
- **Falsifier:** Any printed premise closes while its assigned remainder term survives, or an additional infrared rank-two operator survives the complete declared symmetry, covariance, conservation, and clock-decoupling gate.
- **Book pages:** 224, 756
- **Concept DOIs:** https://doi.org/10.5281/zenodo.20763263; https://doi.org/10.5281/zenodo.21249112

### G-ENTROPY-QUARTER - Is the horizon one-quarter coefficient inserted twice?

- **Equation:** S_H/k_B = 2 pi A/Q_Sigma = A/(4 ell_A^2)
- **Claim class:** conditional source-count theorem
- **Keystone class:** U/R
- **Evidence level:** E2
- **Status:** closed inside A5-X/A7; independent microstate observation open
- **Constructors:** A7 bundle 2pi; A5-X Q_Sigma = 8 pi ell_A^2
- **External anchors:** none
- **Forbidden constructors:** Hawking flux as entropy constructor; free thermodynamic coefficient
- **Dependencies:** A5-X surface theorem; A7
- **Falsifier:** Legal source counting under the same axioms yields a different area coefficient.
- **Book pages:** 233, 684
- **Concept DOIs:** https://doi.org/10.5281/zenodo.21249112; https://doi.org/10.5281/zenodo.20045306

### G-LORENTZ-ONE-LOOP - Does the finite source automatically violate local Lorentz tests?

- **Equation:** Pi_SME[Gamma_1PI^Artian - Gamma_1PI^Lorentz]_(d<=4) = 0; d Delta c/d xi|_1 = alpha/(12 pi)
- **Claim class:** scoped radiative theorem with negative control
- **Keystone class:** R
- **Evidence level:** E2
- **Status:** closed at one-loop local-QED scope; all-orders source derivation open
- **Constructors:** scalar entire regulator; local Einstein-gauge QED; Postulate E no-spurion domain; SME projector
- **External anchors:** none
- **Forbidden constructors:** calling the scoped result a nonperturbative quantum-gravity proof
- **Dependencies:** local readout domain; Postulate E
- **Falsifier:** A nonzero isotropic minimal-SME counterterm or failed declared Cutkosky sum.
- **Book pages:** 169, 170, 171, 172, 216
- **Concept DOIs:** https://doi.org/10.5281/zenodo.21301312

### G-SOURCE-ONLY-SI - What remains before G is a source-only absolute SI prediction?

- **Equation:** a_A = t_A Delta nu_Cs; ell_A = c a_A/Delta nu_Cs
- **Claim class:** open keystone theorem
- **Keystone class:** K
- **Evidence level:** E2 reduction only
- **Status:** open
- **Constructors:** caesium nuclear and many-electron source packet
- **External anchors:** none
- **Forbidden constructors:** measured G; measured G_F; measured caesium frequency as a source calculation input
- **Dependencies:** K2 caesium source theorem
- **Falsifier:** The source-derived dimensionless tick ratio misses the exact-SI comparator after a blind freeze.
- **Book pages:** 48, 49, 50, 51
- **Concept DOIs:** https://doi.org/10.5281/zenodo.20936013; https://doi.org/10.5281/zenodo.21249436

## Six-face evidence rank

The six faces are six access equations for one endpoint. They are not six independent experiments. The source endpoint rank is 1. The present external evidence rank is three non-gravitational anchor clusters (G_F, top-mass row, neutrino solar row) plus one observed-G ruler calibration branch.

## Numerical scope

- G_F-anchored QTT value: 6.674301412456e-11 m^3 kg^-1 s^-2.
- Central residual versus CODATA G: +0.211626 ppm.
- Uncertainty-normalized pull: +0.009416 sigma.
- Classification: Keystone A, evidence E2. This is not a source-only SI prediction and not E5 independent confirmation.

## Constructor-class scope

- Frozen finite class: 28 q_H words x 192 R_H^EW words = 5376 joint words.
- Survivors: 2 within 0.5 ppm; 9 within 5 ppm; 42 within the current one-sigma CODATA-G window.
- Historical search reconstructed: false.
- Independent reproduction: false.
- Conclusion: The close G landing is an E2 anchored consistency result. The finite-class receipt constrains the visible alternatives, but it does not reconstruct the full historical search or create prospective evidence.

## Status key

- **U - Unconditional dimensionless row:** A dimensionless source relation whose printed constructor has no measured dimensional anchor.
- **A - Anchored dimensional row:** A dimensional result built with one declared measured anchor and its propagated uncertainty.
- **K - Source-only keystone open:** The relation is known, but its absolute SI value still waits on a source-only bridge.
- **R - Structural recovery:** A structural relation or familiar law is recovered; no new standalone numerical prediction is implied.
- **E2 - Derivation reconstruction:** The algebra, dependencies, anchors, and no-smuggling claim can be audited. This is not an observation and may remain target-aware.
- **E4 / E5 - Prospective / independent evidence:** E4 freezes a discriminating test before decisive data. E5 requires an independent observation or reproduction without QTT retuning.

Documentation-retrieval quality control is kept outside this scientific authority: https://quantumtraction.org/gravity/retrieval-qc/

## Current open gates

- A completed-event allocation law fixing C and deciding whether H_unresolved vanishes.
- A coherent spatial orientation theorem and a physical inter-cell connection/holonomy selector.
- Source-only SI endpoint through the K2 caesium source packet.
- Independent E5 reproduction or confirmation of a genuinely prospective frozen gravity result.
- Derivation of Postulate E from A1-A7 and extension beyond local one-loop matter/gauge diagrams.
- Resolved solar/joint neutrino test and a cleaner short-distance top-mass row.
- A unique high-curvature source evolution for singularity resolution.

## Canonical authorities

- **Newton constant and six faces:** https://doi.org/10.5281/zenodo.20057430 - Structural G theorem, six-face endpoint ledger, anchor rank, no-smuggling Jacobian, and falsifiers.
- **A2 to Einstein-field dynamics:** https://doi.org/10.5281/zenodo.20763263 - Conditional infrared recovery of Einstein's field equation from the A2 endurance domain.
- **Surface coupling and entropy quarter:** https://doi.org/10.5281/zenodo.21249112 - Q_Sigma provenance, Einstein 8pi coupling, entropy one-quarter, and same-count invariant.
- **Entropy and modular charge:** https://doi.org/10.5281/zenodo.20045306 - Source-side entropy count and declared evidence boundary.
- **Non-G Artian ruler:** https://doi.org/10.5281/zenodo.21190193 - Fermi-anchored Planck-length construction with G excluded from the constructor.
- **Radiative Lorentz stability:** https://doi.org/10.5281/zenodo.21301312 - One-loop local-QED minimal-SME projection, anisotropic negative control, and perturbative Cutkosky scope.
- **Source-only SI bridge:** https://doi.org/10.5281/zenodo.20936013 - The open absolute-SI keystone and caesium-tick reduction.