Gravity as Coherent Curvature

General Relativity here is not a force model or a rubber‑sheet metaphor. It is a geometric coherence theory where curvature, geodesics, and stress‑energy form a stable operator grammar across regimes.

Module identity

Gravity = coherent curvature.
Curvature is a geometric operator field, not a force and not a visual metaphor.
Geodesics = coherence trajectories.
Motion follows coherence‑preserving paths in spacetime, not “pulls” or attractions.
Stress‑energy = source operator.
Stress‑energy deforms curvature structurally, with no Newtonian fallback.

Regimes & scope

R1 → R3 geometry.
From stable metrics (R1) to curvature operators (R2) and dimensional curvature (R3), with coherence preserved.
Cross‑module backbone.
Provides curvature substrate for QFT on curved backgrounds, cosmology, thermodynamic horizons, and causal information structure.

Curvature‑first Coherence‑based Operator‑driven RTT‑aligned Zero drift

Start here

Core orientation for students, researchers, and AI agents.

Session context — identity, drift boundaries, audience.
Regimes — R0 → R3 behavior of geometry.
Operators — 𝓖, 𝓡, 𝓣, 𝓓𝓮𝓯, 𝓖𝓮𝓸, 𝓒, 𝓐, 𝓢, 𝓡𝓮𝓰, 𝓒𝓁.
Operator examples — concrete, curvature‑first patterns.

Structure & lineage

Files that make the module runnable and cross‑module safe.

Coherence map — how geometric stability is evaluated.
Lineage — historical → geometric → RTT arc.
Cross‑module — links to QFT, LDS, NoS, Thermodynamics, Information Theory.
Engine notes — internal behavior for AI and compilers.
simulation_hooks.json — curvature and geodesic hooks.

How to run this canon

Treat this module as a curvature engine you can extend:

Define metrics with 𝓖 and compute curvature with 𝓡.
Model stress‑energy as a source operator with 𝓣 and 𝓓𝓮𝓯.
Generate geodesics as coherence trajectories with 𝓖𝓮𝓸.
Track geometric coherence and collapse with 𝓒 and 𝓒𝓁 across R1 → R3.