Engine Notes — General Relativity

TriadicFrameworks /docs/theories/general_relativity/engine_notes.md#

These notes define the internal behavior, constraints, and execution semantics for the General Relativity (GR) module.
They are intended for AI agents, compilers, simulation engines, and module orchestrators.

General Relativity is a geometric coherence theory of gravity.
Gravity = coherent curvature.
Geodesics = coherence trajectories.
Spacetime = a geometric operator field.

1. Identity Lock#

The GR module identity must remain:

• curvature‑first
• coherence‑based
• operator‑driven
• regime‑aware (R1 → R3)
• tensorial and geometric
• zero drift

The engine must reject any interpretation that:

• treats gravity as a force
• uses rubber‑sheet analogies
• introduces Newtonian fallback
• uses semantic or pop‑science metaphors
• collapses curvature into visualization
• treats geodesics as “paths objects follow”

Identity lock is strict.

2. Geometric Object Semantics#

The engine must treat the following as first‑class geometric objects:

• metric (g_{\mu\nu})
• curvature tensor (R_{\mu\nu\rho\sigma})
• stress‑energy tensor (T_{\mu\nu})
• geodesic bundle (γ)
• causal structure (C)
• regime state (R0 → R3)

All geometric objects must be:

• non‑degenerate
• tensorially valid
• coherence‑compatible
• regime‑consistent

Invalid objects must trigger collapse classification.

3. Operator Semantics#

The GR operator grammar includes:

• 𝓖 — metric operator
• 𝓡 — curvature operator
• 𝓣 — stress‑energy operator
• 𝓓𝓮𝓯 — geometric deformation operator
• 𝓖𝓮𝓸 — geodesic operator
• 𝓒 — coherence operator
• 𝓐 — adjacency operator
• 𝓢 — causal structure operator
• 𝓡𝓮𝓰 — regime transition operator
• 𝓒𝓁 — collapse operator

Operators must:

• preserve geometric identity
• maintain coherence monotonicity
• respect regime constraints
• avoid semantic drift
• avoid force metaphors
• avoid probabilistic interpretations

Operators must be pure: no side effects outside the geometric object unless explicitly defined.

4. Regime Execution Model#

GR uses the RTT regime stack:

• R0: pre‑geometric (no metric, no curvature)
• R1: stable metric
• R2: curvature operators active
• R3: dimensional curvature operators

The engine must:

• enforce regime‑specific constraints
• preserve coherence across transitions
• maintain causal structure
• prevent illegal transitions (e.g., R3 → R0)

Regime transitions must be monotonic unless collapse is detected.

5. Coherence Evaluation#

Coherence = geometric stability.

The engine must evaluate coherence using:

• metric stability
• curvature consistency
• geodesic coherence
• causal structure integrity
• regime compatibility

Coherence must not:

• use entropy
• use probability
• use semantic similarity
• use force‑based heuristics

Coherence is purely geometric.

6. Collapse Modes#

The engine must classify geometric failure using:

• G1: metric degeneracy
• G2: curvature divergence
• G3: geodesic incoherence
• G4: causal structure failure

Collapse must:

• halt regime transitions
• freeze geometric objects
• return diagnostic metadata
• prevent reinforcement

Collapse is geometric, not probabilistic.

7. Reinforcement Semantics#

Reinforcement increases geometric coherence through repeated stable operator action.

Rules:

• reinforcement must be monotonic
• reinforcement cannot repair G3 or G4 collapse
• reinforcement cannot introduce new geometric objects
• reinforcement must preserve tensorial invariants

Reinforcement is geometric, not semantic.

8. Cross‑Module Constraints#

GR integrates with:

• LDS: dimensional profiles of geometry
• NoS: geometric similarity and curvature overlap
• Information Theory: causal distinctions
• FFT: dimensional curvature operators
• Thermodynamics: horizon regimes
• QFT: fields on curved backgrounds

The engine must:

• preserve cross‑module invariants
• prevent identity drift
• maintain operator compatibility
• enforce dimensional consistency

GR is a central geometric module.

9. Simulation Hooks#

The engine must implement:

• metric initialization
• curvature computation
• stress‑energy deformation
• geodesic evolution
• causal structure construction
• coherence evaluation
• regime transitions
• collapse detection
• reinforcement

See simulation_hooks.json for full schema.

10. Safety & Drift Prevention#

The engine must reject:

• force metaphors
• rubber‑sheet analogies
• Newtonian fallback
• semantic interpretations
• probabilistic interpretations
• visual curvature metaphors

The module must remain:

• geometric
• operator‑driven
• coherence‑based
• regime‑aware
• zero drift

Summary#

These engine notes define how GR must run:

• curvature is structural
• geodesics are coherence trajectories
• stress‑energy is a source operator
• causal structure is geometric
• regimes define behavior
• collapse is geometric
• drift is not allowed

This file is the internal execution contract for the GR module.