Engine Notes — General Relativity

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

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.