RGAP — Residual Geometric Admissibility Principle

RGAP is a bounded computational framework for admissibility-constrained inference under degraded observability.

The repository demonstrates a computable distinction between:

• unconstrained optimization,
• ambient physical feasibility,
• residual observational admissibility,
• and, experimentally in v0.2, semantic namespace admissibility.

Core finding:

Lower residual misfit is not automatically higher admissibility. Admissibility must be preserved by the update law itself.

Repository status

• v0.1: frozen kernel and computational proof.
• v0.2 namespace: experimental scaffold for semantic namespace drift; not yet a validated result.

Structure

RGAP/
├── README.md
├── LICENSE
├── .gitignore
├── rgap_kernel_v0_1.md
├── metrics_schema.json
├── RELEASE_NOTES_v0_1.md
├── notes/
│   └── rgap_results_note_v0_1.md
├── results/
│   └── toy_arc_optimizer_free_state_results.json
├── src/
│   └── toy_arc_optimizer_free_state.py
├── v0_1/
│   ├── TECHNICAL_NOTE.md
│   ├── RGAP_v3_sphere_arc_demo.py
│   ├── RGAP_v3_metrics.csv
│   ├── metrics.json
│   ├── metrics.md
│   ├── environment.txt
│   └── environment.yml
├── v0_2_namespace/
│   ├── README.md
│   ├── namespace_drift_simulator.py
│   ├── metrics_schema_namespace.json
│   └── namespace_drift_note_v0_2.md
├── figures/
│   ├── rgap_v01_sphere_arc.png
│   ├── RGAP_v3_results.png
│   ├── rgap_canonical_three_paths.png
│   ├── rgap_v4_metrics.png
│   └── rgap_v4_animation.gif
└── v4_pathwise/
    ├── metrics.json
    └── environment.yml

v0.1 Demonstrated distinction

The frozen v0.1 free-state optimizer compares three update rules:

Method	Misfit	Sphere Error	Arc Error	Verdict
Euclidean	0.068	0.074	0.096	Inadmissible
Sphere-projected	0.122	0.000	0.096	Physically admissible only
Arc-retracted	0.182	0.000	0.000	Fully admissible

The key result is that Euclidean optimization can achieve the lowest residual misfit while remaining structurally inadmissible. Arc-retracted recovery accepts an explicit misfit premium to preserve residual geometry.

v0.2 experimental namespace scaffold

The v0_2_namespace/ directory extends the same update-law comparison into semantic namespace transport.

It compares:

Method	Meaning
Euclidean semantic update	unconstrained embedding-space optimization
Namespace projection	coarse namespace validity
Namespace retraction	residual semantic corridor preservation

The v0.2 layer is experimental and should not be treated as a validated result until metrics demonstrate clear three-tier separation.

Run

python src/toy_arc_optimizer_free_state.py
python v0_2_namespace/namespace_drift_simulator.py

Scope boundary

This repository is not a domain-specific predictive method, operational search tool, accident-reconstruction method, production retrieval system, or claim to solve MH370. It provides toy computational demonstrations of admissibility-preserving inference under degraded observability.

License

MIT License. See LICENSE.