RGE Research Program

A structured research program for recursive geometric entropy and closely related recursive-entropy work.

The central question is simple: what, if anything, stays mathematically stable when entropy is tracked across repeated refinement rather than at a single scale?

This repository separates exact results, tested regularities, corrected claims, and speculative extensions so the program can be read without sorting through mixed drafts.

Current Release

• Release notes: docs/releases/v1.0.0.md
• Changelog: CHANGELOG.md
• Final internal build report: FINAL_REPORT.md
• System inventory: SYSTEM_REPORT.md

If You Are New To The Project

Read these first:

1. docs/overview/start-here.md
2. STATUS.md
3. docs/derivations/refinement-theorems.md
4. docs/derivations/radial-asymptotics.md
5. docs/derivations/bounded-class-theorem.md
6. docs/derivations/partition-scheme-dependence.md
7. docs/foundations/renormalization-and-coarse-graining.md
8. docs/overview/novelty-and-opportunity.md

What This Program Contains

• Foundational papers and source material for RGE and REC.
• A claim-status system that distinguishes theorem-level results from empirical, speculative, and disproved ideas.
• Reproducible validation scripts and tests.
• Archived variants and raw imports for provenance.
• Secondary tooling (RGE256 app/code) kept separate from core theory.
• A dedicated analyzer app for recursive partition experiments and comparison.

Current Evidence Snapshot

Strongest theorem-level items

• S̄(d) ≤ 1 for binary recursive partitions.
• Exact one-step refinement identity:

  S_child = S_parent + Σ_j p_j h₂(α_j)
  

• Binary increment ceiling:

  ΔS = S_child - S_parent ≤ 1
  

• No universal finite upper bound on the unconstrained growth ratio r̃(d)=S(d+1)/S(d).
• Bounded-class ratio theorem: if 0<a≤ΔS(d)≤B, then the ratio is bounded and tends to 1.
• Geometric bound ζ = d_H / D ≤ 1 for volume-convergent recursive geometries (N s^D ≤ 1).
• Equal-shell radial asymptotic:

  S(d) = d + h₂(f) + o(1)
  

  for shell densities f with integrable f log f.
• Exact congruent simplicial and polyhedral subdivision families remain affine with h=0.

Empirical (currently supported)

• Tail fits for the tested line, disk, ball, and cone-profile families agree extremely closely with the differential-entropy offset predicted by the radial asymptotic theorem.
• Finite-depth crossings near 1.25 occur where the affine fit predicts they should, rather than as evidence of a universal asymptotic law.
• Growth ratios for the tested sequence families converge toward 1, not 1.25.
• Across tested partition schemes, the slope class remains stable far more often than the offset class.

Disproved / corrected

• A universal growth ceiling r̃(d) ≤ 2 for arbitrary recursive refinements is false.
• More strongly, the unrestricted binary class admits arbitrarily large growth ratios.
• Universal asymptotic 5/4 entropy-growth resonance is not supported by current tests.

Speculative / open

• Reid-law style 5/4 wave-based entropy law remains speculative without independent physical validation.
• The most promising next step is a renormalization-style classification program that treats refinement as a scale transformation and asks which observables are invariant, which are scheme-dependent, and which are only transient.
• The new analyzer app is useful for this exact question because it exposes ΔS, affine fits, ceiling checks, and family comparison without mixing theorem claims and numerical observations.

What This Program Is Trying To Do

• Build a clean theorem layer for recursive entropy under explicit assumptions.
• Classify recursive geometric families by scale-growth observables such as ΔS, C, h, and finite-depth crossover profiles.
• Separate true invariants from artifacts of partition choice or shallow depth.
• Keep information-theoretic results distinct from wave or physical analogies.
• Turn early broad claims into a tighter program of proofs, counterexamples, and restricted conjectures.

Recursive Partition Analyzer

A usable app now lives at app/recursive-partition-analyzer/.

It is a practical front end for the strongest validated pieces of the program:

• exact recursive split-rule analysis,
• radial research presets,
• entropy and increment curves,
• affine fits S(d) ≈ C·d + h,
• ceiling checks,
• saved-run comparison,
• CSV / JSON / PNG export.

Run it locally with:

cd /Users/stevenreid/Documents/rge-research-program/app/recursive-partition-analyzer
npm install
npm run dev

Quick Start

cd /Users/stevenreid/Documents/rge-research-program

source .venv/bin/activate

PYTHONPATH=src python scripts/validate/run_claim_checks.py
PYTHONPATH=src python scripts/simulate/shape_family_comparison.py
PYTHONPATH=src python scripts/simulate/subdivision_family_comparison.py
PYTHONPATH=src python scripts/simulate/scheme_invariance.py
python -m pytest

Start Reading Here

• docs/overview/start-here.md
• STATUS.md
• docs/overview/proof-status-map.md
• docs/laws/candidate-laws.md
• docs/derivations/refinement-theorems.md
• docs/derivations/radial-asymptotics.md
• docs/foundations/renormalization-and-coarse-graining.md

Repository Map

• papers/: foundational, experimental, hybrid, secondary
• theory/: formal sources and derivation assets
• src/: reusable computation modules
• scripts/: reproducible validation, simulation, and reporting utilities
• tests/: curated consistency, math, and simulation checks
• docs/: guided narrative and status docs
• archive/: preserved variants, raw imports, and older drafts
• tooling/: RGE256 app/code snapshots kept separate from core theory

Tooling and PRNG Layer

This repository includes the RGE-related tooling that belongs in the ecosystem, but keeps it clearly secondary to the theorem program.

Included locally:

• tooling/rge256-core/
• tooling/rge256-app/
• tooling/rge256-lite/

Map:

• docs/overview/tooling-and-prng-map.md

Legacy public GitHub audit:

• docs/archive-notes/github-legacy-audit.md

Separation From RDT

This repository keeps core RGE work separate from broad RDT algorithm and tooling work. RDT-only materials are referenced only where they directly affect RGE definitions, comparisons, or validation logic.

Provenance

• Migration map: data/generated/inventory/migration_map.csv
• Discovery summary: docs/overview/discovery-inventory.md
• Raw imports retained under archive/raw-imports/