Buckholtz IDM/MULTING Study

_{Quality snapshot (verified 2026-07-12, local py3.13): 867 tests pass · 0 skipped · 0 failed · coverage 83% · ruff clean. The CI badge above is the authoritative live status; this line is a dated snapshot, not a self-updating metric.}

Personal study notes and reproducibility scaffolding for understanding Thomas J. Buckholtz's IDM/MULTING framework.

⚠️ IMPORTANT DISCLAIMERS:

• This project does NOT validate, refute, or officially audit the IDM/MULTING theory
• This is a personal learning exercise in epistemic auditing and source verification
• All interpretations and analyses are my own and may contain errors
• This work is not endorsed by Dr. Buckholtz or any institution
• The goal is transparency and learning, not criticism or validation

What this actually reproduces: an AI-service-mediated computation (Table A1 and its fitted beta parameters from ChatGPT / Claude / Gemini), not Buckholtz's physical theory — the H_MULT(z) formula is under-specified in the source. The candidate beta values {4.25, 0.78, 8.10, 0.19} are AI-service outputs, not model versions. Full framing: docs/WHAT_THIS_REPRODUCES.md.

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What This Repository Does

It provides a small reproducibility and epistemic-audit layer for selected definitions, equations, parameters, and claims from Thomas J. Buckholtz's work on Isomeric Dark Matter (IDM) and MULTING (multipole tiers) cosmology.

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The Source

This repository audits the numerical claims in:

Thomas J. Buckholtz, "Gravitational and Dark-Matter Concepts that Can Help Explain and Predict Cosmic Data," Preprints.org (2026). DOI: 10.20944/preprints202511.0598.v6 · mirrored on ResearchGate

Read the preprint first — this repo assumes familiarity with its notation (Table A1, β_d, β_q, IDM isomers, MULTING multipole terms).

About Dr. Thomas J. Buckholtz

Dr. Thomas J. Buckholtz is an independent researcher affiliated with the Ronin Institute for Independent Scholarship (Montclair, NJ) and the National Coalition of Independent Scholars (Brattleboro, VT). His recent work proposes Isomeric Dark Matter (IDM) and MULTING (multipole gravity), a framework in which most elementary particles have six "isomers," five of which associate with dark matter — see the preprint linked above for the full framework.

This repository is an independent, non-affiliated audit of that work's numerical claims. It does not represent Dr. Buckholtz's own code, endorsement, or conclusions — see the disclaimers throughout this README.

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Key Numerical Results (2026-06-17) — NOT_VALIDATION · OUR_RECONSTRUCTION

Test	Result	Script
Eq.32 fermion-gravity link	1.00σ (0.0608%) from PDG 2024/2025	code/eq32_verify.py
IDM N=5 vs Planck 2018 ω_DM/ω_b	5.8σ excluded	code/chi2_idm.py
β_d=4.5 dipole at cluster scale	ε ≈ 6×10⁻⁶ (negligible)	code/beta_rescaling.py
MULTING H(z) ΔAIC vs ΛCDM	+2.5 (ΛCDM preferred)	data/pearson_r_test_results.md
Pearson r MULTING/H_CC	0.62 (MCXC n=443), 0.70 (XMM n=22)	ibid

Strong Inference summary: H4 (empirical mass relations) ✅ · H3 (IDM as CDM) ❌ · H1 (full replacement) ⚠ conf=0.12

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Goals

1. Audit beta_d and beta_q definitions — clarify values, units, normalizations
2. Reproduce selected numerical relations — verify arithmetic (e.g., Eq.15)
3. Classify claims — separate derived / fitted / assumed / unknown
4. Detect numerology — penalize arbitrary formulas without mechanisms
5. Prevent data leakage — ensure beta formulas don't circularly use H0, Omega_m
6. Prepare respectful technical brief — document what's clear and what requires clarification

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Non-goals

• ❌ No full cosmological simulation (no serious H(z) solver)
• ❌ No claim that IDM/MULTING is true
• ❌ No claim that ΛCDM is false
• ❌ No unsupported physics derivations
• ❌ No use of AI-generated supplementary values as verified data

Guiding principle:

Do not implement physics that is not clearly defined. First build the epistemic registry.

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Quick Start

# Clone or download repository
cd buckholtz-idm-multing-mvp

# Create virtual environment
python -m venv .venv

# Activate (Windows)
.venv\Scripts\activate

# Activate (Linux/Mac)
source .venv/bin/activate

# Install dependencies
pip install -r requirements.txt

# Run tests
pytest

# Run with verbose output
pytest -v

# Run specific test
pytest tests/test_eq15_constants.py -v

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Project Structure

buckholtz-idm-multing-mvp/
├── src/              # 38 core modules — epistemic registry, beta provenance, bridge candidates, force-law records
├── tests/            # 49 test files (867 tests) — invariants, controls, dimensional checks, reverse-engineering
├── code/             # standalone verified scripts — eq32_verify, chi2_idm, beta_cv, beta_rescaling
├── scripts/          # 54 pipeline/report scripts — recompute_n4_aic, jeans_nfw_multing, build_report_ru
├── audit/            # self-consistency diagnostics
├── data/             # PDG/CODATA constants + real catalogs (MCXC, XMM T_X) + Moresco+2022 CC H(z)
│                     #   ⚠ author preprint PDF & supplementary CSVs are gitignored (local-only)
├── docs/             # 96 documents — see docs/INDEX.md for the full map
├── paper/            # LaTeX manuscript skeleton (main.tex, refs.bib)
├── reports/          # 21 machine-readable result JSONs
├── notebooks/        # 3 exploration notebooks
├── null_results/     # falsified-hypothesis records (FL protocol)
└── pearl_registry/   # tool-verified side-insights (FL protocol)

Full per-document navigation: docs/INDEX.md. Key source modules: epistemic_registry.py, beta_provenance.py (single source of truth for β), constants.py (fundamental constants only — no cosmological fits), rosetta.py (terminology mapping).

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Status Labels (Epistemic Taxonomy)

Every claim, parameter, and equation is marked with one of these statuses:

Status	Meaning	Example
fact	Verified measurement/observation	Electron mass from PDG
calculation	Reproduced numerical result	Eq.15 numerical reproduction
hypothesis	Proposed but not yet tested	6 isomers structure
inference	Logical conclusion from verified facts	Ratio derived from masses
assumption	Chosen premise without derivation	5 dark / 1 ordinary split
fitted	Phenomenological fit to data	Beta values from H(z) fit
derived	Mathematically derived from other claims	Formula consequence
unknown	Status not determined	Missing information
unclear	Conflicting or ambiguous information	Multiple beta values
requires_source_verification	Source needed or source unclear	Equation mentioned but not sourced

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Test Suite

The full suite is 49 test files / 867 tests (0 skipped, 0 failed) — run pytest. The six below are representative of the core invariants, not the complete list; see tests/ for all.

Core Tests

1. test_eq15_constants.py — Reproduces Eq.15 numerical relation

   • Verifies: (4/3) * (m_tau^2 / m_e^2)^6 ≈ k_e * e^2 / (G * m_e^2)
   • Does NOT establish physical mechanism
   • Does NOT prove the relation is fundamental

2. test_eq15_numerology.py — Tests alternative formulas

   • Checks if Eq.15 is unique or part of large search space
   • Tests: different exponents, prefactors, muon vs tau

3. test_no_cosmology_leakage.py — Prevents circular reasoning

   • Ensures beta formulas don't use H0, Omega_m, Planck fits
   • Flags formulas with uses_cosmological_observations=True

4. test_beta_status_required.py — Enforces registry discipline

   • Every beta must have: symbol, units, status, source, interpretation
   • Conflicting values must have normalization notes

5. test_epistemic_registry.py — Tests invariants

   • Claims marked fact must have sources
   • Parameters marked fact with values must have sources

6. test_assumption_graph.py — Validates dependencies

   • H(z) fit depends on beta_d, beta_q
   • MULTING terms depend on PPN constraints

Running Tests

# All tests
pytest

# With coverage report
pytest --cov=src --cov-report=term-missing

# Specific category
pytest tests/test_eq15*.py -v

# Stop on first failure
pytest -x

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Key Modules

constants.py

Physical constants from PDG 2024/2025 and CODATA 2018.

WARNING: This file contains ONLY fundamental constants (m_e, m_tau, G, k_e, e, c, hbar).
DO NOT add cosmological fitted parameters (H0, Omega_m, etc.) here.

epistemic_registry.py

Core data models: Claim, Parameter, EquationRecord, SourceRef.

Every record MUST have an explicit status to prevent silent assumptions.

beta_definitions.py

Legacy-but-active candidate registry of beta values, each attributed to its AI-service origin (source-confirmed, docs/93):

• beta_d 4.25 — Gemini output
• beta_d 0.78 — ChatGPT output
• beta_q 8.10 — Gemini output
• beta_q 0.19 — ChatGPT output

All marked status="unclear" and NOT Buckholtz model versions. The actual Table A1 caption pair (β_d=4.5, β_q=18.0, Claude) lives in beta_provenance.py, the single source of truth for provenance and use-permission. Always consult beta_provenance.py before using any value for modeling.

numerology_penalty.py

Anti-numerology scoring:

• Complexity penalty for arbitrary choices
• Data leakage penalty for using cosmological observations
• Mechanism bonus for physical derivations

assumption_graph.py

Dependency graph: tracks which claims depend on which assumptions.

Example:

H(z) fit
  ├── beta_d
  ├── beta_q
  ├── cluster radius definition
  └── sub-object kinetic energy definition

data_anchoring.py

Registry of observational datasets with leakage risk flags.

High leakage risk:

• Planck CMB (Omega_m, H0)
• Cosmic chronometers H(z)
• Pantheon+ SNIa

Safe inputs:

• PDG particle masses
• CODATA fundamental constants

rosetta.py

Buckholtz terminology ↔ mainstream physics mapping.

Example:

• "Isomeric Dark Matter" → "Hidden sector / mirror-matter-like dark sector"
• "MULTING" → "Modified gravity with multipole terms"
• "beta_d" → "Phenomenological scale parameter (definition unclear)"

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What This Repository Reproduces

✅ Eq.15 numerical relation — arithmetic verified to ~1% precision
⚠️ Physical mechanism for exponent 6 and prefactor 4/3 is unclear
⚠️ Dimensional analysis requires careful unit tracking

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What Remains Unclear

❓ Beta definitions — Are 4.25/8.10 and 0.78/0.19 different normalizations, versions, or different parameters?
❓ MULTING functional forms — Exact equations for monopole, dipole, quadrupole terms
❓ PPN constraints — Do dipole/quadrupole terms violate Solar System tests?
❓ 6 isomers structure — What defines an "isomer" in this context?
❓ Derived vs fitted — Are beta values phenomenological fits or derivable from IDM structure?

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Dependencies

Source of truth: requirements.txt + pyproject.toml.

python >= 3.11
numpy  scipy  sympy  pandas  matplotlib       # core
pytest  pytest-cov  ruff  mypy                 # dev / CI
astropy  astroquery  requests                  # cluster data pipeline (src/cluster_data_pipeline.py)

Optional:

pydantic
networkx
jupyter

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Contributing

This is a personal research-engineering project for epistemic audit purposes.

If you wish to contribute:

1. Maintain the non-goals (no overclaiming, no refutation)
2. Add sources for all new claims/equations/parameters
3. Mark status explicitly for all new records
4. Write tests for new functionality

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License

MIT License © 2026 Sergey Boyko (ORCID 0009-0009-2178-5701, Ronin Institute for Independent Scholarship)

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Acknowledgments

This repository organizes and audits claims from:

• Thomas J. Buckholtz's work on Isomeric Dark Matter (IDM) and MULTING cosmology

Physical constants from:

• Particle Data Group (PDG) 2024/2025
• CODATA 2018

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Disclaimer

This repository is NOT:

• An endorsement of IDM/MULTING
• A refutation of IDM/MULTING
• A claim about ΛCDM validity
• A complete implementation of IDM/MULTING physics

This repository IS:

• An epistemic audit tool
• A reproducibility scaffold
• A definition clarification aid
• A structured way to separate what is clear from what requires verification

Use responsibly. Science advances through clarity, not through premature claims.