# Tomita Energy Logic: two-paper research draft

Author: Kenju Tomita. Both manuscripts include an AI-assistance disclosure.

Current revision: **1.3**, prepared as research preprints for Ephemerent Research. It includes finite learned-rule and witness-policy experiments, a certified RH residual-line study, a configuration compatibility audit, an explicit custom descent-domain formulation, an adaptive-discovery theorem, sharper periodic tail bounds, compact exact duals, and a certified N=8192 extension with two additional contraction steps. Earlier PDFs and sources are preserved under `output/archive/` in the original workspace.

- Paper I: **Tomita Energy Logic: Toward a Physics-Grounded Foundation for AI Reasoning and Proof**.
- Paper II: **Applying Tomita Energy Logic to Solve the Riemann Hypothesis: A Custom Descent-Based Domain as a Proposed Alternative to Mathematical Logic**.

TEL is a proposed framework and replacement research program. Greater reliability than existing systems has not been demonstrated. **Paper II does not prove RH unconditionally.** Its title states the research objective. It proves a conditional implication whose transfer premise is explicitly unproved and RH-equivalent for the specified complete full-support sampler. Both papers are preprints, not accepted or peer-reviewed journal articles. Article text is copyright 2026 Kenju Tomita, all rights reserved; supplementary materials retain any separately stated licenses.

## Editable sources

`paper/tomita_paradigm/framework/source.md` and `paper/tomita_paradigm/rh_application/source.md` are canonical, relative to the workspace or package root. Each directory also has a generated `manuscript.md` with resolved equation references. Figures and vector math assets are included. The two PDFs are in `output/pdf/`. The original earlier SWC/RH paper is a separate snapshot and has not been overwritten.

## Build

From the package/workspace root, install `paper/requirements.txt` in a suitable Python environment. Then run:

```bash
python3 paper/tomita_paradigm/make_figures.py
python3 paper/tomita_paradigm/build_paper.py framework
python3 paper/tomita_paradigm/build_paper.py rh_application
```

`MATH_PYTHON` may identify a separate Python interpreter with Matplotlib. The builder uses ReportLab and svglib; `STIX_FONT_DIR` may identify the Matplotlib STIX fonts. Otherwise they are discovered automatically. Cached metric files contain original absolute paths, but each build regenerates them locally.

## Quick checks

```bash
python3 -m unittest discover -s research/swc-rh -p 'test_*.py' -q
python3 paper/tomita_paradigm/audit_framework.py
```

The first command runs the 54-test implementation suite. The second runs eight small exact protocol audits, including an exact first-crossing calculation for a specified Bernoulli process. These are not physical experiments or a general implementation of the proposed learned-rule system.

## Version 1.1 experiments

```bash
python3 paper/tomita_paradigm/experiments/run_rule_study.py
python3 paper/tomita_paradigm/experiments/verify_studies.py
python3 paper/tomita_paradigm/experiments/verify_line_results.py
```

These commands check the 70 finite rule-training splits, all 320 saved noisy-policy mass calculations, non-enumerative mass bounds, and the 33 derived RH line enclosures. The line checker reuses the recorded full-domain norm certificate. It does not rerun its 64-million-cell head.

To regenerate the learned policies, install `paper/tomita_paradigm/experiments/requirements.txt` and run `run_sat_study.py` from the same directory path. The protocol is in `experiments/protocol.json`, relative to this README, and the complete generated formulas and rational policy parameters are retained. Reported mass gains exclude training overhead; the noise is simulated, not measured hardware noise.

To recompute the full RH update norm, run `python3 research/swc-rh/residual_line_experiment.py`. To repeat the direct finite quadratic-model comparison, run `python3 paper/tomita_paradigm/experiments/check_full_quadratic.py --rebuild`; its large untrusted Gram cache is omitted from the package. Neither experiment proves a zero infinite-basis limit.

## Version 1.3 research extension

The new bounds and proofs are explained in `research/swc-rh/PROGRESS_EXTENSION.md`. Run:

```bash
python3 research/swc-rh/verify_progress_extension.py
```

This exact checker reloads every compact dual, checks original-basis orthogonality, recomputes the period means and strengthened discrepancy bounds, and checks the j=11 and j=12 contractions with constant 1/2. It reuses the previously checked rational head sums, including the newly evaluated 128-million-cell N=8192 head. The complete N=8192 head can be independently recomputed with `python3 research/swc-rh/extension8192.py --verify`.

To regenerate numerical proposals in a separate extraction, run `gradient_extension.py --produce` first to rebuild the N=4096 cache. The initial compact proposals use `compact_dual_experiment.py`. Run `extension8192.py --produce` to rebuild the N=8192 cache, then `compact_dual_experiment.py --N 8192 --cells 262144`. For the strongest N=4096 dual, run `refine_dual_head.py`, then `compact_dual_experiment.py --N 4096 --cells 1048576 --fit-cells 1048576 --label refined`. These scripts are in `research/swc-rh/`. Numerical proposal bytes may vary with the linear-algebra environment; the saved exact certificates are the reproducible claims, and their checkers use integer/rational arithmetic. Large NumPy caches are intentionally omitted.

The earlier approximate million-cell dual proposal is retained as a negative result. Increasing its support without improving its numerical fit gave a weaker lower certificate. The final reported bounds select the strongest exactly verified certificates.

## Astra configuration finding

The supplied boolean tip is not supported by the checked CLI. Current official documentation specifies `features.context_management.experimental_mode = true` on supported clients, but installed `codex-cli 0.146.0` rejects the nested format and reports the older explicit flag as unknown. The actual global config was left unchanged. The documentation example `experiments/context-management-supported-client.toml` is not installed configuration. No context-management A/B savings claim is made.

## Large certificate checks

The gradient candidates and their full-domain verification are described in `research/swc-rh/GRADIENT_EXTENSION.md`. Rechecking both full errors examines 192 million cells and can take several minutes:

```bash
python3 research/swc-rh/gradient_extension.py --verify
```

The stronger saved dual can be checked separately without numerical optimization:

```bash
python3 - <<'PY'
import gzip, json, sys
sys.path.insert(0, 'research/swc-rh')
from dual_verify import verify_dual
with gzip.open('research/swc-rh/gradient-extension-dual-N4096.json.gz', 'rt') as f:
    lower = verify_dual(json.load(f))
print('Exact lower bound verified:', float(lower))
PY
```

The published zeta-zero verification through height 3*10^12 is an external theorem input; it was not reproduced here. No statistical probability of RH is assigned.

## Provenance and packaging

`research/swc-rh/source-provenance.json` identifies the author-supplied SWC v6 archive and source fingerprints. `PACKAGE_SHA256SUMS` in the ZIP covers every packaged payload file. The historical research `SHA256SUMS` is preserved as an earlier manifest; it does not cover all later additions. Some chronological notes retain absolute links to the original workspace, while executable checkers locate data relative to their files.

The PDF layouts are rendered and reviewed page by page before delivery. The package smoke test verifies every payload checksum, runs the 54 tests, eight audits, new experiment checks, compact duals, and finite contractions from a fresh extraction. No publication, submission, or claim of independent peer review is implied by the draft package.
