# TGA 2.0 — typed alignments with witnesses

Prepared for Matthew Alan Newman, 27 September 2026.

This is a self-contained implementation from the specification in the conversation. No earlier TGA source file was located or modified. It is a small verifier for supported witness schemas, with explicitly typed execution and composition. It is not a general-purpose theorem prover or an automatic merger of research corpora.

## Run

Python 3.10+; standard library only. Tested here with Python 3.12.14.

```sh
python3 tga_verifier.py
python3 tga_verifier.py --report graph-report.json
python3 -m unittest -v test_tga
python3 -O -m unittest -v test_tga
```

`PROOFS.md` supplies mathematical derivations and the trust boundary. The JSON report is data for the atlas or another consumer. It does not execute external code, import uploaded modules, fetch links, or use `eval`.

## Included

- Seven relation categories from the proposed architecture.
- Nineteen supported witnessed edges, including exact golden normalization, explicit β assignment, the rational approximation bound, full-prefix floor equivalence, lossy quotient/geometry/phase maps, exact pair and ledger reconstruction, centered softmax, complex embedding, and full Fourier transforms.
- Full type signatures and image restrictions, explicit inverse contracts, stagewise guards, conservative composition metadata, and source/claim digests.
- An exact certificate for the first disagreement at 42,189,065 using rational interval bounds and floor sums, not floating-point multiplication or a hard-coded `PASS`.
- A six-mark geometry → centered marks → probability → centered marks → complex marks calculation. The geometry-origin loss is retained. The centered subchain alone has an inverse contract.
- A marks → complex marks → specialized Fourier view chain with its image-specific inverse.
- An adversarial suite that rejects unsupported schemas, forged relation labels, broadened domains, changed implementations, missing inverses, numerical-only witnesses, incompatible types, bad ledger data, missing centering, and numerical underflow.

## Deliberate architectural corrections

1. `exact=True` describes the mathematical formula. `arithmetic` separately records exact integer/rational computation or a binary64 preview.
2. A preservation union is not sound in general. Only already justified common properties survive the simple composition rule. Requirements retain their stage and domain.
3. `all(reversible)` is a sufficient certificate rule, not a complete injectivity decision procedure.
4. A bare textual witness is not proof. Registered analytic schemas remain labeled as trusted analytic schemas with supplied written derivations; finite and numerical checks are not promoted to universal results.
5. The full geometry chain is not reversible after dropping origin. A centered-coordinate round trip cannot restore omitted pose information.
6. The DFT of a constrained marked baseline is not interchangeable with an arbitrary complex spectrum.
7. Parameter identification is a declared choice. No optimizer update equation was supplied, so normalized-momentum dynamics are not invented.

## Corpus processing scope

This release implements explicit typed-claim entry, restricted normalization in Q(√5), candidate proposal, witness checking, edge admission, composition, execution, and reporting. Shared symbols can create candidates only. It does not implement automatic document extraction, a minimal-generator optimizer, unbounded closure search, arbitrary transcendental identity proving, or automatic physical interpretation. The report lists these omissions rather than presenting the entire proposed twelve-stage pipeline as implemented.

## Grok / atlas integration

Keep existing atlas and source-work artifacts unchanged. Add this as a versioned supplementary implementation. Run Python during the build or in a separate reproducibility job, not by executing arbitrary uploaded code in a public browser. Publish the checked `graph-report.json`, `PROOFS.md`, code, tests, source hashes, and execution records together.

In the atlas, render each edge's `relation`, `support`, `mathematical_status`, domain, preserves/loses/requires, exact-formula flag, implementation arithmetic, and inverse contract. Keep `proposals_only` separate from admitted edges. Never flatten them into one green verified status. A graph generated from this package is a new graph schema, not a replacement for frozen OMEGA contracts.

The code and this release were tested locally; they have not been installed on omega-naught.grok.me. No website or frozen evidence was changed.