cjc0013/celestial-mellin-carrollian-transform-triangle

Celestial Mellin-Carrollian Transform Triangle

Produced by the Ouroboros AI Research System, under human direction.

This package presents an exact transform calculus connecting energy-space Euler operators, celestial Mellin variables, and Carrollian dilations. Endpoint defects remain explicit because those terms decide whether a particular amplitude or correlator is admissible.

The central maps are:

M[E_i f](Delta) = -Delta_i M[f](Delta) + endpoint defect
F_+[E_i f](u) = -(u_i d/du_i + 1) F_+[f](u) + endpoint defect
M[(log omega_i)^m f] = d^m/dDelta_i^m M[f]

Under a common zero-defect contract, finite polynomial identities in the total energy Euler operator have consistent momentum-space, celestial-Mellin, and Carrollian realizations.

Evidence at a glance

• Proved transform results: 6.
• Passing proof steps: 8 of 8.
• Passing machine-certificate families: 7 of 7.
• Certificate cases checked: 131.
• Certificate failures: 0.
• Direct SHA-256 input commitments: 4.
• Primary-literature anchors: 7.
• Explicit open obligations: 5.

What “data used” means here

The proof packet directly depends on 4 hash-bound input artifacts. The wider celestial workspace contains 581 source/test files across 38 run families. That larger inventory supplied research context and falsifier history; it is not counted as direct proof evidence because the final packet does not carry a file-by-file provenance edge for every item.

Result boundary

This package proves the stated transform identities under their regularity and endpoint hypotheses. It does not identify a gauge-invariant scattering observable, establish the distributional extension used by physical amplitudes, or bind the conditional transfer result to a literal paper formula. LIMITATIONS.md lists the exact evidence needed to close each point.

Package map

• THEOREMS.md — six results, formulas, proof methods, and falsifiers.
• EVIDENCE.md — exact counts and hash commitments.
• LIMITATIONS.md — five missing proofs for a physical application.
• REFERENCES.md — primary literature and relevance.
• AI_DISCLOSURE.md — Ouroboros work and independent checks.
• theorem_receipt.json and validation_summary.json — public-safe machine receipts.
• manifest.json and SHA256SUMS — package integrity.