---
pretty_name: Celestial Mellin-Carrollian Transform Triangle
license: cc-by-4.0
language:
- en
tags:
- celestial-holography
- mellin-transform
- carrollian-physics
- mathematical-physics
- symbolic-computation
- ai-generated
---

# 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:

~~~text
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.