Exact Tableau Certificates for Stretched Littlewood-Richardson Positivity in the Seven-Row, Size-Thirty Box

This research release presents a complete independent residual computation supporting coefficient nonnegativity for stretched Littlewood–Richardson polynomials in a bounded domain: balanced partition triples with each partition having at most seven parts and the unstretched outer partition having size at most thirty. The conclusion concerns ordinary monomial coefficients and holds for every positive integer stretch factor, including stretches whose resulting sizes exceed thirty.

The computation reconstructs all 358,952 residual polynomials in Maseeh Ghodsi’s finite cover. It combines integer tableau counting, finite-moment feasible-point proposals, exact rational affine-hull certificates, Ehrhart–Macdonald reciprocity, and degree-bounded interpolation. The moment construction applies the viewpoint developed in the author’s earlier manuscript, “Sharp Finite-State Realization for Truncated Matricial Moment Problems.” Separate exact certificates establish the affine hull; integer-point averages alone are not assumed to determine it.

The recorded complete replay reports:

• 358,952 residual polynomials reconstructed and verified.
• 358,952 exact affine-hull certificates checked.
• 2,745,084 rational coefficient entries checked, with no negative entries.
• 2,386,133 determining or additional base counts freshly repeated.
• Complete finite-cover replay and no unresolved residual cases.

The release includes the proof manuscript, source code, complete certificate corpus, verification receipts, reproducibility instructions, exact Parquet and JSONL datasets, machine-readable metadata, citation files, and documentation for researchers and AI agents.

Attribution: Maseeh Ghodsi previously stated the bounded positivity theorem and supplied the finite cover, reductions, and associated evidence in arXiv:2609.14357. This release credits and uses that work. Its contribution is the independent residual tableau reconstruction, rational certificates, and complete recount; no priority claim is made for the bounded theorem.

Status and completeness: conventional computer-assisted verification completed for all 358,952 required residual cases. The result remains subject to the documented mathematical and software trust boundary. It does not prove unrestricted stretched Littlewood–Richardson positivity. No proof-assistant formalization, peer-review acceptance, or official benchmark acceptance is claimed