# Algebraic continuation around a rational rank-48 matrix-multiplication scheme

This computational research note records an exact three-parameter rational
surface of rank-48 decompositions for 4×4 matrix multiplication, together with
boundary-core extractions, exact merger-locus audits, and modular Koszul
flattening witnesses.

The main surface certificate evaluates all 4,096 Brent equations across a
10×10×13 interpolation grid modulo five primes. Its Chinese-remainder modulus
exceeds twice the recorded rigorous coefficient bound. The packaged
certificate reports `exact_rational_brent_certificate: true`.

The archive also includes an exact audit of 27 candidate regular merger loci,
a triple-boundary core, and a finite-field Koszul witness giving tensor-rank
lower bound 15 for one recorded boundary core.

These artifacts do not produce a rank-47 or rank-46 decomposition. They do not
prove a global impossibility result, completeness of the continuation family,
or novelty. Numerical residuals, bounded searches, and missing merger loci are
not promoted to theorems.

`exact-artifacts.tar.gz` has SHA-256 digest
`20f8b3824667850f1ed2c56b465b3974f5e7abc9eb3f2370defbccedcddd72a9`.
It contains the source report, provenance ledger, exact certificate/formulas,
selected boundary and Koszul records, and the corresponding verifier scripts.

The record is published as a computational research note with open replay and
formalization tasks. Its canonical status remains reported until an
independent environment replays the full exact certificate.