[MatShep]

The full two-qubit Gaussian-dyadic Clifford tensor alphabet has sharp pointwise independence threshold 9. At every f>=9 its normalized Gram spectrum lies in the sharp interval [315/1024,9855/4096], with sharp Gram condition number 219/28, attained at nine. This resolves the two-qubit next question in #5594 and improves the n=2 sufficient threshold 12 from Ali Romman's #5526. No new kappa, physical supplier or selected-frontier change is claimed.

The isolated research/full-clifford-two-qubit-centre package enumerates 46,080 exact lifts/11,520 projective classes, reduces 59 conjugacy classes to residue blocks of sizes 11,16,11,21, and certifies exact spectra and regular multiplicities at widths 1..12 by integer polynomial/projector identities. It never constructs a dense 11,520-square Gram. An independent determinant-character sum supplies the width-eight null witness; the all-width argument is the Schur product theorem. The proof explicitly distinguishes pointwise sharpness from the merely sufficient fixed-residual test window 9..12.

Validation: registered normal and optimized/warning-strict commands pass on CPython 3.12.14/NumPy 2.3.5/Windows 11, with equal complete JSON outputs; all lifts and class blocks, 64 literal tensor entries and seven rejection controls pass. Committed bytes and read-only, Git-free export replays also passed; reproduction commands and scope are in the package README. Hosted CI and independent human/formal acceptance are separate. NumPy is the sole pinned replay dependency; no symbolic eigensolver or predecessor executable is used.

The group count itself was already independently enumerated for a different task in JoyboyBrian/#5051; the new result is its tensor spectrum and quantitative bounds. Credit Ali Romman/#5526, MatShep/#5549/#5594, DLamdata/#5547, josecarlosgonzalezroque-design/#5570 and their retained lineage (NOTICE.md has exact context pins). Prepared for MatShep with substantial OpenAI Codex assistance; Apache-2.0. Current canonical main, guidance, handoffs and targeted open/closed PR/Issue/Discussion overlap were checked with bounded coverage. The next question is whether 4n+1 remains sharp beyond two qubits; no such general claim is made.

Submission refresh: canonical main df0137efd35e11b4445734bf612bdd4c7ebc330c now selects PR5599. Applicable submission guidance and priority revision remain unchanged. The frozen package retains its historical PR5413 source context and original base; this isolated algebraic result does not depend on or modify either frontier. Astra performed only a brief obvious-error and bounded overlap check, not a full replay or deep proof audit.