[dipamc]

Truncated SVD previously billed only 4mnk while returning exact economy-SVD factors. Near-full-rank calls could recover the missing triplet in quadratic work, or zero-pad a matrix and request all its original components, for substantially less than the full-SVD price.

Use the approved rank-dependent formulas for 1 <= k < b, with a=max(m,n) and b=min(m,n):

Result	Charge
With vectors	min(4mnk + 6(m+n)k² + 20k³, 6ab² + 20b³)
Values only	min(4mnk + 2(m+n)k² + 2k³, 2ab² + 2b³)

The shared cost helper drives svd, svd(compute_uv=False), svdvals, and analytical cost queries. Full calls and their existing thin/full-vector/values-only prices remain unchanged, as do exact numerical outputs, upfront budget checks, dtype/complex/weight factors, and batch multiplication. This does not depend on other open PRs and does not bump or publish a package version.

The formulas are analytical pricing conventions, not literal counts of the NumPy backend. They close the reported large-matrix near-full-rank/padding discounts, but do not establish a universal lower bound on small-matrix or composite reconstruction algorithms. Documentation removes that earlier absolute claim.

Validation

• New/updated pricing regressions first failed on the previous implementation: 24 failed, 58 passed.
• Full default core suite: 10,702 passed, 125 skipped, 2 xfailed; coverage 85.40% (85% gate).
• Focused SVD/linalg/accounting/cost tests: 729 passed.
• Actual ZMQ client/server integration with a NumPy-free client: 63 passed, including new vector/values/svdvals, cap and batched cases.
• Fast differential parity: 135 passed.
• Ruff lint/format passed; Pyright: 0 errors, 4 preexisting warnings.
• Generated API docs verification, client synchronization, and package-version synchronization passed.

Tests exercise the reported complement and zero-padding routes, rectangular/transposed shapes, small-matrix residual behavior, both values-only entry points, production float/complex multipliers, and rejection before backend execution when the new price exceeds budget.

Cost model, public docstrings/examples, registry notes, generated ops.json and the Unreleased billing-impact notes are updated. Per-command hooks were bypassed to avoid resyncing a shared virtualenv; the direct checks above were executed on this branch. GitHub CI will verify the supported-version matrix.