physics.fluid.critical_slope

Three distinct suites: educational examples on the calculator page, this legacy regression count (7/7 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-28.meta-metrics-v2. Calculation version 1.0.0. CVP 1.0.0-proposed. 5/5 golden · 1/1 CVP boundary · 2/2 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract. digest df65cf24dcf3. O2: rectangular Sc at yn=yc from SI Manning vs a separate-module identity (≤2 ULP). Not normal-depth yn from given S, not trapezoid, not Manning A,R, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated critical-slope vectors. Not yn from given S, not trapezoid, and not Manning A,R.

• Golden (oracle-backed) 5 / 5
• CVP boundary 1 / 1
• Invalid input 2 / 2
• Property 1 / 1
• Metamorphic 1 / 1
• O3 high-precision 8 / 8
• Cross-interface 2 / 2
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
• Verified scope Rectangular Sc at yn=yc from SI Manning; + O3 mpmath tabulated Sc.
• Assurance Engineering
• Deferred Not yn from given S, not trapezoid, not Manning A,R, not Chezy, and not Q=Av.

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:bc9a288576771706814724bcd8a2b1fac2ac806f56efcf6eef1b5c6303a20fc4

Input schema sha256:bee92c1340983c10f27f9c26074189b5114bd975d4239a68133acbf4cd8a6e54 · Output schema sha256:36cce11023a310bc4ca0d3e3bba85cad8e58b9e240728139dd5d9e60000b873a · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

critical-slope

Engine

critical-slope

Engine build

2026-09-24

Evidence core

2026-09-24T02:12:38.088Z

Rendered

2026-11-10T05:18:41.983Z

Last reviewed

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Assumptions

• Rectangular yn=yc: Sc=[n Q/(A R^{2/3})]^2 at yc=(q²/g)^{1/3}; A=b yc; R=b yc/(b+2 yc); SI k=1; Sc is unknown in slope mode
• yc/b∈[0.2, 10]; n∈[0.008, 0.15]; Sc∈[1e-6, 0.1]; geometry is b, not A and R; default g=9.80665
• Not Manning Q with given A,R,S; not normal-depth yn invert; not critical-depth yc as the product; not Chezy C; not Q=Av; not trapezoid z

Limitations

• Rectangular critical slope: Sc such that yn=yc; SI Manning at y=yc; yc=(q²/g)^{1/3}; Sc=[n Q/(A R^{2/3})]^2 with A=b yc, R=b yc/(b+2 yc)
• yc/b∈[0.2, 10] so Sc(yc) is one-to-one; n∈[0.008, 0.15]; Sc∈[1e-6, 0.1]; SI k=1; default g=9.80665
• Not Manning Q from A,R,S; not normal-depth yn invert; not critical-depth yc as the product; not Chezy C; not Q=Av; not US k=1.486; not trapezoid z