math.special

Three distinct suites: educational examples on the calculator page, this legacy regression count (58/58 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.

STALE · Build schema 1.10.6 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-07.erf-erfc-stability-iface2. Calculation version 1.10.1. CVP 1.0.0-proposed. 68/68 golden · 8/8 CVP boundary · 10/10 invalid · 1/1 property · 6/6 cross-interface · 1/1 cross-calculator · 6/6 CVP contract. digest 16a87620e73e.

• Golden (oracle-backed) 68 / 68
• CVP boundary 8 / 8
• Invalid input 10 / 10
• Property 1 / 1
• Cross-interface 6 / 6
• Cross-calculator 1 / 1
• 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 all published modes
• Assurance Core

• 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 sha256:1a92dde71760f9232f1a1d7919af0612802bf2119e6804dd9dedf17079b8f596

Input schema sha256:7f068758dc2ba7781b12d2bb43e61014cb5fcf5047f606d48beac349a0a119f3 · Output schema sha256:2b11725c380bb4ce4dfc71c3156009b6eba13f39d9a3cd225704f7aa3c5a42af · 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

special-functions

Engine

special-functions

Engine build

2026-10-06

Evidence core

2026-10-06T23:25:07.890Z

Rendered

2026-10-06T23:25:43.435Z

Last reviewed

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Assumptions

• Known numerical limitation: Bessel J/Y/K series can produce severe errors at large arguments inside the accepted domain; the 1.10.1 erf/erfc correction does not fix those modes.
• Real argument
• Gamma poles at non-positive integers
• lgamma is real for x > 0
• Bessel J integer n=0…8, |x|≤80
• Bessel Y integer n=0…8, x>0
• Bessel I integer n=0…8, |x|≤80
• Bessel K integer n=0…8, x>0
• Lambert W_0 for x ≥ −1/e
• Lambert W_{-1} for −1/e ≤ x < 0
• Complete Euler B(x,y) for x>0, y>0
• Incomplete B_x(a,b) for a>0, b>0, 0≤x≤1
• Unnormalized sinc(x)=sin(x)/x, sinc(0)=1
• Normalized sinc(x)=sin(πx)/(πx), sinc(0)=1
• The Result Card includes an engine-linked Live graph for erf, erfc, Γ, ln Γ, J_n / Y_n / I_n / K_n, W₀ / W₋₁, B(x, y) vs x (y held), incomplete B_x on [0, 1], sinc, and normalized sinc. Same special-functions engine as REST/MCP. Integer n! stays on /factorial. Not CAS.

Limitations

• Real argument only
• Not factorial — integer n! stays on math.factorial
• Gamma poles at non-positive integers
• lgamma is real for x > 0 on this seed
• Bessel J / Y / I / K integer n=0…8, |x|≤80 for J and I, x>0 for Y and K
• Lambert W_0 for x ≥ −1/e; W_{-1} for −1/e ≤ x < 0
• Complete Euler B(x,y) for x>0, y>0; incomplete B_x(a,b) for a>0, b>0, 0≤x≤1
• Unnormalized sinc(x)=sin(x)/x and normalized sinc(x)=sin(πx)/(πx), both with sinc(0)=1
• unknown mode (including cas, factorial) → INVALID_MODE