math.exponential_growth

Three distinct suites: educational examples on the calculator page, this legacy regression count (20/20 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 1.0.10 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 2026-10-28.meta-metrics-v2. Calculation version 1.0.10. CVP 1.0.0-proposed. 69/69 golden · 6/6 CVP boundary · 10/10 invalid · 3/3 property · 1/1 metamorphic · 3/3 round-trip · 13/13 O3 · 65/65 cross-interface · 4/4 URL→result→graph · 29/29 CVP contract. digest 3c510e301f33. Listed independent reference vectors only; no whole-domain/runtime guarantee.

• Golden (oracle-backed) 69 / 69
• CVP boundary 6 / 6
• Invalid input 10 / 10
• Property 3 / 3
• Metamorphic 1 / 1
• Round-trip 3 / 3
• O3 high-precision 13 / 13
• Cross-interface 65 / 65
• URL → result → graph 4 / 4
• CVP contract 29 / 29
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 65/65. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session.
• Assurance Engineering

• 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
• input schema declares xt PASS
• input schema accepts inverse time PASS
• input schema accepts verify PASS
• input schema rejects two fields PASS
• output schema defines consistency PASS
• input schema forward PASS
• rest forward output schema PASS
• rest forward consistency PASS
• input schema forward continuous PASS
• rest forward continuous output schema PASS
• rest forward continuous consistency PASS
• input schema inverse time PASS
• rest inverse time output schema PASS
• rest inverse time consistency PASS
• input schema inverse x0 PASS
• rest inverse x0 output schema PASS
• rest inverse x0 consistency PASS
• input schema inverse rate PASS
• rest inverse rate output schema PASS
• rest inverse rate consistency PASS
• input schema verify PASS
• rest verify output schema PASS
• rest verify consistency PASS
• rest success payload validates schema PASS

Fingerprint sha256:68947c81a7e1e01ead66fea13c45ac50d22f17a830a8bb2bc160e954bffeb57d

Input schema sha256:13a1effa428dd818fc8ef364cfff535cb4df0c12eb408082956e6754db077e94 · Output schema sha256:385313ac973965b21ef22040ca11ef747adfce7b6f7f5fce800529c78abfd27e · 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

exponential-growth

Engine

exponential-growth

Engine build

2026-10-27

Evidence core

2026-10-27T05:26:03.915Z

Rendered

2026-10-28T03:01:57.886Z

Last reviewed

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Assumptions

• Constant rate over the interval (real populations often need logistic models long-term).
• CalculatorX defines the periodic model domain as r > −100% so the growth factor stays positive and inverse/logarithmic solving remains well-defined.

Limitations

• Periodic x(t)=x0(1+r/100)^t requires r>-100%; continuous x(t)=x0 exp(k t) uses ratePct=k per time unit, not percent. Signed amplitudes allowed; inverse time/rate require matching nonzero signs.
• Provide any three fields or four to compare calculated xt using display quantization. Zero rate/time can make inverses undefined or nonunique. Blank/null fields are missing.
• Strict decimal/scientific text up to512 characters; nonzero input rounding tozero rejects NUMERIC_UNDERFLOW. Conflicting aliases/unknown fields/models reject. Output is finite unrounded binary64; overflow/underflow reject.
• Independent Decimal1200/1600 fixed vectors use predeclared4e-12 relative budget plus2 subnormal quanta, strictzero/sign/type. Legacy O3 remains separately tested32ULP. No whole-domain or cross-runtime guarantee; inverse conditioning degrades at zero rate/time and amplitude ratios near1.
• Typing local; shared URLs, REST and MCP transmit inputs and may enter logs. Native exports retain scalar and provided raw inputs.