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 1.0.8 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 2026-10-13.growth-range-node22. Calculation version 1.0.8. CVP 1.0.0-proposed. 25/25 golden · 6/6 CVP boundary · 10/10 invalid · 3/3 property · 1/1 metamorphic · 3/3 round-trip · 13/13 O3 · 21/21 cross-interface · 4/4 URL→result→graph · 29/29 CVP contract. digest 204be80f9a80.

• Golden (oracle-backed) 25 / 25
• 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 21 / 21
• URL → result → graph 4 / 4
• CVP contract 29 / 29
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 21/21. 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 sha256:2c8dc99f1c6df7834ee885960fbc4ff30cb6aeec4aa94dca9121e0723957ab45

Input schema sha256:0deb990c7aa4333ba2eadc0828480ac0ead69f1cbcb75bdc5d3b1a7e49831f87 · Output schema sha256:ea35734c54417fc660e43c871c9049d02fa4059792cb3109aef99a631754901b · 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

2026-10-13

Evidence core

2026-10-13T06:17:35.580Z

Rendered

2026-10-13T06:26:15.518Z

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 model requires r > −100% → RATE_MUST_BE_GT_MINUS_100
• Non-finite inputs → INVALID_NUMBER