{ "capability_id": "math.percent_change", "tool_id": "percent-change", "engine": "percent-change", "calculation_version": "1.1.1", "generated_at": "2026-10-22T08:54:35.069Z", "engine_build": "2026-10-22", "test_count": 8, "passed": 8, "failed": 0, "tests_summary": { "golden": { "passed": 6, "total": 6 }, "boundary": { "passed": 2, "total": 2 }, "property": { "passed": 0, "total": 0 } }, "engine_tested": true, "expert_reviewed": false, "internally_reviewed": false, "review_kind": null, "source_checked": true, "reviewed_by": null, "reviewer_role": null, "last_reviewed": null, "expert_review": { "status": "optional_not_performed", "reviewer": null, "scope": [ "formula", "input semantics", "assumptions", "limitations", "sources", "tests" ], "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance." }, "internal_review": { "status": "not_applicable", "reviewer": null }, "page": "https://www.calculatorx.com/calc/math/percentage-change", "api": "https://www.calculatorx.com/api/v1/calc/percent-change", "schema_input": "https://www.calculatorx.com/schemas/math.percent_change.input.json", "schema_output": "https://www.calculatorx.com/schemas/math.percent_change.output.json", "assumptions": [ "Interactive evaluation runs locally in the browser. Shared URLs and REST evaluate the same versioned engine (query SSR).", "CVP interface evidence is UI (SSR) query-result HTML, REST, and MCP (MCP reuses the calc API handler). That is interface-result consistency, not a live browser session, cache switching, or end-to-end UI test.", "Signed-change convention: denominator is |V₁|, so a move from −100 to −50 is a +50% increase. Some definitions use V₁ without absolute value or restrict to positive baselines.", "Two active fields normally determine the output. Explicit solve_for selects the output. Choose Check all3 to enter all three and check consistency. Shared URLs and machine inputs with all three also check consistency before solving.", "Solving for V₁ is not always unique. The engine returns both valid initials when they exist." ], "limitations": [ "Signed change uses |v1|; nonzero initial value required. Inverse preserves both signed branches or infinite/no-solution outcomes.", "Exact rational expressions of normalized binary64 inputs, one ties-even rounding per published field; not exact decimal measurement arithmetic.", "Reject nonzero underflow/overflow in inputs, secondary fields or valid candidate branches; no partial candidate set. Rescale. Near±100 inverse percentages are ill-conditioned.", "8ULP same-sign nonzero triple consistency, strict zero; preserve requested percent when solving final even if final rounds unchanged." ], "boundary_conditions": [ "V₁ = 0 → INITIAL_VALUE_ZERO (percent change undefined)", "Fewer than two inputs → MISSING_REQUIRED_INPUT", "Invalid solve_for → INVALID_SOLVE_FOR", "Positive-initial reverse branch: 1 + P/100 = 0 (P = −100%) is omitted", "Negative-initial reverse branch: 1 − P/100 = 0 (P = +100%) is omitted", "Solve V₁ may have 0, 1, or 2 solutions", "V₂ = 0, P = −100%, solve V₁ → INFINITELY_MANY (any V₁ > 0)", "V₂ = 0, P = +100%, solve V₁ → INFINITELY_MANY (any V₁ < 0)", "V₂ = 0 and P ≠ ±100%, solve V₁ → NO_REAL_SOLUTION", "All three values not matching within 8 ULP (same-sign nonzero; strict zero) → status inconsistent, code INCONSISTENT_INPUTS" ], "sources": [ { "title": "Curran-Everett — Explorations in statistics: the analysis of change", "section": "Relative change as (final − initial) / initial", "url": "https://journals.physiology.org/doi/full/10.1152/advan.00018.2015", "supports": "Documents a relative-change definition that divides directly by the initial value rather than |initial|. Negative-baseline percentage change is therefore not a single universal convention.", "kind": "reference", "accessed": "2026-08-28" }, { "title": "CalculatorX signed-change convention", "section": "|V₁| denominator, piecewise inverse, and multiple V₁ solutions", "supports": "% change = (V₂−V₁)/|V₁|×100% (undefined at V₁ = 0). Inverse: V₂ = V₁(1+P/100) if V₁>0 and V₁(1−P/100) if V₁<0. Solving V₁ publishes both signed branches, INFINITELY_MANY at V₂=0 with P=±100%, and NO_REAL_SOLUTION when no branch is valid.", "kind": "definition" }, { "title": "NIST — SI Unit Rules and Style Conventions", "section": "Percent and fractions", "url": "https://physics.nist.gov/cuu/Units/checklist.html", "supports": "The symbol % represents the number 0.01. Thus p% = p/100 and a part of p% of base b equals b×p/100; inverse percentage equations are algebraic rearrangements. CalculatorX’s negative-baseline signed-change convention is separately specified, not attributed to NIST. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.", "kind": "reference", "publisher": "National Institute of Standards and Technology" } ], "methods": [], "fingerprint": "sha256:554dc7588111216564ee2b53e5d72d2798bcb0124ebd3fb6a797ade2c5a9f165", "tier": "engine_tested", "verification": { "tests": { "passed": 8, "total": 8, "golden": 6, "boundary": 2, "property": 0 }, "contract_checks": { "passed": 6, "total": 6 } }, "evidence_core_generated_at": "2026-10-22T01:11:44.702Z", "rendered_at": "2026-10-22T08:54:35.069Z", "release_integrity": { "status": "verified", "scope": "workspace", "production_attestation_required": true, "calculation_version": "1.1.1", "artifacts": { "engine": "1.1.1", "page": "1.1.1", "capability": "1.1.1", "evidence": "1.1.1", "input_schema": "1.1.1", "output_schema": "1.1.1", "mcp_contract": "1.1.1" }, "digests": { "input_schema_sha256": "f79b06c286ee7e4fc44ee2ffc438f5f196fe0916dd8500e05340a65c5b1aef9a", "output_schema_sha256": "3bfdc00173d02aaf9da8bd155d8633952ed38f7d7a67f2a9fa18fca67ac8ef7c", "evidence_sha256": "49ea8926cfdda9d9192c3eb699cbb64bcf055e5b2f8177040324e6cd19f08ee1", "evidence_core_sha256": "49ea8926cfdda9d9192c3eb699cbb64bcf055e5b2f8177040324e6cd19f08ee1", "capability_sha256": "081c2c0ef1ea3e35a1ab572d611bebcc2ca39790862bd3b89b4d46ced84c5151", "engine_sha256": "a664ae25cd2134de7de43a99352933043215473589aec38c9416508150cb1008", "mcp_contract_sha256": "a1a8617719bef45391ee6917dc1783a01de2eedf297e7596b3cb5017cd0e1560" }, "contract_checks": { "total": 6, "passed": 6, "failed": 0, "items": [ { "id": "release-artifacts-aligned", "status": "pass", "detail": "1.1.1" }, { "id": "schema-output-required-declared", "status": "pass" }, { "id": "schema-valid-input-executes", "status": "pass" }, { "id": "engine-success-output-validates-schema", "status": "pass" }, { "id": "schema-rejects-incomplete-input", "status": "pass" }, { "id": "rest-success-payload-validates-schema", "status": "pass" } ] }, "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json" }, "tests": [], "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }