{ "protocol": { "name": "CVP", "version": "1.0.0-proposed", "revision": "2026-09-13", "spec_sha256": "f62725968356c92930531cd6085db76e216da06e95be53d636b0d2cf3218b148", "spec": "https://www.calculatorx.com/developers/cvp/spec/1.0" }, "document_status": "proposed", "calculator": { "id": "scientific-notation", "version": "1.1.1", "title": "Scientific Notation Calculator", "formula_family": "scientific_notation", "capability_id": "math.scientific_notation", "verification_revision": "2026-09-16.sources-no-wolfram" }, "profile": "core", "verified_scope": "all published modes", "status": "VERIFIED", "verification_status": "VERIFIED", "production_freshness": "CURRENT", "overall_trust": "VERIFIED", "runner": { "name": "cvp-runner", "version": "1.0.0" }, "environment": { "runtime": "node", "runtime_version": "20.19.2", "numeric_model": "IEEE-754 binary64", "os": "darwin" }, "suite": { "id": "scientific-notation", "version": "1.1.1", "uri": "https://www.calculatorx.com/evidence/math.scientific_notation/1.1.1.json", "verification_revision": "2026-09-16.sources-no-wolfram" }, "obligation_set": [ "CVP-PROV-01", "CVP-MODEL-01", "CVP-SCOPE-01", "CVP-UNIT-01", "CVP-REF-01", "CVP-GOLD-01", "CVP-BND-01", "CVP-INV-01", "CVP-NUM-01", "CVP-COV-01", "CVP-CONTRACT-01", "CVP-DEP-01", "CVP-ART-01", "CVP-PROD-01", "CVP-PROP-01", "CVP-META-01", "CVP-ROUND-01", "CVP-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "OpenStax Elementary Algebra 2e — Scientific Notation", "kind": "other", "reference": "5.2 An application of exponents: scientific notation", "url": "https://openstax.org/books/elementary-algebra-2e/pages/5-2-an-application-of-exponents-scientific-notation" }, { "label": "BIPM SI Brochure (9th edition)", "kind": "standard", "reference": "Table 8 — SI prefixes (powers of 10³)", "url": "https://www.bipm.org/en/publications/si-brochure" }, { "label": "NIST SI prefixes", "kind": "standard", "reference": "SI prefixes from 10⁻³⁰ to 10³⁰", "url": "https://www.nist.gov/pml/owm/metric-si-prefixes" } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Scientific / engineering notation and scientific arithmetic" }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module scientific-notation oracle — convert / normalize / engineering / operate", "engine": { "name": "scientific-notation-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "O2 backs convert coefficient ≤2 ULP and operate reconstructed-value ≤2 ULP vs IUT", "engine": { "name": "scientific-notation-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } } ], "notes": "Golden expected values use a separate O2 module (not IUT transcription). O2 shares Node/V8 binary64 with the IUT (same_runtime_as_iut). Convert/normalize/engineering: ≤2 ULP on the scientific (or engineering) coefficient, exact exponent. Operate uses a distinct reconstructed-value ≤2 ULP claim plus exact normalized exponent." }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "x = A × 10ⁿ, 1 ≤ |A| < 10 except 0; engineering n ≡ 0 (mod 3); operate ±×÷ then normalize" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "Declared CVP coverage is all four published modes (convert, normalize, engineering, operate) plus invalid-domain. Page published examples and IUT engine automated checks are separate suites." }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O2 expected_values/numerical_behavior (same_runtime_as_iut). Operate uses reconstructed-value ULP, not convert coefficient-ULP." }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "4/4 legacy golden; 21/21 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "1/1 CVP boundary · 2/2 legacy Evidence boundary" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "2 Evidence illegal-input + 5/5 oracle-backed error-code (exact_error_match, not ULP)" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "Convert/normalize/engineering: ≤2 ULP coefficient, exact exponent. Operate: ≤2 ULP reconstructed binary64 + exact normalized exponent. Not a whole-domain guarantee beyond recorded vectors." }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "5/5 declared partitions (convert, normalize, engineering, operate, invalid-domain) · 4 legacy golden / 1 CVP boundary unique cases · 2 Evidence invalid-input (may overlap boundary)" }, "CVP-CONTRACT-01": { "result": "PASS", "applicability": "required", "notes": "3/3 CVP contract" }, "CVP-DEP-01": { "result": "PASS", "applicability": "required", "notes": "engine scientific-notation; IEEE-754 binary64 (IUT/O2 share Node/V8)" }, "CVP-ART-01": { "result": "PASS", "applicability": "required", "notes": "release_integrity.status=verified · digests: artifact_evidence_sha256=Evidence core (Trust freshness) · cvp_evidence_digest=artifacts.evidence_digest (fingerprint v2) · evidence_bundle_sha256=legacy Evidence JSON bytes · evidence_catalog_digest=attested_catalog_sha256 · production_sha256=bound production report · see artifacts.digest_registry" }, "CVP-PROD-01": { "result": "PASS", "applicability": "required", "notes": "this calculator CURRENT · bound snapshot pass @ 2026-09-16T06:43:50.908Z · live site-wide report stale @ 2026-09-16T06:44:05.108Z (2 other capabilities) · local checks pass · attestation_id=9864b02dd59e627629179439ae27934aea8c6fd24193702e66c56019c5e3e050 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-09-16T06:43:50.908Z · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-16T06:44:05.108Z · Public schema 1.1.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.1.1 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · cvp-latest-alias-agrees=pass · cvp-immutable-manifest-fetch=pass · cvp-immutable-manifest-sha256=pass · cvp-latest-alias-matches-immutable=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=31e075dd2788e7c13520557df716a4e118f4844aca3908f8b06acf4a41fad0cc · verified_at=2026-09-16T06:43:14.861Z · evidence_attested_at=2026-09-16T06:43:14.861Z · last_confirmed_current_at=2026-09-16T06:43:50.908Z · rendered_at=2026-09-16T06:44:05.151Z · binds=cvp_core_sha256", "check_result": "PASS", "production_state": "CURRENT", "binding_current": true }, "CVP-DIM-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "Unitless core calculator — no physical dimension algebra" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "5/5 property" }, "CVP-META-01": { "result": "PASS", "applicability": "applicable", "notes": "2/2 metamorphic" }, "CVP-ROUND-01": { "result": "PASS", "applicability": "applicable", "notes": "2/2 round-trips" }, "CVP-XCAL-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "No related calculator in the same formula family / no related-identity peers declared — control not in obligation set" }, "CVP-IFACE-01": { "result": "PASS", "applicability": "applicable", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session." }, "CVP-ORACLE-01": { "result": "SKIP", "applicability": "higher_assurance", "notes": "O2 present; O3 not required this wave" }, "CVP-EXP-01": { "result": "SKIP", "applicability": "optional", "notes": "named expert review not performed" } }, "tests": { "golden": { "passed": 21, "total": 21, "failed": 0, "case_ids": [ "g-convert-4.2e-4", "g-convert-decimal", "g-convert-unicode", "g-convert-zero", "g-convert-12300", "g-convert-near10", "g-convert-over10", "g-convert-1e308", "g-convert-1e-308", "g-convert-subnormal", "g-norm-32e4", "g-norm-10e0", "g-norm-zero", "g-eng-1.234e8", "g-eng-1e-3", "g-eng-999", "g-eng-4.2e-4", "g-op-mul", "g-op-div", "g-op-add", "g-op-sub" ] }, "boundary": { "passed": 1, "total": 1, "failed": 0, "case_ids": [ "missing-value" ] }, "invalid": { "passed": 7, "total": 7, "failed": 0, "case_ids": [ "bad-mode", "missing-value", "g-inv-div0", "g-inv-overflow", "g-inv-underflow", "g-inv-missing", "g-inv-bad-mode" ], "comparison": "exact_error_match", "records": [ { "id": "g-inv-div0", "comparison": "exact_error_match", "expected": { "code": "DIVISION_BY_ZERO" }, "actual": { "code": "DIVISION_BY_ZERO" }, "match": true }, { "id": "g-inv-overflow", "comparison": "exact_error_match", "expected": { "code": "RESULT_OVERFLOW" }, "actual": { "code": "RESULT_OVERFLOW" }, "match": true }, { "id": "g-inv-underflow", "comparison": "exact_error_match", "expected": { "code": "RESULT_UNDERFLOW" }, "actual": { "code": "RESULT_UNDERFLOW" }, "match": true }, { "id": "g-inv-missing", "comparison": "exact_error_match", "expected": { "code": "MISSING_REQUIRED_INPUT" }, "actual": { "code": "MISSING_REQUIRED_INPUT" }, "match": true }, { "id": "g-inv-bad-mode", "comparison": "exact_error_match", "expected": { "code": "INVALID_MODE" }, "actual": { "code": "INVALID_MODE" }, "match": true } ] }, "property": { "passed": 5, "total": 5, "failed": 0, "case_ids": [ "prop-convert-range", "prop-zero", "prop-eng-mod3", "prop-norm-range", "prop-operate-range" ], "definition_ids": [ "normalized-coef", "zero-is-zero", "engineering-mod-3", "normalize-canonical", "operate-normalized" ] }, "round_trip": { "passed": 2, "total": 2, "failed": 0, "case_ids": [ "rt-convert-sci-dec", "rt-convert-4.2e-4" ] }, "metamorphic": { "passed": 2, "total": 2, "failed": 0, "case_ids": [ "meta-times-ten", "meta-operate-mul-ten" ], "definition_ids": [ "scale-10", "operate-scale-10" ] }, "contract": { "passed": 3, "total": 3, "failed": 0 }, "cross_interface": { "passed": 4, "total": 4, "failed": 0, "case_ids": [ "iface-convert", "iface-normalize", "iface-engineering", "iface-operate" ] } }, "coverage": { "partitions": [ { "id": "convert", "description": "Decimal / E / Unicode → scientific", "exercised": true, "case_count": 15 }, { "id": "normalize", "description": "Non-canonical A, exponent cross-10, zero", "exercised": true, "case_count": 4 }, { "id": "engineering", "description": "± exponents, n ≡ 0 (mod 3), SI hint", "exercised": true, "case_count": 5 }, { "id": "operate", "description": "±×÷, normalize, reconstructed binary64", "exercised": true, "case_count": 6 }, { "id": "invalid-domain", "description": "Illegal input, overflow / underflow, division by zero", "exercised": true, "case_count": 7 } ] }, "numerical": { "representation": "IEEE-754 binary64 scientific normalize", "tolerance": { "type": "ulp", "value": 2, "rationale": "Convert / normalize / engineering: ≤2 ULP on the scientific coefficient; integer exponent must match exactly. Declared a priori.", "declared_before_evaluation": true }, "operate_tolerance": { "type": "ulp", "value": 2, "rationale": "Operate: ≤2 ULP on the reconstructed binary64 of A×10ⁿ after ±×÷, plus exact normalized exponent. This is not the convert coefficient-ULP claim.", "declared_before_evaluation": true }, "claim_scope": "Convert / normalize / engineering: ≤2 ULP on scientific coefficient, exact exponent. Operate: ≤2 ULP on reconstructed binary64 plus exact normalized exponent. Invalid domain: matching error codes (overflow / underflow / division by zero / missing). Not a whole-domain guarantee beyond recorded vectors.", "max_error_observed": 1, "records": [ { "id": "g-convert-4.2e-4", "reference": { "coef": 4.2, "exp": -4, "eng_coef": 420, "eng_exp": -6, "reconstructed": 0.00042, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "4.2 × 10⁻⁴", "scientific": "4.2 × 10⁻⁴", "e_notation": "4.2e-4", "engineering": "420 × 10⁻⁶", "decimal": "0.00042", "order": -4, "si": "micro (µ)", "coef": 4.2, "exp": -4, "eng_coef": 420, "eng_exp": -6, "parsed": 0.00042, "input": "4.2e-4", "inputs_summary": "4.2e-4", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "4.2e-4 · eng 420 × 10⁻⁶ · order −4", "steps": [ "Input: 4.2e-4", "Parsed value: 0.00042", "Scientific: 4.2 × 10⁻⁴ (1 ≤ |A| < 10)", "E-notation: 4.2e-4", "Engineering: 420 × 10⁻⁶ · SI: micro (µ)", "Order of magnitude: −4", "Real / standard: 0.00042", "Decimal shift: move point 4 place(s) right to get 4.2." ], "equivalents": [ [ "Scientific", "4.2 × 10⁻⁴" ], [ "E notation", "4.2e-4" ], [ "Engineering", "420 × 10⁻⁶" ], [ "Decimal", "0.00042" ] ] }, "error_ulp": 0, "threshold_ulp": 2, "fields": { "exp": { "ok": true }, "coef": { "ok": true, "error_ulp": 0 } }, "suite": "golden" }, { "id": "g-convert-decimal", "reference": { "coef": 4.2, "exp": -4, "eng_coef": 420, "eng_exp": -6, "reconstructed": 0.00042, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "4.2 × 10⁻⁴", "scientific": "4.2 × 10⁻⁴", "e_notation": "4.2e-4", "engineering": "420 × 10⁻⁶", "decimal": "0.00042", "order": -4, "si": "micro (µ)", "coef": 4.2, "exp": -4, "eng_coef": 420, "eng_exp": -6, "parsed": 0.00042, "input": "0.00042", "inputs_summary": "0.00042", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "4.2e-4 · eng 420 × 10⁻⁶ · order −4", "steps": [ "Input: 0.00042", "Parsed value: 0.00042", "Scientific: 4.2 × 10⁻⁴ (1 ≤ |A| < 10)", "E-notation: 4.2e-4", "Engineering: 420 × 10⁻⁶ · SI: micro (µ)", "Order of magnitude: −4", "Real / standard: 0.00042", "Decimal shift: move point 4 place(s) right to get 4.2." ], "equivalents": [ [ "Scientific", "4.2 × 10⁻⁴" ], [ "E notation", "4.2e-4" ], [ "Engineering", "420 × 10⁻⁶" ], [ "Decimal", "0.00042" ] ] }, "error_ulp": 0, "threshold_ulp": 2, "fields": { "exp": { "ok": true }, "coef": { "ok": true, "error_ulp": 0 } }, "suite": "golden" }, { "id": "g-convert-unicode", "reference": { "coef": 3.2, "exp": 5, "eng_coef": 320, "eng_exp": 3, "reconstructed": 320000, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "3.2 × 10⁵", "scientific": "3.2 × 10⁵", "e_notation": "3.2e5", "engineering": "320 × 10³", "decimal": "320000", "order": 5, "si": "kilo (k)", "coef": 3.2, "exp": 5, "eng_coef": 320, "eng_exp": 3, "parsed": 320000, "input": "3.2×10⁵", "inputs_summary": "3.2×10⁵", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "3.2e5 · eng 320 × 10³ · order 5", "steps": [ "Input: 3.2×10⁵", "Parsed value: 320000", "Scientific: 3.2 × 10⁵ (1 ≤ |A| < 10)", "E-notation: 3.2e5", "Engineering: 320 × 10³ · SI: kilo (k)", "Order of magnitude: 5", "Real / standard: 320000", "Decimal shift: move point 5 place(s) left to get 3.2." ], "equivalents": [ [ "Scientific", "3.2 × 10⁵" ], [ "E notation", "3.2e5" ], [ "Engineering", "320 × 10³" ], [ "Decimal", "320000" ] ] }, "error_ulp": 0, "threshold_ulp": 2, "fields": { "exp": { "ok": true }, "coef": { "ok": true, "error_ulp": 0 } }, "suite": "golden" }, { "id": "g-convert-zero", "reference": { "coef": 0, "exp": 0, "eng_coef": 0, "eng_exp": 0, "reconstructed": 0, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "0", "scientific": "0", "e_notation": "0e0", "engineering": "0", "decimal": "0", "order": 0, "si": "(unit)", "coef": 0, "exp": 0, "eng_coef": 0, "eng_exp": 0, "parsed": 0, "input": "0", "inputs_summary": "0", "mode_label": "Convert", "formula": "0 → 0", "explainer": "0e0 · eng 0 · order 0", "steps": [ "Input: 0", "Parsed value: 0", "Scientific: 0 (zero is not written as A × 10ⁿ with 1 ≤ |A| < 10)", "E-notation: 0e0", "Engineering: 0 · SI: (unit)", "Order of magnitude: 0", "Real / standard: 0" ], "equivalents": [ [ "Scientific", "0" ], [ "E notation", "0e0" ], [ "Engineering", "0" ], [ "Decimal", "0" ] ] }, "error_ulp": 0, "threshold_ulp": 2, "fields": { "exp": { "ok": true }, "coef": { "ok": true, "error_ulp": 0 } }, "suite": "golden" }, { "id": "g-convert-12300", "reference": { "coef": 1.23, "exp": 4, "eng_coef": 12.3, "eng_exp": 3, "reconstructed": 12300, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "1.23 × 10⁴", "scientific": "1.23 × 10⁴", "e_notation": "1.23e4", "engineering": "12.3 × 10³", "decimal": "12300", "order": 4, "si": "kilo (k)", "coef": 1.23, "exp": 4, "eng_coef": 12.3, "eng_exp": 3, "parsed": 12300, "input": "12300", "inputs_summary": "12300", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "1.23e4 · eng 12.3 × 10³ · order 4", "steps": [ "Input: 12300", "Parsed value: 12300", "Scientific: 1.23 × 10⁴ (1 ≤ |A| < 10)", "E-notation: 1.23e4", "Engineering: 12.3 × 10³ · SI: kilo (k)", "Order of magnitude: 4", "Real / standard: 12300", "Decimal shift: move point 4 place(s) left to get 1.23." ], "equivalents": [ [ "Scientific", "1.23 × 10⁴" ], [ "E notation", "1.23e4" ], [ "Engineering", "12.3 × 10³" ], [ "Decimal", "12300" ] ] }, "error_ulp": 0, "threshold_ulp": 2, "fields": { "exp": { "ok": true }, "coef": { "ok": true, "error_ulp": 0 } }, "suite": "golden" }, { "id": "g-convert-near10", "reference": { "coef": 9.999999999999998, "exp": 0, "eng_coef": 9.999999999999998, "eng_exp": 0, "reconstructed": 9.999999999999998, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "9.999999999999998 × 10⁰", "scientific": "9.999999999999998 × 10⁰", "e_notation": "9.999999999999998e0", "engineering": "9.999999999999998 × 10⁰", "decimal": "10", "order": 0, "si": "(unit)", "coef": 9.999999999999998, "exp": 0, "eng_coef": 9.999999999999998, "eng_exp": 0, "parsed": 9.999999999999998, "input": "9.999999999999998", "inputs_summary": "9.999999999999998", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "9.999999999999998e0 · eng 9.999999999999998 × 10⁰ · order 0", "steps": [ "Input: 9.999999999999998", "Parsed value: 10", "Scientific: 9.999999999999998 × 10⁰ (1 ≤ |A| < 10)", "E-notation: 9.999999999999998e0", "Engineering: 9.999999999999998 × 10⁰ · SI: (unit)", "Order of magnitude: 0", "Real / standard: 10" ], "equivalents": [ [ "Scientific", "9.999999999999998 × 10⁰" ], [ "E notation", "9.999999999999998e0" ], [ "Engineering", "9.999999999999998 × 10⁰" ], [ "Decimal", "10" ] ] }, "error_ulp": 0, "threshold_ulp": 2, "fields": { "exp": { "ok": true }, "coef": { "ok": true, "error_ulp": 0 } }, "suite": "golden" }, { "id": "g-convert-over10", "reference": { "coef": 1.0000000000000002, "exp": 1, "eng_coef": 10.000000000000002, "eng_exp": 0, "reconstructed": 10.000000000000002, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "1 × 10¹", "scientific": "1 × 10¹", "e_notation": "1e1", "engineering": "10 × 10⁰", "decimal": "10", "order": 1, "si": "(unit)", "coef": 1.0000000000000002, "exp": 1, "eng_coef": 10.000000000000002, "eng_exp": 0, "parsed": 10.000000000000002, "input": "10.000000000000002", "inputs_summary": "10.000000000000002", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "1e1 · eng 10 × 10⁰ · order 1", "steps": [ "Input: 10.000000000000002", 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order −4", "steps": [ "Input: 4.2e-4", "Parsed value: 0.00042", "Scientific: 4.2 × 10⁻⁴ (1 ≤ |A| < 10)", "E-notation: 4.2e-4", "Engineering: 420 × 10⁻⁶ · SI: micro (µ)", "Order of magnitude: −4", "Real / standard: 0.00042", "Decimal shift: move point 4 place(s) right to get 4.2." ], "equivalents": [ [ "Scientific", "4.2 × 10⁻⁴" ], [ "E notation", "4.2e-4" ], [ "Engineering", "420 × 10⁻⁶" ], [ "Decimal", "0.00042" ] ] }, "error_ulp": 1, "threshold_ulp": 2, "suite": "round-trip", "hops": { "forward": { "reference": { "coef": 4.2, "exp": -4, "eng_coef": 420, "eng_exp": -6, "reconstructed": 0.00042, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "4.2 × 10⁻⁴", "scientific": "4.2 × 10⁻⁴", "e_notation": "4.2e-4", "engineering": "420 × 10⁻⁶", "decimal": "0.00042", "order": -4, "si": "micro (µ)", "coef": 4.2, "exp": -4, "eng_coef": 420, "eng_exp": -6, "parsed": 0.00042, "input": "4.2e-4", "inputs_summary": "4.2e-4", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "4.2e-4 · eng 420 × 10⁻⁶ · order −4", "steps": [ "Input: 4.2e-4", "Parsed value: 0.00042", "Scientific: 4.2 × 10⁻⁴ (1 ≤ |A| < 10)", "E-notation: 4.2e-4", "Engineering: 420 × 10⁻⁶ · SI: micro (µ)", "Order of magnitude: −4", "Real / standard: 0.00042", "Decimal shift: move point 4 place(s) right to get 4.2." ], "equivalents": [ [ "Scientific", "4.2 × 10⁻⁴" ], [ "E notation", "4.2e-4" ], [ "Engineering", "420 × 10⁻⁶" ], [ "Decimal", "0.00042" ] ] }, "error_ulp": 0 }, "reverse": { "reference": 0.00042, "actual": 0.00041999999999999996, "error_ulp": 1 } } }, { "id": "meta-times-ten", "reference": 1, "actual": 1, "error_ulp": 0, "threshold_ulp": 2, "suite": "metamorphic", "hops": { "base": { "reference": { "coef": 1.23, "exp": 4, "eng_coef": 12.3, "eng_exp": 3, "reconstructed": 12300, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "1.23 × 10⁴", "scientific": "1.23 × 10⁴", "e_notation": "1.23e4", "engineering": "12.3 × 10³", "decimal": "12300", "order": 4, "si": "kilo (k)", "coef": 1.23, "exp": 4, "eng_coef": 12.3, "eng_exp": 3, "parsed": 12300, "input": "12300", "inputs_summary": "12300", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "1.23e4 · eng 12.3 × 10³ · order 4", "steps": [ "Input: 12300", "Parsed value: 12300", "Scientific: 1.23 × 10⁴ (1 ≤ |A| < 10)", "E-notation: 1.23e4", "Engineering: 12.3 × 10³ · SI: kilo (k)", "Order of magnitude: 4", "Real / standard: 12300", "Decimal shift: move point 4 place(s) left to get 1.23." ], "equivalents": [ [ "Scientific", "1.23 × 10⁴" ], [ "E notation", "1.23e4" ], [ "Engineering", "12.3 × 10³" ], [ "Decimal", "12300" ] ] }, "error_ulp": 0 }, "follow": { "reference": { "coef": 1.23, "exp": 5, "eng_coef": 123, "eng_exp": 3, "reconstructed": 123000, "mode": "convert" }, "actual": { "mode": "convert", "calculation_version": "1.1.1", "heading": "Scientific notation", "value": "1.23 × 10⁵", "scientific": "1.23 × 10⁵", "e_notation": "1.23e5", "engineering": "123 × 10³", "decimal": "123000", "order": 5, "si": "kilo (k)", "coef": 1.23, "exp": 5, "eng_coef": 123, "eng_exp": 3, "parsed": 123000, "input": "123000", "inputs_summary": "123000", "mode_label": "Convert", "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0", "explainer": "1.23e5 · eng 123 × 10³ · order 5", "steps": [ "Input: 123000", "Parsed value: 123000", "Scientific: 1.23 × 10⁵ (1 ≤ |A| < 10)", "E-notation: 1.23e5", "Engineering: 123 × 10³ · SI: kilo (k)", "Order of magnitude: 5", "Real / standard: 123000", "Decimal shift: move point 5 place(s) left to get 1.23." ], "equivalents": [ [ "Scientific", "1.23 × 10⁵" ], [ "E notation", "1.23e5" ], [ "Engineering", "123 × 10³" ], [ "Decimal", "123000" ] ] }, "error_ulp": 0 }, "relation": { "reference": 1, "actual": 1, "error_ulp": 0 } } }, { "id": "meta-operate-mul-ten", "reference": 1, "actual": 1, "error_ulp": 0, "threshold_ulp": 2, "suite": "metamorphic", "hops": { "base": { "reference": { "coef": 6, "exp": 10, "eng_coef": 60, "eng_exp": 9, "reconstructed": 60000000000, "mode": "operate", "op": "mul" }, "actual": { "mode": "operate", "calculation_version": "1.1.1", "heading": "X × Y", "value": "6 × 10¹⁰", "scientific": "6 × 10¹⁰", "e_notation": "6e10", "engineering": "60 × 10⁹", "decimal": "60000000000", "order": 10, "coef": 6, "exp": 10, "eng_coef": 60, "eng_exp": 9, "parsed": 60000000000, "op": "mul", "inputs_summary": "3e4 × 2e6", "mode_label": "Operate", "formula": "(A×10ᵐ)(B×10ⁿ) = (A·B)×10^(m+n)", "explainer": "6e10 · real 60000000000", "steps": [ "X = 3 × 10⁴ = 3e4", "Y = 2 × 10⁶ = 2e6", "Multiply coefficients: 3 × 2 = 6", "Add exponents: 4 + 6 = 10", "Normalize → 6 × 10¹⁰", "E-notation: 6e10", "Engineering: 60 × 10⁹ (giga (G))" ], "equivalents": [ [ "Scientific", "6 × 10¹⁰" ], [ "E notation", "6e10" ], [ "Engineering", "60 × 10⁹" ], [ "Decimal", "60000000000" ] ] }, "error_ulp": 0 }, "follow": { "reference": { "coef": 6, "exp": 11, "eng_coef": 600, "eng_exp": 9, "reconstructed": 600000000000, "mode": "operate", "op": "mul" }, "actual": { "mode": "operate", "calculation_version": "1.1.1", "heading": "X × Y", "value": "6 × 10¹¹", "scientific": "6 × 10¹¹", "e_notation": "6e11", "engineering": "600 × 10⁹", "decimal": "600000000000", "order": 11, "coef": 6, "exp": 11, "eng_coef": 600, "eng_exp": 9, "parsed": 600000000000, "op": "mul", "inputs_summary": "3e4 × 2e7", "mode_label": "Operate", "formula": "(A×10ᵐ)(B×10ⁿ) = (A·B)×10^(m+n)", "explainer": "6e11 · real 600000000000", "steps": [ "X = 3 × 10⁴ = 3e4", "Y = 2 × 10⁷ = 2e7", "Multiply coefficients: 3 × 2 = 6", "Add exponents: 4 + 7 = 11", "Normalize → 6 × 10¹¹", "E-notation: 6e11", "Engineering: 600 × 10⁹ (giga (G))" ], "equivalents": [ [ "Scientific", "6 × 10¹¹" ], [ "E notation", "6e11" ], [ "Engineering", "600 × 10⁹" ], [ "Decimal", "600000000000" ] ] }, "error_ulp": 0 }, "relation": { "reference": 1, "actual": 1, "error_ulp": 0 } } } ] }, "interfaces": { "compared": [ "ui-ssr", "rest", "mcp" ], "result": "PASS", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session." }, "artifacts": { "evidence_bundle_sha256": "895b6715a7c21e9aeeab8dccf3610c0ab6d2814571c86d7bef3c901e5264f2ae", "evidence_digest": "4a53cbc5afe21e9c0e6533f04cffe5630b2889d038101056e026b031bb1cf651", "production_sha256": "31e075dd2788e7c13520557df716a4e118f4844aca3908f8b06acf4a41fad0cc", "attested_catalog_sha256": "f89399c8dda78af9b2d784bf34d77b786cf749392d54e5e00bd3707c3fcdd13e", "production_checks": [ { "id": "math.scientific_notation:output-const", "status": "pass", "detail": "output const 1.1.1 vs capability 1.1.1", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z" }, { "id": "math.scientific_notation:evidence-sha256", "status": "pass", "detail": "f8ddc450cf49", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z" }, { "id": "math.scientific_notation:semantic-contract", "status": "pass", "detail": "6/6", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z" }, { "id": "math.scientific_notation:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.1.1 vs origin 1.1.1", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z" }, { "id": "math.scientific_notation:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.scientific_notation/1.1.1/2026-09-16.sources-no-wolfram/core/4a53cbc5afe2", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z", "projection_compared": false }, { "id": "math.scientific_notation:cvp-latest-alias-agrees", "status": "pass", "detail": "math.scientific_notation/1.1.1/2026-09-16.sources-no-wolfram/core/4a53cbc5afe2", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z", "projection_compared": false }, { "id": "math.scientific_notation:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z" }, { "id": "math.scientific_notation:cvp-immutable-manifest-sha256", "status": "pass", "detail": "4a53cbc5afe2", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z" }, { "id": "math.scientific_notation:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.scientific_notation/1.1.1/2026-09-16.sources-no-wolfram/core/4a53cbc5afe2", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z", "projection_compared": false }, { "id": "math.scientific_notation:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z" }, { "id": "math.scientific_notation:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-16T06:43:14.861Z" } ], "digest_registry": { "digest_algorithm": "sha256", "canonicalization": "json-sorted-keys-utf8", "entries": [ { "name": "cvp_core_sha256", "field": "artifacts.cvp_core_sha256", "digest_scope": "cvp_verification_fingerprint_v2", "value": "4a53cbc5afe21e9c0e6533f04cffe5630b2889d038101056e026b031bb1cf651", "note": "Immutable verification core; excludes attestation/live-status and Evidence contract counts" }, { "name": "cvp_evidence_digest", "field": "artifacts.evidence_digest", "digest_scope": "cvp_verification_fingerprint_v2", "value": "4a53cbc5afe21e9c0e6533f04cffe5630b2889d038101056e026b031bb1cf651", "note": "Alias of cvp_core_sha256 (historical field name)" }, { "name": "artifact_evidence_sha256", "field": "release_integrity.digests.evidence_core_sha256", "digest_scope": "evidence_artifact_core", "value": "f8ddc450cf499d7311cc29afa5cf7deebc14a243b17fd3d9b3bdff0b394b1e28", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "f89399c8dda78af9b2d784bf34d77b786cf749392d54e5e00bd3707c3fcdd13e", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "4a53cbc5afe21e9c0e6533f04cffe5630b2889d038101056e026b031bb1cf651" }, "dependencies": [ { "name": "scientific-notation-engine", "version": "1.1.1" }, { "name": "scientific-notation-reference-oracle", "version": "1.0.0" }, { "name": "node", "version": "20.19.2" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "9864b02dd59e627629179439ae27934aea8c6fd24193702e66c56019c5e3e050", "attested_at": "2026-09-16T06:43:14.861Z", "last_confirmed_current_at": "2026-09-16T06:43:50.908Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-09-16T06:43:50.908Z", "live_updated_at": "2026-09-16T06:44:05.108Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-09-16T06:43:50.908Z", "site_stale_count": 2 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 2, "site_stale_capability_count": 2, "evidence_attested_at": "2026-09-16T06:43:14.861Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.1.1", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-09-16T06:43:14.861Z", "generated_at": "2026-09-16T06:43:14.861Z", "rendered_at": "2026-09-16T06:44:05.151Z", "notes": "verified_at/generated_at mark the first publication of this cvp_core_sha256 (artifacts.evidence_digest alias) for suite verification. evidence_attested_at/attested_at is the first production bind of that core digest. last_confirmed_current_at is the latest site-wide report that still confirms CURRENT. rendered_at is this JSON serialization and is not part of cvp_core_sha256 / evidence_digest. Production attestation binds cvp_core_sha256 (binds evidence_digest). Causal order: verified_at ≤ evidence_attested_at ≤ last_confirmed_current_at. attestation.bound_snapshot.site_stale_count is the site-wide stale capability count at Manifest bind time — not a live value. Fetch attestation.live_site_status.href for the current site report." }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.scientific_notation/1.1.1.json", "evidence_page": "https://www.calculatorx.com/evidence/math.scientific_notation/1.1.1", "calculator": "https://www.calculatorx.com/calc/math/scientific-notation", "schema": "https://www.calculatorx.com/developers/cvp/schema/cvp-evidence-1.0.json", "protocol": "https://www.calculatorx.com/developers/cvp/spec/1.0", "manifest": "https://www.calculatorx.com/evidence/math.scientific_notation/1.1.1.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.scientific_notation/1.1.1/2026-09-16.sources-no-wolfram.cvp.json", "manifest_core": "https://www.calculatorx.com/evidence/math.scientific_notation/1.1.1/2026-09-16.sources-no-wolfram.4a53cbc5afe2.cvp.json" } }