{ "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": "quadratic", "version": "1.1.0", "title": "Quadratic Formula Calculator", "formula_family": "quadratic", "capability_id": "math.quadratic", "verification_revision": "2026-09-16.sources-no-wolfram" }, "profile": "core", "status": "STALE", "verification_status": "VERIFIED", "production_freshness": "STALE", "overall_trust": "VERIFIED_STALE", "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": "quadratic", "version": "1.1.0", "uri": "https://www.calculatorx.com/evidence/math.quadratic/1.1.0.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-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "OpenStax Intermediate Algebra 2e — Quadratic Formula", "kind": "other", "reference": "9.3 x = (−b ± √(b² − 4ac)) / (2a)", "url": "https://openstax.org/books/intermediate-algebra-2e/pages/9-3-solve-quadratic-equations-using-the-quadratic-formula" }, { "label": "OpenStax College Algebra 2e — Quadratic Functions", "kind": "other", "reference": "5.1 Vertex and axis of y = ax² + bx + c", "url": "https://openstax.org/books/college-algebra-2e/pages/5-1-quadratic-functions" } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Quadratic formula and discriminant" }, { "class": "O3", "reference_scope": "expected_values", "scope": "expected_values", "label": "Precomputed mpmath/MPFR quadratic formula (80 dps) rounded to nearest binary64 — not Node Math.sqrt", "engine": { "name": "quadratic-mpmath-o3", "precision_bits": 265, "independent_of_iut": true, "library": "mpmath 1.4.1", "mpmath_dps": 80, "generator_version": "1.1.0", "generator_sha256": "12da7b31ab9e473da87785fbee89724cb6f37f499659b3811c3390381ad92452", "table_sha256": "fc1f865264afe8d5530628988bafa02ce2fe9f13133550a26bb9bdca54ff938a", "seed": "20260909.stable-q", "source": "https://www.calculatorx.com/developers/cvp/reproduce/quadratic-o3-tables.json", "public_table": "/developers/cvp/reproduce/quadratic-o3-tables.json", "public_generator": "/developers/cvp/reproduce/generate-quadratic-o3.py" } }, { "class": "O3", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O3 table vs IUT Δ/roots; ≤4 ULP on tabulated vectors only, not the whole coefficient space", "engine": { "name": "quadratic-mpmath-o3", "precision_bits": 265, "independent_of_iut": true, "library": "mpmath 1.4.1", "mpmath_dps": 80, "generator_version": "1.1.0", "generator_sha256": "12da7b31ab9e473da87785fbee89724cb6f37f499659b3811c3390381ad92452", "table_sha256": "fc1f865264afe8d5530628988bafa02ce2fe9f13133550a26bb9bdca54ff938a", "seed": "20260909.stable-q", "source": "https://www.calculatorx.com/developers/cvp/reproduce/quadratic-o3-tables.json", "public_table": "/developers/cvp/reproduce/quadratic-o3-tables.json", "public_generator": "/developers/cvp/reproduce/generate-quadratic-o3.py" } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module quadratic oracle — independent formula", "engine": { "name": "quadratic-reference", "precision_bits": 53, "independent_of_iut": true } }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O2 module backs ≤4 ULP root/delta comparison vs IUT", "engine": { "name": "quadratic-reference", "precision_bits": 53, "independent_of_iut": true } } ], "notes": "Golden expected values prefer an O3 mpmath/MPFR table (independent of Node Math.sqrt). O2 is a live binary64 oracle for identities and fraction parsing. O2 and O3 both use the cancellation-safe q-form in published ± order." }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "x = (−b ± √Δ)/(2a), evaluated with cancellation-safe q-form" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "Declared partitions are two-real, repeated, complex, irrational, near-double-root, large-scale, fraction-input, cancellation, invalid-domain — not a claim that every quadratic is covered. Near-double-root, large-scale, and cancellation are numerical-boundary partitions and are in the O3 tabulated ULP claim." }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O3 expected_values/numerical_behavior (mpmath table) + O2 live identities" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "6/6 legacy golden; 9/9 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "3/3 CVP boundary · 3/3 legacy Evidence boundary" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "3 invalid-domain cases" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a)." }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "9/9 declared partitions (two-real, repeated, complex, irrational, near-double-root, large-scale, fraction-input, cancellation, invalid-domain) · 6 legacy golden / 3 CVP boundary unique cases · 3 Evidence invalid-input (may overlap boundary)" }, "CVP-CONTRACT-01": { "result": "PASS", "applicability": "required", "notes": "4/4 CVP contract" }, "CVP-DEP-01": { "result": "PASS", "applicability": "required", "notes": "engine quadratic; Node binary64" }, "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": "STALE (freshness / digest drift after last PASS snapshot) · site report stale · local checks pass · local production checks PASS; site attestation is not CURRENT — final status must stay STALE, not VERIFIED · attestation_id=dc12f2ce4567db43f0e9ba9605321946fc4da979690f924d0397cf5ac1c35ed7 · STALE · Last attested schema matched 1.1.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · schema_const=1.1.0 · 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 · cvp-reproduce-manifest-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=f6cb4d2e537e53707495b91a6b3c62b3a5e6a7aa76de7b0e8d65ccdf514fd7c9 · verified_at=2026-09-20T08:59:54.925Z · evidence_attested_at=2026-09-20T08:59:54.925Z · last_confirmed_current_at=2026-09-20T08:59:54.925Z · rendered_at=2026-09-20T09:01:12.037Z · binds=cvp_core_sha256 · STALE · Last attested schema matched 1.1.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓", "check_result": "PASS", "production_state": "STALE", "binding_current": false }, "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": "1/1 metamorphic" }, "CVP-ROUND-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "No inverse / round-trip vectors in pack — control not in obligation set" }, "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. Core profile does not include Live-graph integration. Label collision, near-double-root markers, viewport switching, and pointer interaction need independent visual tests." }, "CVP-ORACLE-01": { "result": "PASS", "applicability": "higher_assurance", "notes": "O3 9/9 tabulated vectors vs IUT · ≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a)." }, "CVP-EXP-01": { "result": "SKIP", "applicability": "optional", "notes": "named expert review not performed" } }, "tests": { "golden": { "passed": 9, "total": 9, "failed": 0, "case_ids": [ "g-two-real", "g-repeated", "g-complex", "g-irrational", "g-near-double", "g-large-scale", "g-fraction", "g-downward", "g-cancellation" ] }, "boundary": { "passed": 3, "total": 3, "failed": 0, "case_ids": [ "not-quadratic", "missing-a", "boundary-quad-a0" ] }, "invalid": { "passed": 3, "total": 3, "failed": 0, "case_ids": [ "not-quadratic", "missing-a", "boundary-quad-a0" ] }, "property": { "passed": 5, "total": 5, "failed": 0, "case_ids": [ "prop-vieta-sum", "prop-vieta-prod", "prop-cancellation-vieta-sum", "prop-cancellation-vieta-prod", "prop-cancellation-residual" ], "definition_ids": [ "vieta-sum", "vieta-product", "polynomial-residual" ] }, "round_trip": { "passed": 0, "total": 0, "failed": 0, "case_ids": [] }, "metamorphic": { "passed": 1, "total": 1, "failed": 0, "case_ids": [ "meta-scale-eq" ], "definition_ids": [ "scale-coefficients" ] }, "contract": { "passed": 4, "total": 4, "failed": 0 }, "cross_interface": { "passed": 2, "total": 2, "failed": 0, "case_ids": [ "iface-q", "iface-frac" ] }, "o3": { "passed": 9, "total": 9, "failed": 0, "case_ids": [ "o3-two-real", "o3-repeated", "o3-complex", "o3-irrational", "o3-near-double", "o3-fraction", "o3-downward", "o3-large-scale", "o3-cancellation" ], "generator_id": "quadratic-mpmath-o3", "seed": "20260909.stable-q", "table_sha256": "fc1f865264afe8d5530628988bafa02ce2fe9f13133550a26bb9bdca54ff938a", "max_error_ulp": 0.67108864, "reproduce": "python3 generate-quadratic-o3.py", "table_url": "/developers/cvp/reproduce/quadratic-o3-tables.json", "generator_url": "/developers/cvp/reproduce/generate-quadratic-o3.py", "claim_scope": "≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a).", "reproduce_url": "https://www.calculatorx.com/evidence/math.quadratic/reproduce" } }, "coverage": { "partitions": [ { "id": "two-real", "description": "Δ > 0 two distinct real roots", "exercised": true, "case_count": 6 }, { "id": "repeated", "description": "Δ = 0 repeated real root", "exercised": true, "case_count": 3 }, { "id": "complex", "description": "Δ < 0 complex conjugate roots", "exercised": true, "case_count": 3 }, { "id": "irrational", "description": "Δ > 0 not a perfect square", "exercised": true, "case_count": 3 }, { "id": "near-double-root", "description": "Numerical boundary: Δ ≈ 0 close real roots", "exercised": true, "case_count": 2 }, { "id": "large-scale", "description": "Numerical boundary: widely separated real roots (O3 tabulated ULP)", "exercised": true, "case_count": 2 }, { "id": "fraction-input", "description": "Fractional coefficients (parser + roots)", "exercised": true, "case_count": 2 }, { "id": "cancellation", "description": "Numerical boundary: b² ≫ 4ac (O3 tabulated ULP; cancellation-safe q-form)", "exercised": true, "case_count": 6 }, { "id": "invalid-domain", "description": "a = 0 or missing coefficients", "exercised": true, "case_count": 3 } ] }, "numerical": { "representation": "IEEE-754 binary64 quadratic formula", "tolerance": { "type": "ulp", "value": 4, "rationale": "Independent Δ/roots vs IUT; ≤4 ULP on primary roots/delta. Declared a priori. O3 tabulated vectors (including cancellation and large-scale) use the same threshold.", "declared_before_evaluation": true }, "claim_scope": "≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a).", "max_error_observed": 0.67108864, "records": [ { "id": "g-two-real", "reference": { "a": 1, "b": -5, "c": 6, "delta": 1, "x1": 3, "x2": 2, "root_type": "two_real" }, "actual": { "a": 1, "b": -5, "c": 6, "mode": "solve", "delta": 1, "xv": 2.5, "yv": -0.25, "axis": 2.5, "y_intercept": 6, "opens": "up", "opens_label": "Upward", "root_type": "two_real", "mode_label": "Two distinct real roots", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ > 0 → two distinct real roots.", "equation": "x² − 5x + 6 = 0", "inputs_summary": "a=1 · b=-5 · c=6", "calculation_version": "1.1.0", "x1": 3, "x2": 2, "value": "3, 2", "display": { "equation": "x² − 5x + 6 = 0", "delta": "1", "x1": "3", "x2": "2", "roots": "3, 2", "vertex": "(2.5, −0.25)", "vertex_x": "2.5", "vertex_y": "−0.25", "axis": "2.5", "y_intercept": "6", "opens": "Upward", "factorization": "(x − 2)(x − 3) = 0", "exact": "", "equation_lhs": "x² − 5x + 6" }, "steps": [ "x² − 5x + 6 = 0", "", "Δ = b² − 4ac", " = (−5)² − 4(1)(6)", " = 25 − 24", " = 1", "", "x = (−b ± √Δ) / 2a", " = (5 ± √1) / 2", "x₁ = 3", "x₂ = 2", "", "Vertex:", "xᵥ = −b / 2a = 2.5", "yᵥ = −0.25", "", "Axis: x = 2.5", "", "Factor form: (x − 2)(x − 3) = 0" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "golden" }, { "id": "g-repeated", "reference": { "a": 1, "b": -4, "c": 4, "delta": 0, "x1": 2, "x2": 2, "root_type": "repeated" }, "actual": { "a": 1, "b": -4, "c": 4, "mode": "solve", "delta": 0, "xv": 2, "yv": 0, "axis": 2, "y_intercept": 4, "opens": "up", "opens_label": "Upward", "root_type": "repeated", "mode_label": "One repeated real root", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ = 0 → one repeated real root.", "equation": "x² − 4x + 4 = 0", "inputs_summary": "a=1 · b=-4 · c=4", "calculation_version": "1.1.0", "x1": 2, "x2": 2, "value": "2", "display": { "equation": "x² − 4x + 4 = 0", "delta": "0", "x1": "2", "x2": "2", "roots": "2", "vertex": "(2, 0)", "vertex_x": "2", "vertex_y": "0", "axis": "2", "y_intercept": "4", "opens": "Upward", "factorization": "(x − 2)² = 0", "exact": "", "equation_lhs": "x² − 4x + 4" }, "steps": [ "x² − 4x + 4 = 0", "", "Δ = b² − 4ac", " = (−4)² − 4(1)(4)", " = 16 − 16", " = 0", "", "x = −b / 2a", " = 2", "", "Vertex:", "xᵥ = −b / 2a = 2", "yᵥ = 0", "", "Axis: x = 2", "", "Factor form: (x − 2)² = 0" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "golden" }, { "id": "g-complex", "reference": { "a": 1, "b": 2, "c": 5, "delta": -16, "real": -1, "imag": 2, "root_type": "complex" }, "actual": { "a": 1, "b": 2, "c": 5, "mode": "solve", "delta": -16, "xv": -1, "yv": 4, "axis": -1, "y_intercept": 5, "opens": "up", "opens_label": "Upward", "root_type": "complex", "mode_label": "Two complex conjugate roots", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ < 0 → two complex conjugate roots.", "equation": "x² + 2x + 5 = 0", "inputs_summary": "a=1 · b=2 · c=5", "calculation_version": "1.1.0", "real": -1, "imag": 2, "value": "-1 ± 2i", "display": { "equation": "x² + 2x + 5 = 0", "delta": "−16", "x1": "−1 + 2i", "x2": "−1 − 2i", "roots": "−1 ± 2i", "vertex": "(−1, 4)", "vertex_x": "−1", "vertex_y": "4", "axis": "−1", "y_intercept": "5", "opens": "Upward", "factorization": "", "exact": "", "equation_lhs": "x² + 2x + 5" }, "steps": [ "x² + 2x + 5 = 0", "", "Δ = b² − 4ac", " = 2² − 4(1)(5)", " = 4 − 20", " = −16", "", "x = (−b ± √|Δ| i) / 2a", " = −1 ± 2i", "", "Vertex:", "xᵥ = −b / 2a = −1", "yᵥ = 4", "", "Axis: x = −1" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "golden" }, { "id": "g-irrational", "reference": { "a": 1, "b": -8, "c": 5, "delta": 44, "x1": 7.3166247903554, "x2": 0.6833752096446002, "root_type": "two_real" }, "actual": { "a": 1, "b": -8, "c": 5, "mode": "solve", "delta": 44, "xv": 4, "yv": -11, "axis": 4, "y_intercept": 5, "opens": "up", "opens_label": "Upward", "root_type": "two_real", "mode_label": "Two distinct real roots", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ > 0 → two distinct real roots.", "equation": "x² − 8x + 5 = 0", "inputs_summary": "a=1 · b=-8 · c=5", "calculation_version": "1.1.0", "x1": 7.3166247903554, "x2": 0.6833752096446002, "value": "7.31662479, 0.6833752096", "display": { "equation": "x² − 8x + 5 = 0", "delta": "44", "x1": "7.31662479", "x2": "0.6833752096", "roots": "7.31662479, 0.6833752096", "vertex": "(4, −11)", "vertex_x": "4", "vertex_y": "−11", "axis": "4", "y_intercept": "5", "opens": "Upward", "factorization": "", "exact": "4 ± √11", "equation_lhs": "x² − 8x + 5" }, "steps": [ "x² − 8x + 5 = 0", "", "Δ = b² − 4ac", " = (−8)² − 4(1)(5)", " = 64 − 20", " = 44", "", "x = (−b ± √Δ) / 2a", " = (8 ± √44) / 2", " = 4 ± √11", "x₁ = 7.31662479", "x₂ = 0.6833752096", "", "Vertex:", "xᵥ = −b / 2a = 4", "yᵥ = −11", "", "Axis: x = 4" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "golden" }, { "id": "g-near-double", "reference": { "a": 1, "b": -5, 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6.2499" }, "steps": [ "x² − 5x + 6.2499 = 0", "", "Δ = b² − 4ac", " = (−5)² − 4(1)(6.2499)", " = 25 − 24.9996", " = 0.0004", "", "x = (−b ± √Δ) / 2a", " = (5 ± √0.0004) / 2", "x₁ = 2.51", "x₂ = 2.49", "", "Vertex:", "xᵥ = −b / 2a = 2.5", "yᵥ = −0.0001", "", "Axis: x = 2.5" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "golden" }, { "id": "g-large-scale", "reference": { "a": 1, "b": -100, "c": 1, "delta": 9996, "x1": 99.98999899979995, "x2": 0.010001000200050014, "root_type": "two_real" }, "actual": { "a": 1, "b": -100, "c": 1, "mode": "solve", "delta": 9996, "xv": 50, "yv": -2499, "axis": 50, "y_intercept": 1, "opens": "up", "opens_label": "Upward", "root_type": "two_real", "mode_label": "Two distinct real roots", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ > 0 → two distinct real roots.", "equation": "x² − 100x + 1 = 0", "inputs_summary": "a=1 · b=-100 · c=1", "calculation_version": "1.1.0", "x1": 99.98999899979995, "x2": 0.010001000200050014, "value": 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"roots": "2.51, 2.49", "vertex": "(2.5, −0.0001)", "vertex_x": "2.5", "vertex_y": "−0.0001", "axis": "2.5", "y_intercept": "6.2499", "opens": "Upward", "factorization": "", "exact": "", "equation_lhs": "x² − 5x + 6.2499" }, "steps": [ "x² − 5x + 6.2499 = 0", "", "Δ = b² − 4ac", " = (−5)² − 4(1)(6.2499)", " = 25 − 24.9996", " = 0.0004", "", "x = (−b ± √Δ) / 2a", " = (5 ± √0.0004) / 2", "x₁ = 2.51", "x₂ = 2.49", "", "Vertex:", "xᵥ = −b / 2a = 2.5", "yᵥ = −0.0001", "", "Axis: x = 2.5" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "o3" }, { "id": "o3-fraction", "reference": { "a": 0.5, "b": -1.5, "c": 1, "delta": 0.25, "x1": 2, "x2": 1, "root_type": "two_real" }, "actual": { "a": 0.5, "b": -1.5, "c": 1, "mode": "solve", "delta": 0.25, "xv": 1.5, "yv": -0.125, "axis": 1.5, "y_intercept": 1, "opens": "up", "opens_label": "Upward", "root_type": "two_real", "mode_label": "Two distinct real roots", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ > 0 → two distinct real roots.", "equation": "(1/2)x² − (3/2)x + 1 = 0", "inputs_summary": "a=0.5 · b=-1.5 · c=1", "calculation_version": "1.1.0", "x1": 2, "x2": 1, "value": "2, 1", "display": { "equation": "(1/2)x² − (3/2)x + 1 = 0", "delta": "0.25", "x1": "2", "x2": "1", "roots": "2, 1", "vertex": "(1.5, −0.125)", "vertex_x": "1.5", "vertex_y": "−0.125", "axis": "1.5", "y_intercept": "1", "opens": "Upward", "factorization": "(1/2)(x − 1)(x − 2) = 0", "exact": "", "equation_lhs": "(1/2)x² − (3/2)x + 1" }, "steps": [ "(1/2)x² − (3/2)x + 1 = 0", "", "Δ = b² − 4ac", " = (−1.5)² − 4(0.5)(1)", " = 2.25 − 2", " = 0.25", "", "x = (−b ± √Δ) / 2a", " = (1.5 ± √0.25) / 1", "x₁ = 2", "x₂ = 1", "", "Vertex:", "xᵥ = −b / 2a = 1.5", "yᵥ = −0.125", "", "Axis: x = 1.5", "", "Factor form: (1/2)(x − 1)(x − 2) = 0" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "o3" }, { "id": "o3-downward", "reference": { "a": -1, "b": 5, "c": -6, "delta": 1, "x1": 2, "x2": 3, "root_type": "two_real" }, "actual": { "a": -1, "b": 5, "c": -6, "mode": "solve", "delta": 1, "xv": 2.5, "yv": 0.25, "axis": 2.5, "y_intercept": -6, "opens": "down", "opens_label": "Downward", "root_type": "two_real", "mode_label": "Two distinct real roots", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ > 0 → two distinct real roots.", "equation": "−x² + 5x − 6 = 0", "inputs_summary": "a=-1 · b=5 · c=-6", "calculation_version": "1.1.0", "x1": 2, "x2": 3, "value": "2, 3", "display": { "equation": "−x² + 5x − 6 = 0", "delta": "1", "x1": "2", "x2": "3", "roots": "2, 3", "vertex": "(2.5, 0.25)", "vertex_x": "2.5", "vertex_y": "0.25", "axis": "2.5", "y_intercept": "−6", "opens": "Downward", "factorization": "−(x − 2)(x − 3) = 0", "exact": "", "equation_lhs": "−x² + 5x − 6" }, "steps": [ "−x² + 5x − 6 = 0", "", "Δ = b² − 4ac", " = 5² − 4(−1)(−6)", " = 25 − 24", " = 1", "", "x = (−b ± √Δ) / 2a", " = (−5 ± √1) / −2", "x₁ = 2", "x₂ = 3", "", "Vertex:", "xᵥ = −b / 2a = 2.5", "yᵥ = 0.25", "", "Axis: x = 2.5", "", "Factor form: −(x − 2)(x − 3) = 0" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "o3" }, { "id": "o3-large-scale", "reference": { "a": 1, "b": -100, "c": 1, "delta": 9996, "x1": 99.98999899979995, "x2": 0.010001000200050014, "root_type": "two_real" }, "actual": { "a": 1, "b": -100, "c": 1, "mode": "solve", "delta": 9996, "xv": 50, "yv": -2499, "axis": 50, "y_intercept": 1, "opens": "up", "opens_label": "Upward", "root_type": "two_real", "mode_label": "Two distinct real roots", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ > 0 → two distinct real roots.", "equation": "x² − 100x + 1 = 0", "inputs_summary": "a=1 · b=-100 · c=1", "calculation_version": "1.1.0", "x1": 99.98999899979995, "x2": 0.010001000200050014, "value": "99.989999, 0.0100010002", "display": { "equation": "x² − 100x + 1 = 0", "delta": "9996", "x1": "99.989999", "x2": "0.0100010002", "roots": "99.989999, 0.0100010002", "vertex": "(50, −2499)", "vertex_x": "50", "vertex_y": "−2499", "axis": "50", "y_intercept": "1", "opens": "Upward", "factorization": "", "exact": "50 ± 7√51", "equation_lhs": "x² − 100x + 1" }, "steps": [ "x² − 100x + 1 = 0", "", "Δ = b² − 4ac", " = (−100)² − 4(1)(1)", " = 10000 − 4", " = 9996", "", "x = (−b ± √Δ) / 2a", " = (100 ± √9996) / 2", " = 50 ± 7√51", "x₁ = 99.989999", "x₂ = 0.0100010002", "", "Vertex:", "xᵥ = −b / 2a = 50", "yᵥ = −2499", "", "Axis: x = 50" ] }, "error_ulp": 0, "threshold_ulp": 4, "suite": "o3" }, { "id": "o3-cancellation", "reference": { "a": 1, "b": -100000000, "c": 1, "delta": 9999999999999996, "x1": 99999999.99999999, "x2": 1e-8, "root_type": "two_real" }, "actual": { "a": 1, "b": -100000000, "c": 1, "mode": "solve", "delta": 9999999999999996, "xv": 50000000, "yv": -2499999999999999, "axis": 50000000, "y_intercept": 1, "opens": "up", "opens_label": "Upward", "root_type": "two_real", "mode_label": "Two distinct real roots", "formula": "x = (−b ± √Δ)/(2a)", "heading": "Roots", "explainer": "Δ > 0 → two distinct real roots.", "equation": "x² − 100000000x + 1 = 0", "inputs_summary": "a=1 · b=-100000000 · c=1", "calculation_version": "1.1.0", "x1": 100000000, "x2": 1e-8, "value": "100000000, 1e-8", "display": { "equation": "x² − 100000000x + 1 = 0", "delta": "9999999999999996", "x1": "100000000", "x2": "1e−8", "roots": "100000000, 1e−8", "vertex": "(50000000, −2499999999999999)", "vertex_x": "50000000", "vertex_y": "−2499999999999999", "axis": "50000000", "y_intercept": "1", "opens": "Upward", "factorization": "", "exact": "50000000 ± √2499999999999999", "equation_lhs": "x² − 100000000x + 1" }, "steps": [ "x² − 100000000x + 1 = 0", "", "Δ = b² − 4ac", " = (−100000000)² − 4(1)(1)", " = 10000000000000000 − 4", " = 9999999999999996", "", "x = (−b ± √Δ) / 2a", " = (100000000 ± √9999999999999996) / 2", " = 50000000 ± √2499999999999999", "x₁ = 100000000", "x₂ = 1e−8", "", "Vertex:", "xᵥ = −b / 2a = 50000000", "yᵥ = −2499999999999999", "", "Axis: x = 50000000" ] }, "error_ulp": 0.67108864, "threshold_ulp": 4, "suite": "o3" } ] }, "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. Core profile does not include Live-graph integration. Label collision, near-double-root markers, viewport switching, and pointer interaction need independent visual tests." }, "artifacts": { "evidence_bundle_sha256": "cc217b0856408b88469b5ece0a208d97e08a29105466456eb8de8c6defbb086a", "evidence_digest": "5e416940420dad0417370d8d7116fe69df568890d801df94aaf4e8919a22ac0e", "production_sha256": "f6cb4d2e537e53707495b91a6b3c62b3a5e6a7aa76de7b0e8d65ccdf514fd7c9", "attested_catalog_sha256": "ac2cbf30217968c29bf895593a4d4e79f6e3dc6addf1bc2de0213655d7d44eef", "production_checks": [ { "id": "math.quadratic:output-const", "status": "pass", "detail": "output const 1.0.4 vs capability 1.0.4", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" }, { "id": "math.quadratic:evidence-sha256", "status": "pass", "detail": "57f20c7d3d9f", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" }, { "id": "math.quadratic:semantic-contract", "status": "pass", "detail": "9/9", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" }, { "id": "math.quadratic:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.0.4 vs origin 1.0.4", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" }, { "id": "math.quadratic:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.quadratic/1.1.0/2026-09-16.sources-no-wolfram/core/5e416940420d", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z", "projection_compared": false }, { "id": "math.quadratic:cvp-latest-alias-agrees", "status": "pass", "detail": "math.quadratic/1.1.0/2026-09-16.sources-no-wolfram/core/5e416940420d", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z", "projection_compared": false }, { "id": "math.quadratic:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" }, { "id": "math.quadratic:cvp-immutable-manifest-sha256", "status": "pass", "detail": "07d7671fb2dd", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" }, { "id": "math.quadratic:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.quadratic/1.1.0/2026-09-16.sources-no-wolfram/core/5e416940420d", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z", "projection_compared": false }, { "id": "math.quadratic:cvp-reproduce-manifest-agree", "status": "pass", "detail": "2026-09-16.sources-no-wolfram · fc1f865264af", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" }, { "id": "math.quadratic:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" }, { "id": "math.quadratic:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-09-20T08:59:54.925Z" } ], "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": "5e416940420dad0417370d8d7116fe69df568890d801df94aaf4e8919a22ac0e", "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": "5e416940420dad0417370d8d7116fe69df568890d801df94aaf4e8919a22ac0e", "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": "1362b79bd19bfd7ac83cb8484aa45369e45a145f9bf517f2f9ce32192f669a30", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "ac2cbf30217968c29bf895593a4d4e79f6e3dc6addf1bc2de0213655d7d44eef", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "5e416940420dad0417370d8d7116fe69df568890d801df94aaf4e8919a22ac0e" }, "dependencies": [ { "name": "quadratic-engine", "version": "1.1.0" }, { "name": "quadratic-reference-oracle", "version": "1.0.0" }, { "name": "quadratic-mpmath-o3-table", "version": "quadratic-mpmath-o3" }, { "name": "node", "version": "20.19.2" } ], "attestation": { "status": "STALE", "href": "/.well-known/calculatorx-production-attestation.json", "id": "dc12f2ce4567db43f0e9ba9605321946fc4da979690f924d0397cf5ac1c35ed7", "attested_at": "2026-09-20T08:59:54.925Z", "last_confirmed_current_at": "2026-09-20T08:59:54.925Z", "site_attestation_current": false, "capability_attestation_current": false, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-09-18T21:41:55.460Z", "live_updated_at": "2026-09-20T08:59:55.039Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-09-18T21:41:55.460Z", "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, "stale_reason": "STALE · Last attested schema matched 1.1.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓", "evidence_attested_at": "2026-09-20T08:59:54.925Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.1.0", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-09-20T08:59:54.925Z", "generated_at": "2026-09-20T08:59:54.925Z", "rendered_at": "2026-09-20T09:01:12.037Z", "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.quadratic/1.1.0.json", "evidence_page": "https://www.calculatorx.com/evidence/math.quadratic/1.1.0", "calculator": "https://www.calculatorx.com/calc/math/quadratic", "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.quadratic/1.1.0.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.quadratic/1.1.0/2026-09-16.sources-no-wolfram.cvp.json", "reproduce": "https://www.calculatorx.com/evidence/math.quadratic/reproduce", "o3_table": "https://www.calculatorx.com/developers/cvp/reproduce/quadratic-o3-tables.json", "o3_generator": "https://www.calculatorx.com/developers/cvp/reproduce/generate-quadratic-o3.py", "manifest_core": "https://www.calculatorx.com/evidence/math.quadratic/1.1.0/2026-09-16.sources-no-wolfram.5e416940420d.cvp.json" } }