{ "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": "z-transform", "version": "1.0.5", "title": "Z Transform Calculator", "formula_family": "z_transform", "capability_id": "math.transform.z", "verification_revision": "2026-10-19.z-input-contract-review" }, "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": "22.20.0", "numeric_model": "IEEE-754 binary64", "os": "darwin" }, "suite": { "id": "z-transform", "version": "1.0.5", "uri": "https://www.calculatorx.com/evidence/math.transform.z/1.0.5.json", "verification_revision": "2026-10-19.z-input-contract-review" }, "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-DIM-01", "CVP-PROP-01", "CVP-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "ISO 80000-2:2019 Quantities and units — Mathematics", "kind": "standard", "reference": "Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.", "url": "https://www.iso.org/standard/64973.html" }, { "label": "Oppenheim & Schafer, Discrete-Time Signal Processing — unilateral Z table", "kind": "other", "reference": "Z{a^n}=z/(z−a); Z{1}=z/(z−1); ROC |z|>pole" }, { "label": "MIT Signals and Systems — Lecture 22: The z-Transform", "kind": "other", "reference": "The z-transform, its relation to the discrete-time Fourier transform, inverse transform and region of convergence. A rational expression alone does not identify the time sequence without its ROC. Mathematical reference only; not validation or endorsement of this implementation.", "url": "https://ocw.mit.edu/courses/res-6-007-signals-and-systems-spring-2011/resources/lecture-22-the-z-transform/" } ] }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "Independent high-precision actual-input table identities vs stable binary64 evaluation" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "Unilateral table: a^n, step, ramp, n a^n, sin, cos, damped sin/cos. Discovery /inverse-z. Not DFT, not Laplace, not residue, not CAS." }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O2 expected_values + O2 numerical_behavior" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "3/3 legacy golden; 656/656 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "1/1 numeric-edge Evidence + 1/1 near-singularity numeric; illegal enum/system is Invalid only" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "2 Evidence illegal-input + 20/20 oracle-backed error-code (exact_error_match, not ULP)" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "max_error_observed_ulp=0; policy declared a priori" }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "3/3 declared partitions (z, inverse, invalid-domain) · 3 legacy golden / 2 CVP boundary unique cases · 2 Evidence invalid-input (may overlap boundary)" }, "CVP-CONTRACT-01": { "result": "PASS", "applicability": "required", "notes": "5/5 CVP contract · release-artifacts-aligned=PASS · schema-output-required-declared=PASS · schema-valid-input-executes=PASS · engine-success-output-validates-schema=PASS · rest-success-payload-validates-schema=PASS" }, "CVP-DEP-01": { "result": "PASS", "applicability": "required", "notes": "engine z-transform; 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": "this calculator CURRENT · bound snapshot pass @ 2026-10-19T07:58:46.038Z · live site-wide report stale @ 2026-10-19T07:59:01.815Z (1 other capabilities) · local checks pass · attestation_id=c64cc612dc6c3a945c8f29b84029807be91aeb07eee35eea41b94b1b8594e211 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-10-19T07:58:46.038Z · Live production status STALE (1 capability; 375 remain CURRENT) @ 2026-10-19T07:59:01.815Z · Public schema 1.0.5 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.5 · 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=589b90803730d03fdb921029dbc9e570b3d8a9047e839174126db3b72f2cd1c6 · verified_at=2026-10-19T03:15:31.965Z · evidence_attested_at=2026-10-19T03:15:31.965Z · last_confirmed_current_at=2026-10-19T07:58:46.038Z · rendered_at=2026-10-19T07:59:02.384Z · binds=cvp_core_sha256", "check_result": "PASS", "production_state": "CURRENT", "binding_current": true }, "CVP-DIM-01": { "result": "PASS", "applicability": "applicable", "notes": "scalar X(z) or x[n]" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "1/1 property · enumerated fixed assertions (not generated; no seed)" }, "CVP-META-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "No input→output transformation vectors in pack — control not in obligation set" }, "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. Error-path engine·REST·MCP 8/8 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity." }, "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" } }, "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. Error-path engine·REST·MCP 8/8 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity." }, "artifacts": { "evidence_bundle_sha256": "4a0212acd55b734e40c9eb48d9056646e880a8e3e36577bbb1c82f8ce4f097ca", "evidence_digest": "d640971981edaee0726c5f96bd54fcbb9a3ceee31a1a96c9ec04daf3661bd120", "production_sha256": "589b90803730d03fdb921029dbc9e570b3d8a9047e839174126db3b72f2cd1c6", "attested_catalog_sha256": "93b711f8b5b8d602c9f2ecfb852b561e5cd33585603555116fdf45f0bd4f1957", "production_checks": [ { "id": "math.transform.z:output-const", "status": "pass", "detail": "output const 1.0.5 vs capability 1.0.5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z" }, { "id": "math.transform.z:evidence-sha256", "status": "pass", "detail": "b859ce68e0e7", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z" }, { "id": "math.transform.z:semantic-contract", "status": "pass", "detail": "10/10", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z" }, { "id": "math.transform.z:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.0.5 vs origin 1.0.5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z" }, { "id": "math.transform.z:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.transform.z/1.0.5/2026-10-19.z-input-contract-review/core/d640971981ed", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z", "projection_compared": false }, { "id": "math.transform.z:cvp-latest-alias-agrees", "status": "pass", "detail": "math.transform.z/1.0.5/2026-10-19.z-input-contract-review/core/d640971981ed", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z", "projection_compared": false }, { "id": "math.transform.z:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z" }, { "id": "math.transform.z:cvp-immutable-manifest-sha256", "status": "pass", "detail": "d640971981ed", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z" }, { "id": "math.transform.z:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.transform.z/1.0.5/2026-10-19.z-input-contract-review/core/d640971981ed", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z", "projection_compared": false }, { "id": "math.transform.z:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z" }, { "id": "math.transform.z:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-19T03:15:31.965Z" } ], "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": "d640971981edaee0726c5f96bd54fcbb9a3ceee31a1a96c9ec04daf3661bd120", "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": "d640971981edaee0726c5f96bd54fcbb9a3ceee31a1a96c9ec04daf3661bd120", "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": "b859ce68e0e7a96bff55330cb747f05b7109503af6d6e34fe834400b9c8458c9", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "93b711f8b5b8d602c9f2ecfb852b561e5cd33585603555116fdf45f0bd4f1957", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "d640971981edaee0726c5f96bd54fcbb9a3ceee31a1a96c9ec04daf3661bd120" }, "dependencies": [ { "name": "z-transform-engine", "version": "1.0.5" }, { "name": "z-transform-reference-oracle", "version": "1.0.0" }, { "name": "node", "version": "22.20.0" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "c64cc612dc6c3a945c8f29b84029807be91aeb07eee35eea41b94b1b8594e211", "attested_at": "2026-10-19T03:15:31.965Z", "last_confirmed_current_at": "2026-10-19T07:58:46.038Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-10-19T07:58:46.038Z", "live_updated_at": "2026-10-19T07:59:01.815Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-10-19T07:58:46.038Z", "site_stale_count": 1 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 1, "site_stale_capability_count": 1, "evidence_attested_at": "2026-10-19T03:15:31.965Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.0.5", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-10-19T03:15:31.965Z", "generated_at": "2026-10-19T03:15:31.965Z", "rendered_at": "2026-10-19T07:59:02.384Z", "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." }, "tests": { "golden": { "passed": 656, "total": 656, "failed": 0 }, "boundary": { "passed": 2, "total": 2, "failed": 0 }, "invalid": { "passed": 22, "total": 22, "failed": 0, "comparison": "exact_error_match" }, "property": { "passed": 1, "total": 1, "failed": 0, "kind": "fixed" }, "round_trip": { "passed": 0, "total": 0, "failed": 0 }, "metamorphic": { "passed": 0, "total": 0, "failed": 0 }, "contract": { "passed": 5, "total": 5, "failed": 0 }, "cross_interface": { "passed": 26, "total": 26, "failed": 0 } }, "numerical": { "representation": "binary64; 12 significant digits without nonzero clamping", "tolerance": { "type": "relative", "value": 2e-11, "rationale": "Each nonzero scalar compared relative to itself; exact zero must remain zero. Explicit output, phase-product and inverse quantization exclusions retain separate mathematical references. Exact product-rounding phase budget 2e-12 times the estimated trig magnitude; inverse half-ULP floor budget 1e-11. Host transcendental accuracy is empirically reviewed, not formally certified.", "declared_before_evaluation": true }, "max_error_observed": 0 }, "coverage": { "partitions": [ { "id": "z", "description": "z", "exercised": true, "case_count": 607 }, { "id": "inverse", "description": "inverse", "exercised": true, "case_count": 59 }, { "id": "invalid-domain", "description": "Invalid inputs", "exercised": true, "case_count": 22 } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "X(z)=Σ x[n] z^{−n}; table pairs of one capability" }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Independent forward Z extreme phases and periodic neighborhoods, 900/1200 dps, agreement 1e-150; no IUT", "engine": { "name": "mpmath forward-phase-reference", "precision_bits": 2993, "independent_of_iut": true, "same_runtime_as_iut": false } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Independent 900/1200-dps exact-binary64 phase/product identities, agreement 1e-150; explicit phase/quantization exclusions separate from output range", "engine": { "name": "mpmath 900/1200-dps phase-reference", "precision_bits": 2993, "independent_of_iut": true, "same_runtime_as_iut": false } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Offline independent actual-binary64 rational/trig table identities at 200/300 dps; scale-reference.json, agreement 1e-150; no IUT", "engine": { "name": "mpmath 200/300-dps scale-reference", "precision_bits": 668, "independent_of_iut": true, "same_runtime_as_iut": false } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module Z oracle — textbook causal pairs Z{a^n}=z/(z−a), Z{1}=z/(z−1) (not IUT table transcription)", "engine": { "name": "z-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Independent binary64 textbook identities; current pack declares the comparison policy", "engine": { "name": "z-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.transform.z/1.0.5.json", "evidence_page": "https://www.calculatorx.com/evidence/math.transform.z/1.0.5", "calculator": "https://www.calculatorx.com/calc/math/z-transform", "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.transform.z/1.0.5.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.transform.z/1.0.5/2026-10-19.z-input-contract-review.cvp.json", "manifest_core": "https://www.calculatorx.com/evidence/math.transform.z/1.0.5/2026-10-19.z-input-contract-review.d640971981ed.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }