{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:QQQMNPOYGHDZSLCS3MMIM6ER2H","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4e76314dc6859d4c64a6ebf6afd4aea4219ea8ae653927e84859b6c5d019c006","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2007-04-21T17:55:13Z","title_canon_sha256":"e5a5d0c9427884a9044cb471400860689ffc2ed340609bad3d368f173878f7a2"},"schema_version":"1.0","source":{"id":"0704.2842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.2842","created_at":"2026-06-03T22:06:00Z"},{"alias_kind":"arxiv_version","alias_value":"0704.2842v1","created_at":"2026-06-03T22:06:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.2842","created_at":"2026-06-03T22:06:00Z"},{"alias_kind":"pith_short_12","alias_value":"QQQMNPOYGHDZ","created_at":"2026-06-03T22:06:00Z"},{"alias_kind":"pith_short_16","alias_value":"QQQMNPOYGHDZSLCS","created_at":"2026-06-03T22:06:00Z"},{"alias_kind":"pith_short_8","alias_value":"QQQMNPOY","created_at":"2026-06-03T22:06:00Z"}],"graph_snapshots":[{"event_id":"sha256:3d220e765fd73d7b62cb4a25d5cfe463edb4e5bf8706db3fe2ca1f12e718ed98","target":"graph","created_at":"2026-06-03T22:06:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0704.2842/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A discrete Laplace transform and its inversion formula are obtained by using a quadrature of the continuous Fourier transform which is given in terms of Hermite polynomials and its zeros. This approach yields a convergent discrete formula for the two-sided Laplace transform if the function to be transformed falls off rapidly to zero and satisfy certain conditions of integrability, achieving convergence also for singular functions. The inversion formula becomes a quadrature formula for the Bromwich integral. This procedure also yields a quadrature formula for the Mellin transform and its corres","authors_text":"Francisco Mejia, Rafael G. Campos","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2007-04-21T17:55:13Z","title":"Quadrature formulas for the Laplace and Mellin transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.2842","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f6c2a429b0b759e192d55b7ef3b501f958b0e43880135b9ec1c8009996cbf279","target":"record","created_at":"2026-06-03T22:06:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4e76314dc6859d4c64a6ebf6afd4aea4219ea8ae653927e84859b6c5d019c006","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2007-04-21T17:55:13Z","title_canon_sha256":"e5a5d0c9427884a9044cb471400860689ffc2ed340609bad3d368f173878f7a2"},"schema_version":"1.0","source":{"id":"0704.2842","kind":"arxiv","version":1}},"canonical_sha256":"8420c6bdd831c7992c52db18867891d1c275fca973610a791c106d545878ea80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8420c6bdd831c7992c52db18867891d1c275fca973610a791c106d545878ea80","first_computed_at":"2026-06-03T22:06:00.591622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:00.591622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R52FiEkWM7Oof6N+u/VFrcONF1LmJEakcE4q5cn3E4xse6eLIynBnyqFGQmgUBfjHVsqfFsohrNoPYE4V3zOAg==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:00.592127Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.2842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6c2a429b0b759e192d55b7ef3b501f958b0e43880135b9ec1c8009996cbf279","sha256:3d220e765fd73d7b62cb4a25d5cfe463edb4e5bf8706db3fe2ca1f12e718ed98"],"state_sha256":"f0db1ccb9d005a35216bbf28eca465efafc4413e85abbc4cfadecac811cec9f0"}