{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:KDGOJKEAKMKJGQV73VTO72V3PA","short_pith_number":"pith:KDGOJKEA","canonical_record":{"source":{"id":"2301.08931","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-01-21T10:00:54Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bf0337418440392fb83a5286a7a00182fd090d7c5b0e5c46675545b07e10e6ee","abstract_canon_sha256":"0664b2b5d12fda1af61d4db5c4867a464b8748dec414551cdc895e07c76f862f"},"schema_version":"1.0"},"canonical_sha256":"50cce4a88053149342bfdd66efeabb7827ced4bfedff69b21ebada8a6d9c2897","source":{"kind":"arxiv","id":"2301.08931","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.08931","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"2301.08931v3","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.08931","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"KDGOJKEAKMKJ","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_16","alias_value":"KDGOJKEAKMKJGQV7","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_8","alias_value":"KDGOJKEA","created_at":"2026-07-05T06:33:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:KDGOJKEAKMKJGQV73VTO72V3PA","target":"record","payload":{"canonical_record":{"source":{"id":"2301.08931","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-01-21T10:00:54Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bf0337418440392fb83a5286a7a00182fd090d7c5b0e5c46675545b07e10e6ee","abstract_canon_sha256":"0664b2b5d12fda1af61d4db5c4867a464b8748dec414551cdc895e07c76f862f"},"schema_version":"1.0"},"canonical_sha256":"50cce4a88053149342bfdd66efeabb7827ced4bfedff69b21ebada8a6d9c2897","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:33:32.546596Z","signature_b64":"RzPR/rtMS4J7zZPrNlNNJFXdJRqLlQqRpjueGMxRFz65H779nqSBjLlmWPF4ysXp2g2ZgA6Te1j+7cwuOfyFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50cce4a88053149342bfdd66efeabb7827ced4bfedff69b21ebada8a6d9c2897","last_reissued_at":"2026-07-05T06:33:32.546192Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:33:32.546192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.08931","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ragswPAp2eQFlmTcUU2JwGjgWZKv+9+RFKHQRdlMl80NxcoLjjkjPlvvkrYqrT8H5XXHe03mG927C2NzxxJfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T14:58:25.772264Z"},"content_sha256":"4a6b2d195a7174b79ffee3f3298b7257111ddc3014e8dac76fe1c1848d92d32b","schema_version":"1.0","event_id":"sha256:4a6b2d195a7174b79ffee3f3298b7257111ddc3014e8dac76fe1c1848d92d32b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:KDGOJKEAKMKJGQV73VTO72V3PA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential sum approximations of finite completely monotonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Yohei M. Koyama","submitted_at":"2023-01-21T10:00:54Z","abstract_excerpt":"Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function with a finite positive integral interval of the integral representation. We consider the exponential sum approximation of a finite completely monotonic function based on the Gaussian quadrature with a variable transformation. If the variable transformation is analytic on an open Bernstein ellipse, the maximum absolute error decreases at least geometrically with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.08931","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.08931/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0OKKCjC45WfsVRGHwgiITGhkUxLgJrTaOSWph+pD4c+1ZGOZXJMVLQPZ0xXDgmLda6t7AbkStHjMg/8qI7YPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T14:58:25.772776Z"},"content_sha256":"2262714e3349815738bcadaf603244f53050c6b8aad313e26b8c1884a2d381b0","schema_version":"1.0","event_id":"sha256:2262714e3349815738bcadaf603244f53050c6b8aad313e26b8c1884a2d381b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KDGOJKEAKMKJGQV73VTO72V3PA/bundle.json","state_url":"https://pith.science/pith/KDGOJKEAKMKJGQV73VTO72V3PA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KDGOJKEAKMKJGQV73VTO72V3PA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T14:58:25Z","links":{"resolver":"https://pith.science/pith/KDGOJKEAKMKJGQV73VTO72V3PA","bundle":"https://pith.science/pith/KDGOJKEAKMKJGQV73VTO72V3PA/bundle.json","state":"https://pith.science/pith/KDGOJKEAKMKJGQV73VTO72V3PA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KDGOJKEAKMKJGQV73VTO72V3PA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KDGOJKEAKMKJGQV73VTO72V3PA","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":"0664b2b5d12fda1af61d4db5c4867a464b8748dec414551cdc895e07c76f862f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-01-21T10:00:54Z","title_canon_sha256":"bf0337418440392fb83a5286a7a00182fd090d7c5b0e5c46675545b07e10e6ee"},"schema_version":"1.0","source":{"id":"2301.08931","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.08931","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"2301.08931v3","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.08931","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"KDGOJKEAKMKJ","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_16","alias_value":"KDGOJKEAKMKJGQV7","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_8","alias_value":"KDGOJKEA","created_at":"2026-07-05T06:33:32Z"}],"graph_snapshots":[{"event_id":"sha256:2262714e3349815738bcadaf603244f53050c6b8aad313e26b8c1884a2d381b0","target":"graph","created_at":"2026-07-05T06:33:32Z","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/2301.08931/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function with a finite positive integral interval of the integral representation. We consider the exponential sum approximation of a finite completely monotonic function based on the Gaussian quadrature with a variable transformation. If the variable transformation is analytic on an open Bernstein ellipse, the maximum absolute error decreases at least geometrically with","authors_text":"Yohei M. Koyama","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-01-21T10:00:54Z","title":"Exponential sum approximations of finite completely monotonic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.08931","kind":"arxiv","version":3},"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":"sha256:4a6b2d195a7174b79ffee3f3298b7257111ddc3014e8dac76fe1c1848d92d32b","target":"record","created_at":"2026-07-05T06:33:32Z","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":"0664b2b5d12fda1af61d4db5c4867a464b8748dec414551cdc895e07c76f862f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-01-21T10:00:54Z","title_canon_sha256":"bf0337418440392fb83a5286a7a00182fd090d7c5b0e5c46675545b07e10e6ee"},"schema_version":"1.0","source":{"id":"2301.08931","kind":"arxiv","version":3}},"canonical_sha256":"50cce4a88053149342bfdd66efeabb7827ced4bfedff69b21ebada8a6d9c2897","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50cce4a88053149342bfdd66efeabb7827ced4bfedff69b21ebada8a6d9c2897","first_computed_at":"2026-07-05T06:33:32.546192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:33:32.546192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RzPR/rtMS4J7zZPrNlNNJFXdJRqLlQqRpjueGMxRFz65H779nqSBjLlmWPF4ysXp2g2ZgA6Te1j+7cwuOfyFCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:33:32.546596Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.08931","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a6b2d195a7174b79ffee3f3298b7257111ddc3014e8dac76fe1c1848d92d32b","sha256:2262714e3349815738bcadaf603244f53050c6b8aad313e26b8c1884a2d381b0"],"state_sha256":"c27e97c845c043d0c4917cd27872a3c8340415e5eae284e1cfeb59436fe53f33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHnnSzleB9XbZFqT3kctwF72Hm7dmkXRnAuCTgJIFbaX2+xLvcJWFX89nwFAM5q+jdRXaEJZJzUu8aTyTiDNAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T14:58:25.776943Z","bundle_sha256":"b33a4e17efee42fb63a397a099fdee374398f6de5a57c0db780ddfdf4aca755d"}}