{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:M2YMZWWH26TR3OBXNYPMIZ23UL","short_pith_number":"pith:M2YMZWWH","canonical_record":{"source":{"id":"1702.03718","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T10:59:24Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9eba7db3b2dd274449bfcbacf6a7eb35af65ce96655dc6798752d164b670bd9e","abstract_canon_sha256":"7522f644fc8813390c473e31748ea9a832439e2ea025d58c24d5a813ccc9ece3"},"schema_version":"1.0"},"canonical_sha256":"66b0ccdac7d7a71db8376e1ec4675ba2f9f6619a088f47e3b844c79591c03691","source":{"kind":"arxiv","id":"1702.03718","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03718","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03718v2","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03718","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"M2YMZWWH26TR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"M2YMZWWH26TR3OBX","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"M2YMZWWH","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:M2YMZWWH26TR3OBXNYPMIZ23UL","target":"record","payload":{"canonical_record":{"source":{"id":"1702.03718","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T10:59:24Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9eba7db3b2dd274449bfcbacf6a7eb35af65ce96655dc6798752d164b670bd9e","abstract_canon_sha256":"7522f644fc8813390c473e31748ea9a832439e2ea025d58c24d5a813ccc9ece3"},"schema_version":"1.0"},"canonical_sha256":"66b0ccdac7d7a71db8376e1ec4675ba2f9f6619a088f47e3b844c79591c03691","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:13.738819Z","signature_b64":"KHu/Cv+hd7DMa/+PvhhW2mB7200NS+TWEeXr2mlr/nL3oVpOd0tQ/03CFiXhYgOKBIFdyVIm3f3qfeYMjJGPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66b0ccdac7d7a71db8376e1ec4675ba2f9f6619a088f47e3b844c79591c03691","last_reissued_at":"2026-05-18T00:38:13.738136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:13.738136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.03718","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PEqPVcw3NORd+lz2SwI4Ddsf3ZuV0vZtufPuxlUyopqajc5AJ4w35wDUHE5QbNRoEuuvRTw/NSsNAV1o5sAiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T21:24:30.903828Z"},"content_sha256":"91fa65d3beaf97f8bb2afd80846ef3872abaafb25ebad4a36a9d89844c57d588","schema_version":"1.0","event_id":"sha256:91fa65d3beaf97f8bb2afd80846ef3872abaafb25ebad4a36a9d89844c57d588"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:M2YMZWWH26TR3OBXNYPMIZ23UL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Roman harmonic numbers revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Javier Sesma","submitted_at":"2017-02-13T10:59:24Z","abstract_excerpt":"Two decades ago, Steven Roman, Daniel E. Loeb and Gian-Carlo Rota introduced a family of harmonic numbers in their study of harmonic logarithms. We propose to refer to those numbers as {\\it Roman harmonic numbers}. With the purpose of revitalizing the study of these mathematical objects, we recall here their known properties and unveil additional ones. An integral representation, several generating relations, and a collection of sum rules involving those numbers are presented. It is also shown that higher derivatives of the Pochhammer and reciprocal Pochhammer symbols are easily expressed in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03718","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tq5GIsHgLjNHvMKQrIvgvR0eF1jYtO3y3Dm3de7O/7izkyd2yI3RobAlTJDvbMmMuLpXyQDcOM+NKO3etNNmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T21:24:30.904174Z"},"content_sha256":"cac95f07dab8e753537279c2410cb5298a20f53eb876025696c2bc23e600af9a","schema_version":"1.0","event_id":"sha256:cac95f07dab8e753537279c2410cb5298a20f53eb876025696c2bc23e600af9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2YMZWWH26TR3OBXNYPMIZ23UL/bundle.json","state_url":"https://pith.science/pith/M2YMZWWH26TR3OBXNYPMIZ23UL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2YMZWWH26TR3OBXNYPMIZ23UL/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":"2026-06-29T21:24:30Z","links":{"resolver":"https://pith.science/pith/M2YMZWWH26TR3OBXNYPMIZ23UL","bundle":"https://pith.science/pith/M2YMZWWH26TR3OBXNYPMIZ23UL/bundle.json","state":"https://pith.science/pith/M2YMZWWH26TR3OBXNYPMIZ23UL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2YMZWWH26TR3OBXNYPMIZ23UL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M2YMZWWH26TR3OBXNYPMIZ23UL","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":"7522f644fc8813390c473e31748ea9a832439e2ea025d58c24d5a813ccc9ece3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T10:59:24Z","title_canon_sha256":"9eba7db3b2dd274449bfcbacf6a7eb35af65ce96655dc6798752d164b670bd9e"},"schema_version":"1.0","source":{"id":"1702.03718","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03718","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03718v2","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03718","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"M2YMZWWH26TR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"M2YMZWWH26TR3OBX","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"M2YMZWWH","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:cac95f07dab8e753537279c2410cb5298a20f53eb876025696c2bc23e600af9a","target":"graph","created_at":"2026-05-18T00:38:13Z","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"},"paper":{"abstract_excerpt":"Two decades ago, Steven Roman, Daniel E. Loeb and Gian-Carlo Rota introduced a family of harmonic numbers in their study of harmonic logarithms. We propose to refer to those numbers as {\\it Roman harmonic numbers}. With the purpose of revitalizing the study of these mathematical objects, we recall here their known properties and unveil additional ones. An integral representation, several generating relations, and a collection of sum rules involving those numbers are presented. It is also shown that higher derivatives of the Pochhammer and reciprocal Pochhammer symbols are easily expressed in t","authors_text":"Javier Sesma","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T10:59:24Z","title":"The Roman harmonic numbers revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03718","kind":"arxiv","version":2},"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":"sha256:91fa65d3beaf97f8bb2afd80846ef3872abaafb25ebad4a36a9d89844c57d588","target":"record","created_at":"2026-05-18T00:38:13Z","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":"7522f644fc8813390c473e31748ea9a832439e2ea025d58c24d5a813ccc9ece3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T10:59:24Z","title_canon_sha256":"9eba7db3b2dd274449bfcbacf6a7eb35af65ce96655dc6798752d164b670bd9e"},"schema_version":"1.0","source":{"id":"1702.03718","kind":"arxiv","version":2}},"canonical_sha256":"66b0ccdac7d7a71db8376e1ec4675ba2f9f6619a088f47e3b844c79591c03691","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66b0ccdac7d7a71db8376e1ec4675ba2f9f6619a088f47e3b844c79591c03691","first_computed_at":"2026-05-18T00:38:13.738136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:13.738136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KHu/Cv+hd7DMa/+PvhhW2mB7200NS+TWEeXr2mlr/nL3oVpOd0tQ/03CFiXhYgOKBIFdyVIm3f3qfeYMjJGPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:13.738819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03718","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91fa65d3beaf97f8bb2afd80846ef3872abaafb25ebad4a36a9d89844c57d588","sha256:cac95f07dab8e753537279c2410cb5298a20f53eb876025696c2bc23e600af9a"],"state_sha256":"3d09873faf01b523640206218f56ec31049deaaecbe055b9c4f11bdeb66cafb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yGFS8VkEMdDad4MSeUOF8nvS1Gn4IvF0EXq9UnWocsACAYm4Ft3pUKE4zfumXXlIrWy3qXUEiwmGiN5aH6imDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T21:24:30.906298Z","bundle_sha256":"53039952a5b4c8c75e7a9253c13507605bbfebd9b7268b112e529023b18501f8"}}