{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HGVLWTCHE4NJAUNA4RGNJWBB2H","short_pith_number":"pith:HGVLWTCH","canonical_record":{"source":{"id":"1012.3934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-17T17:34:20Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0db8b9b9d419987a73fbc69fe4b11c21e5017a5fabc10353415186e733aa9839","abstract_canon_sha256":"a7c83fc88af3f1755e5ba8c4a8d8ef3d6cb74f3293616c46ead905cb68cf03c5"},"schema_version":"1.0"},"canonical_sha256":"39aabb4c47271a9051a0e44cd4d821d1e41cdc3098323c44ec1ff711f8e0e311","source":{"kind":"arxiv","id":"1012.3934","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3934","created_at":"2026-05-18T04:33:03Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3934v1","created_at":"2026-05-18T04:33:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3934","created_at":"2026-05-18T04:33:03Z"},{"alias_kind":"pith_short_12","alias_value":"HGVLWTCHE4NJ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HGVLWTCHE4NJAUNA","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HGVLWTCH","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HGVLWTCHE4NJAUNA4RGNJWBB2H","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-17T17:34:20Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0db8b9b9d419987a73fbc69fe4b11c21e5017a5fabc10353415186e733aa9839","abstract_canon_sha256":"a7c83fc88af3f1755e5ba8c4a8d8ef3d6cb74f3293616c46ead905cb68cf03c5"},"schema_version":"1.0"},"canonical_sha256":"39aabb4c47271a9051a0e44cd4d821d1e41cdc3098323c44ec1ff711f8e0e311","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:03.586243Z","signature_b64":"l7noWKtwQk1BmkLsduDgWA/4n2US0nYekKbfhlgIlDR7Udto9QgUsLm30XkzCyA+0UMsKhBGi9JVT7DwLBE9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39aabb4c47271a9051a0e44cd4d821d1e41cdc3098323c44ec1ff711f8e0e311","last_reissued_at":"2026-05-18T04:33:03.585747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:03.585747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3934","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+FCzT5kAY1av0EK2MPtieZmSWeq83aoB4J9kPOC5FxPVGdureU3necohoFyR+s2q340puFmKpov4wo7WbT+FCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:57:17.637176Z"},"content_sha256":"36bb29534d8f878a254601a47465d5adce41900fb81322c7bf81f7cb0c6a9c62","schema_version":"1.0","event_id":"sha256:36bb29534d8f878a254601a47465d5adce41900fb81322c7bf81f7cb0c6a9c62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HGVLWTCHE4NJAUNA4RGNJWBB2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some inversion formulas and formulas for Stirling numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Zhi-Hong Sun","submitted_at":"2010-12-17T17:34:20Z","abstract_excerpt":"In the paper we present some new inversion formulas and two new formulas for Stirling numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3934","kind":"arxiv","version":1},"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":"2026-05-18T04:33:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ihV72QlOiJtLSIsN65SbIusSudouxjkKjf4MNUHiwmDXN3lc/dbDhZ9JbCrUG3oTmlekPqSzsaLPUub0qT7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:57:17.637538Z"},"content_sha256":"a9bd1d77eb0ae4164279ff965d6be66f1675560a36decb2f371ca30d2a978d73","schema_version":"1.0","event_id":"sha256:a9bd1d77eb0ae4164279ff965d6be66f1675560a36decb2f371ca30d2a978d73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HGVLWTCHE4NJAUNA4RGNJWBB2H/bundle.json","state_url":"https://pith.science/pith/HGVLWTCHE4NJAUNA4RGNJWBB2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HGVLWTCHE4NJAUNA4RGNJWBB2H/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":"2026-06-29T22:57:17Z","links":{"resolver":"https://pith.science/pith/HGVLWTCHE4NJAUNA4RGNJWBB2H","bundle":"https://pith.science/pith/HGVLWTCHE4NJAUNA4RGNJWBB2H/bundle.json","state":"https://pith.science/pith/HGVLWTCHE4NJAUNA4RGNJWBB2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HGVLWTCHE4NJAUNA4RGNJWBB2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HGVLWTCHE4NJAUNA4RGNJWBB2H","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":"a7c83fc88af3f1755e5ba8c4a8d8ef3d6cb74f3293616c46ead905cb68cf03c5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-17T17:34:20Z","title_canon_sha256":"0db8b9b9d419987a73fbc69fe4b11c21e5017a5fabc10353415186e733aa9839"},"schema_version":"1.0","source":{"id":"1012.3934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3934","created_at":"2026-05-18T04:33:03Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3934v1","created_at":"2026-05-18T04:33:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3934","created_at":"2026-05-18T04:33:03Z"},{"alias_kind":"pith_short_12","alias_value":"HGVLWTCHE4NJ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HGVLWTCHE4NJAUNA","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HGVLWTCH","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:a9bd1d77eb0ae4164279ff965d6be66f1675560a36decb2f371ca30d2a978d73","target":"graph","created_at":"2026-05-18T04:33:03Z","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":"In the paper we present some new inversion formulas and two new formulas for Stirling numbers.","authors_text":"Zhi-Hong Sun","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-17T17:34:20Z","title":"Some inversion formulas and formulas for Stirling numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3934","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":"sha256:36bb29534d8f878a254601a47465d5adce41900fb81322c7bf81f7cb0c6a9c62","target":"record","created_at":"2026-05-18T04:33:03Z","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":"a7c83fc88af3f1755e5ba8c4a8d8ef3d6cb74f3293616c46ead905cb68cf03c5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-17T17:34:20Z","title_canon_sha256":"0db8b9b9d419987a73fbc69fe4b11c21e5017a5fabc10353415186e733aa9839"},"schema_version":"1.0","source":{"id":"1012.3934","kind":"arxiv","version":1}},"canonical_sha256":"39aabb4c47271a9051a0e44cd4d821d1e41cdc3098323c44ec1ff711f8e0e311","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39aabb4c47271a9051a0e44cd4d821d1e41cdc3098323c44ec1ff711f8e0e311","first_computed_at":"2026-05-18T04:33:03.585747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:03.585747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l7noWKtwQk1BmkLsduDgWA/4n2US0nYekKbfhlgIlDR7Udto9QgUsLm30XkzCyA+0UMsKhBGi9JVT7DwLBE9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:03.586243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36bb29534d8f878a254601a47465d5adce41900fb81322c7bf81f7cb0c6a9c62","sha256:a9bd1d77eb0ae4164279ff965d6be66f1675560a36decb2f371ca30d2a978d73"],"state_sha256":"16e72f04b6b1b158ea6fae82986427248e3cadb8806f5e5f3ea53ebb3ff2a71d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VL26R08VUkPQxFovqlnS6//ss5MRRKhkbHuelM4wRWRVUjhY+2eDz9lYeLqtfJu0cnNK/H4cV/3/RCwI48q7AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T22:57:17.639478Z","bundle_sha256":"639c2a7846cc746d0377d48ebeb9643f490b96a8adc43b651146dd88c7ed4f0d"}}