{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GP7262NKHUM4JIFIIZ2LLZVDGY","short_pith_number":"pith:GP7262NK","canonical_record":{"source":{"id":"1504.01318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-06T16:54:59Z","cross_cats_sorted":[],"title_canon_sha256":"369f2558704139ff6ff0b615f949c5a590320f67e75a3e4085c2e2c81b4df7c0","abstract_canon_sha256":"e27502511bf39bc5afdb8139825261aec2c4b74002838405fe2fb195b64301f9"},"schema_version":"1.0"},"canonical_sha256":"33ffaf69aa3d19c4a0a84674b5e6a3361bff10f52bea7521ff538aa5e5fffe88","source":{"kind":"arxiv","id":"1504.01318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01318","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01318v1","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01318","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"GP7262NKHUM4","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GP7262NKHUM4JIFI","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GP7262NK","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GP7262NKHUM4JIFIIZ2LLZVDGY","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-06T16:54:59Z","cross_cats_sorted":[],"title_canon_sha256":"369f2558704139ff6ff0b615f949c5a590320f67e75a3e4085c2e2c81b4df7c0","abstract_canon_sha256":"e27502511bf39bc5afdb8139825261aec2c4b74002838405fe2fb195b64301f9"},"schema_version":"1.0"},"canonical_sha256":"33ffaf69aa3d19c4a0a84674b5e6a3361bff10f52bea7521ff538aa5e5fffe88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:46.213408Z","signature_b64":"2uS5xZ9PIWdtS8zDwxxKx1ein2xu2IQyfuNireeJy1KO0DMqffnpcFTUSgc7x0DBMMf4hWA3Y7OdB7bgJ88pBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33ffaf69aa3d19c4a0a84674b5e6a3361bff10f52bea7521ff538aa5e5fffe88","last_reissued_at":"2026-05-18T00:44:46.213026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:46.213026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01318","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":"2026-05-18T00:44:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zpK3UO82VOtl4z3BSpVwvRM+psMH8Hez/nfaSID7LEYlSfMou2CbLhx5MvdUTjaKxwWmZruSlJJkGzP+FbZRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T00:44:38.902565Z"},"content_sha256":"bf8f817567360d3071fb8131749c1830463b3c5add1224b621079b9e237b78b6","schema_version":"1.0","event_id":"sha256:bf8f817567360d3071fb8131749c1830463b3c5add1224b621079b9e237b78b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GP7262NKHUM4JIFIIZ2LLZVDGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Symbolic Approach to Some Indentities for Bernoulli-Barnes Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christophe Vignat, Lin Jiu, Victor H. Moll","submitted_at":"2015-04-06T16:54:59Z","abstract_excerpt":"A symbolic method is used to establish some properties of the Bernoulli-Barnes polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01318","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":"2026-05-18T00:44:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ixYygV2EHrxR3uW/FDs2z9REIxex9wkIau+4zCBahH56j9F1Ue385nLzcTDpwp3faPcGgYgXJKwwYhyUl/DnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T00:44:38.903208Z"},"content_sha256":"d634d9d57bbe8dc4b14dffc4f4a9034fcc7223879db28583f093f8ede948b27b","schema_version":"1.0","event_id":"sha256:d634d9d57bbe8dc4b14dffc4f4a9034fcc7223879db28583f093f8ede948b27b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GP7262NKHUM4JIFIIZ2LLZVDGY/bundle.json","state_url":"https://pith.science/pith/GP7262NKHUM4JIFIIZ2LLZVDGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GP7262NKHUM4JIFIIZ2LLZVDGY/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":"2026-05-20T00:44:38Z","links":{"resolver":"https://pith.science/pith/GP7262NKHUM4JIFIIZ2LLZVDGY","bundle":"https://pith.science/pith/GP7262NKHUM4JIFIIZ2LLZVDGY/bundle.json","state":"https://pith.science/pith/GP7262NKHUM4JIFIIZ2LLZVDGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GP7262NKHUM4JIFIIZ2LLZVDGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GP7262NKHUM4JIFIIZ2LLZVDGY","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":"e27502511bf39bc5afdb8139825261aec2c4b74002838405fe2fb195b64301f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-06T16:54:59Z","title_canon_sha256":"369f2558704139ff6ff0b615f949c5a590320f67e75a3e4085c2e2c81b4df7c0"},"schema_version":"1.0","source":{"id":"1504.01318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01318","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01318v1","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01318","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"GP7262NKHUM4","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GP7262NKHUM4JIFI","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GP7262NK","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:d634d9d57bbe8dc4b14dffc4f4a9034fcc7223879db28583f093f8ede948b27b","target":"graph","created_at":"2026-05-18T00:44:46Z","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":"A symbolic method is used to establish some properties of the Bernoulli-Barnes polynomials.","authors_text":"Christophe Vignat, Lin Jiu, Victor H. Moll","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-06T16:54:59Z","title":"A Symbolic Approach to Some Indentities for Bernoulli-Barnes Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01318","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:bf8f817567360d3071fb8131749c1830463b3c5add1224b621079b9e237b78b6","target":"record","created_at":"2026-05-18T00:44:46Z","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":"e27502511bf39bc5afdb8139825261aec2c4b74002838405fe2fb195b64301f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-06T16:54:59Z","title_canon_sha256":"369f2558704139ff6ff0b615f949c5a590320f67e75a3e4085c2e2c81b4df7c0"},"schema_version":"1.0","source":{"id":"1504.01318","kind":"arxiv","version":1}},"canonical_sha256":"33ffaf69aa3d19c4a0a84674b5e6a3361bff10f52bea7521ff538aa5e5fffe88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33ffaf69aa3d19c4a0a84674b5e6a3361bff10f52bea7521ff538aa5e5fffe88","first_computed_at":"2026-05-18T00:44:46.213026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:46.213026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2uS5xZ9PIWdtS8zDwxxKx1ein2xu2IQyfuNireeJy1KO0DMqffnpcFTUSgc7x0DBMMf4hWA3Y7OdB7bgJ88pBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:46.213408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf8f817567360d3071fb8131749c1830463b3c5add1224b621079b9e237b78b6","sha256:d634d9d57bbe8dc4b14dffc4f4a9034fcc7223879db28583f093f8ede948b27b"],"state_sha256":"80cf56d4ebc5c6a4d7f8abc9fbcb960691480892486938e77f8f3d8589e13c43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2b9OKHdrcV5DgcEMh2iyIwqXN7a3VN6+ssCa3lhB7BR7e2PHo/yLkKaSpeupFsCUUIqXbiuZIYMnvK1L2sf5Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T00:44:38.906758Z","bundle_sha256":"9099be502f4f30050638b366143af38dbedbbeeceae0db3ec62a9420a171bcc1"}}