{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:T4PWIIYQWDKLI73PKDX7OU3LH3","short_pith_number":"pith:T4PWIIYQ","canonical_record":{"source":{"id":"2004.08512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-18T02:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"4b105804ee3839a7ce5d5bfffceaa5e08d59d0c708771f3015dd683181156f36","abstract_canon_sha256":"0c037cfb875049dfa1b569ce09c9fb289b2ed817ef96dc079c3be592fd096789"},"schema_version":"1.0"},"canonical_sha256":"9f1f642310b0d4b47f6f50eff7536b3ee093a676dc47ca51daf14defa60ce325","source":{"kind":"arxiv","id":"2004.08512","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.08512","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"2004.08512v1","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.08512","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"T4PWIIYQWDKL","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"pith_short_16","alias_value":"T4PWIIYQWDKLI73P","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"pith_short_8","alias_value":"T4PWIIYQ","created_at":"2026-07-05T00:56:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:T4PWIIYQWDKLI73PKDX7OU3LH3","target":"record","payload":{"canonical_record":{"source":{"id":"2004.08512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-18T02:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"4b105804ee3839a7ce5d5bfffceaa5e08d59d0c708771f3015dd683181156f36","abstract_canon_sha256":"0c037cfb875049dfa1b569ce09c9fb289b2ed817ef96dc079c3be592fd096789"},"schema_version":"1.0"},"canonical_sha256":"9f1f642310b0d4b47f6f50eff7536b3ee093a676dc47ca51daf14defa60ce325","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:56:06.602049Z","signature_b64":"5nJYhqqNuOu0HzivJYIZOK22B2/wK3emk4Bq/AW4NH+h38nK7kBhTYWzajoigRF1jvWJlWWw2lwGKbqS0zKaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f1f642310b0d4b47f6f50eff7536b3ee093a676dc47ca51daf14defa60ce325","last_reissued_at":"2026-07-05T00:56:06.601640Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:56:06.601640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.08512","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":"2026-07-05T00:56:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PdRV+qOWED7n3zaQ+/bJObpbYczeJmGibacb1c+UCR+g7+g0jaLRciN7MGycSAvSH52Xo0dxAok5glKnpBTSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T03:43:24.989423Z"},"content_sha256":"4e2e736192ae3fad097ffd4d3777af6458b8937952ca6846b71fcd9155f4a7b3","schema_version":"1.0","event_id":"sha256:4e2e736192ae3fad097ffd4d3777af6458b8937952ca6846b71fcd9155f4a7b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:T4PWIIYQWDKLI73PKDX7OU3LH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The index of nilpotent Lie poset algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Nicholas Mayers, Nicholas Russoniello, Vincent Coll","submitted_at":"2020-04-18T02:58:58Z","abstract_excerpt":"We establish combinatorial formulas for the index of a class of matrix Lie algebras whose matrix forms are encoded by strict partial orderings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.08512","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.08512/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":"2026-07-05T00:56:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUc99UKuoUd8GvQASsXuzBA5OsNP0+60J/rkUVnQAlPU4w7/abNCoyV3z3/5lChRIxqHLU7yKZuyzIyIEkGMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T03:43:24.989980Z"},"content_sha256":"49ed04aadd4ac1f26ea8b309dfc52e291ceca32b62a5e48d6b250a81b3413dc3","schema_version":"1.0","event_id":"sha256:49ed04aadd4ac1f26ea8b309dfc52e291ceca32b62a5e48d6b250a81b3413dc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4PWIIYQWDKLI73PKDX7OU3LH3/bundle.json","state_url":"https://pith.science/pith/T4PWIIYQWDKLI73PKDX7OU3LH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4PWIIYQWDKLI73PKDX7OU3LH3/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":"2026-08-24T03:43:24Z","links":{"resolver":"https://pith.science/pith/T4PWIIYQWDKLI73PKDX7OU3LH3","bundle":"https://pith.science/pith/T4PWIIYQWDKLI73PKDX7OU3LH3/bundle.json","state":"https://pith.science/pith/T4PWIIYQWDKLI73PKDX7OU3LH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4PWIIYQWDKLI73PKDX7OU3LH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:T4PWIIYQWDKLI73PKDX7OU3LH3","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":"0c037cfb875049dfa1b569ce09c9fb289b2ed817ef96dc079c3be592fd096789","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-18T02:58:58Z","title_canon_sha256":"4b105804ee3839a7ce5d5bfffceaa5e08d59d0c708771f3015dd683181156f36"},"schema_version":"1.0","source":{"id":"2004.08512","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.08512","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"2004.08512v1","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.08512","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"T4PWIIYQWDKL","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"pith_short_16","alias_value":"T4PWIIYQWDKLI73P","created_at":"2026-07-05T00:56:06Z"},{"alias_kind":"pith_short_8","alias_value":"T4PWIIYQ","created_at":"2026-07-05T00:56:06Z"}],"graph_snapshots":[{"event_id":"sha256:49ed04aadd4ac1f26ea8b309dfc52e291ceca32b62a5e48d6b250a81b3413dc3","target":"graph","created_at":"2026-07-05T00:56:06Z","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/2004.08512/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish combinatorial formulas for the index of a class of matrix Lie algebras whose matrix forms are encoded by strict partial orderings.","authors_text":"Nicholas Mayers, Nicholas Russoniello, Vincent Coll","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-18T02:58:58Z","title":"The index of nilpotent Lie poset algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.08512","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":"sha256:4e2e736192ae3fad097ffd4d3777af6458b8937952ca6846b71fcd9155f4a7b3","target":"record","created_at":"2026-07-05T00:56:06Z","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":"0c037cfb875049dfa1b569ce09c9fb289b2ed817ef96dc079c3be592fd096789","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-18T02:58:58Z","title_canon_sha256":"4b105804ee3839a7ce5d5bfffceaa5e08d59d0c708771f3015dd683181156f36"},"schema_version":"1.0","source":{"id":"2004.08512","kind":"arxiv","version":1}},"canonical_sha256":"9f1f642310b0d4b47f6f50eff7536b3ee093a676dc47ca51daf14defa60ce325","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f1f642310b0d4b47f6f50eff7536b3ee093a676dc47ca51daf14defa60ce325","first_computed_at":"2026-07-05T00:56:06.601640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:56:06.601640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5nJYhqqNuOu0HzivJYIZOK22B2/wK3emk4Bq/AW4NH+h38nK7kBhTYWzajoigRF1jvWJlWWw2lwGKbqS0zKaBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:56:06.602049Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.08512","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e2e736192ae3fad097ffd4d3777af6458b8937952ca6846b71fcd9155f4a7b3","sha256:49ed04aadd4ac1f26ea8b309dfc52e291ceca32b62a5e48d6b250a81b3413dc3"],"state_sha256":"368340441978de39db7c103a3e7b74905c214ba9c8cea3213423f587e4f34481"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vy5WnAQ2Kpj3sD+4NAm/c1ecPKEb4X4Ve3ngCsvdlPN4obpo3BWkXs7C3V9K5N8FzUqaE+YN1HaLj/+UqatWDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T03:43:24.995520Z","bundle_sha256":"8ff1887b02b0528f43b2772c46db5ef613a3796e65ca0425b856cb41cd976529"}}