{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z2XYODBFP5CS3E46CVBR7BMWJR","short_pith_number":"pith:Z2XYODBF","canonical_record":{"source":{"id":"1304.1331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-04-04T11:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"aa1cefba7a7480f9b114d6d906588faf9a587415b9c8879f24db27ed33d58078","abstract_canon_sha256":"5cd3017d1d0dbb59977b8392990e3138f5fee1c28e42b6a75bd47dbb24d5d4fb"},"schema_version":"1.0"},"canonical_sha256":"ceaf870c257f452d939e15431f85964c4494ff1d10f815ee1a57a33128394591","source":{"kind":"arxiv","id":"1304.1331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1331","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1331v1","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1331","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z2XYODBFP5CS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z2XYODBFP5CS3E46","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z2XYODBF","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z2XYODBFP5CS3E46CVBR7BMWJR","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-04-04T11:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"aa1cefba7a7480f9b114d6d906588faf9a587415b9c8879f24db27ed33d58078","abstract_canon_sha256":"5cd3017d1d0dbb59977b8392990e3138f5fee1c28e42b6a75bd47dbb24d5d4fb"},"schema_version":"1.0"},"canonical_sha256":"ceaf870c257f452d939e15431f85964c4494ff1d10f815ee1a57a33128394591","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:53.149915Z","signature_b64":"hqUWZCGwv9VBpavo3hmFQXO0uIFaaV/IQXbIbDYczz908r1XR1N62IkEwVQFg41U0aTsRaIZLEeu3Kx0CGA6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceaf870c257f452d939e15431f85964c4494ff1d10f815ee1a57a33128394591","last_reissued_at":"2026-05-18T02:26:53.149541Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:53.149541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1331","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":"2026-05-18T02:26:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ctg3nBvIV1TrFBKt+6t+T5+EPWhxoq0vToiUBUC3fGHM2OvFlZbVdLXA75ju3IzsWJrOE1pVLD67m0j+u87CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:44:24.340657Z"},"content_sha256":"36ac813c5ed62037ee64e41dfefc28cc5ad1c20aa54ec27faf7d0d5ed861498b","schema_version":"1.0","event_id":"sha256:36ac813c5ed62037ee64e41dfefc28cc5ad1c20aa54ec27faf7d0d5ed861498b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z2XYODBFP5CS3E46CVBR7BMWJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A decomposition formula for the weighted commutator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Nelson Martins-Ferreira, Tim Van der Linden","submitted_at":"2013-04-04T11:42:57Z","abstract_excerpt":"We decompose the weighted subobject commutator of M. Gran, G. Janelidze and A. Ursini as a join of a binary and a ternary commutator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1331","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":"2026-05-18T02:26:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5nafpNDCtPuYOL3dDZF2HtyroUNmgR7SnbD8zGxJmHn5F/SLYz/58PDG241u8/qmHryPiKQQfPNCSqyQtfU6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:44:24.341335Z"},"content_sha256":"c4b3fa7c16a2cb97dcedb51a01706057df63bf2532f543ee9b0ffe54d7f04ff4","schema_version":"1.0","event_id":"sha256:c4b3fa7c16a2cb97dcedb51a01706057df63bf2532f543ee9b0ffe54d7f04ff4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2XYODBFP5CS3E46CVBR7BMWJR/bundle.json","state_url":"https://pith.science/pith/Z2XYODBFP5CS3E46CVBR7BMWJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2XYODBFP5CS3E46CVBR7BMWJR/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":"2026-05-26T08:44:24Z","links":{"resolver":"https://pith.science/pith/Z2XYODBFP5CS3E46CVBR7BMWJR","bundle":"https://pith.science/pith/Z2XYODBFP5CS3E46CVBR7BMWJR/bundle.json","state":"https://pith.science/pith/Z2XYODBFP5CS3E46CVBR7BMWJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2XYODBFP5CS3E46CVBR7BMWJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z2XYODBFP5CS3E46CVBR7BMWJR","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":"5cd3017d1d0dbb59977b8392990e3138f5fee1c28e42b6a75bd47dbb24d5d4fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-04-04T11:42:57Z","title_canon_sha256":"aa1cefba7a7480f9b114d6d906588faf9a587415b9c8879f24db27ed33d58078"},"schema_version":"1.0","source":{"id":"1304.1331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1331","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1331v1","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1331","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z2XYODBFP5CS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z2XYODBFP5CS3E46","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z2XYODBF","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:c4b3fa7c16a2cb97dcedb51a01706057df63bf2532f543ee9b0ffe54d7f04ff4","target":"graph","created_at":"2026-05-18T02:26:53Z","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":"We decompose the weighted subobject commutator of M. Gran, G. Janelidze and A. Ursini as a join of a binary and a ternary commutator.","authors_text":"Nelson Martins-Ferreira, Tim Van der Linden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-04-04T11:42:57Z","title":"A decomposition formula for the weighted commutator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1331","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":"sha256:36ac813c5ed62037ee64e41dfefc28cc5ad1c20aa54ec27faf7d0d5ed861498b","target":"record","created_at":"2026-05-18T02:26:53Z","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":"5cd3017d1d0dbb59977b8392990e3138f5fee1c28e42b6a75bd47dbb24d5d4fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-04-04T11:42:57Z","title_canon_sha256":"aa1cefba7a7480f9b114d6d906588faf9a587415b9c8879f24db27ed33d58078"},"schema_version":"1.0","source":{"id":"1304.1331","kind":"arxiv","version":1}},"canonical_sha256":"ceaf870c257f452d939e15431f85964c4494ff1d10f815ee1a57a33128394591","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceaf870c257f452d939e15431f85964c4494ff1d10f815ee1a57a33128394591","first_computed_at":"2026-05-18T02:26:53.149541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:53.149541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hqUWZCGwv9VBpavo3hmFQXO0uIFaaV/IQXbIbDYczz908r1XR1N62IkEwVQFg41U0aTsRaIZLEeu3Kx0CGA6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:53.149915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36ac813c5ed62037ee64e41dfefc28cc5ad1c20aa54ec27faf7d0d5ed861498b","sha256:c4b3fa7c16a2cb97dcedb51a01706057df63bf2532f543ee9b0ffe54d7f04ff4"],"state_sha256":"5236f09591cc43606e1d6edb2444b6afdd21a92aad7efec1b01877e8267e6078"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7FMtPezUdc8xbFiPeFsmvw0EAukvM80xLxScuhmgKBKQ9eqP0qMb18Vx+EjAK8GTK2ckc1o0Xll8rDehwNwtCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:44:24.344539Z","bundle_sha256":"8a3d3a8d166b66b24d15820882e7e93b741621d68ef417899e911733ae597a98"}}