{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VFW7Q54SEA3EZKXTHRWTWSU6H3","short_pith_number":"pith:VFW7Q54S","canonical_record":{"source":{"id":"2412.15913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-20T14:05:04Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"6c13ef042b0cc7c9e27a371a3ab7e480e4cc38c575a4e8f86fdb761ee12d5e86","abstract_canon_sha256":"c89f740de8be017497a6f5331533e2269e1e4b009640ae8e5d9d91586b7917ae"},"schema_version":"1.0"},"canonical_sha256":"a96df8779220364caaf33c6d3b4a9e3ef27c66860a2a256af2d3aa6e15bd1f53","source":{"kind":"arxiv","id":"2412.15913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15913","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15913v1","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15913","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"VFW7Q54SEA3E","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"pith_short_16","alias_value":"VFW7Q54SEA3EZKXT","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"pith_short_8","alias_value":"VFW7Q54S","created_at":"2026-07-05T09:52:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VFW7Q54SEA3EZKXTHRWTWSU6H3","target":"record","payload":{"canonical_record":{"source":{"id":"2412.15913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-20T14:05:04Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"6c13ef042b0cc7c9e27a371a3ab7e480e4cc38c575a4e8f86fdb761ee12d5e86","abstract_canon_sha256":"c89f740de8be017497a6f5331533e2269e1e4b009640ae8e5d9d91586b7917ae"},"schema_version":"1.0"},"canonical_sha256":"a96df8779220364caaf33c6d3b4a9e3ef27c66860a2a256af2d3aa6e15bd1f53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:31.981697Z","signature_b64":"G7UWcqrhUQ70WetSGr4K/CfRAUtyCaXrbEbPMnT7LvDF9wENOFD0FssWKqfAfh+b0BiJLuArKIGI7mP83gLZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a96df8779220364caaf33c6d3b4a9e3ef27c66860a2a256af2d3aa6e15bd1f53","last_reissued_at":"2026-07-05T09:52:31.981326Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:31.981326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.15913","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":"2026-07-05T09:52:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7zwxUEvjA0DPFT6kjxgqD57j8OO2b5vAl7NYBJPc9zY8jp+W8Bcf2bEyW9xysXkqCw8v3f7Z4Qq6wefhalA/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:57:25.601599Z"},"content_sha256":"786db107d18f4408c453e1575a59a1385af9f83c4260229d9239bb2bf4fa9689","schema_version":"1.0","event_id":"sha256:786db107d18f4408c453e1575a59a1385af9f83c4260229d9239bb2bf4fa9689"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VFW7Q54SEA3EZKXTHRWTWSU6H3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonexistence of phantom categories on very general noncommutative projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Koshiro Murai","submitted_at":"2024-12-20T14:05:04Z","abstract_excerpt":"We show that very general noncommutative projective planes do not admit phantom categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15913","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/2412.15913/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":"2026-07-05T09:52:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m9WfCzCtotIhsjM8Y3RIyuPcdUaHdaC20jfcW3D2tyFpHG2H1O5+JSD+ZnAcw3Sjs7l5lvQnR9CfktWIr5BnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:57:25.602159Z"},"content_sha256":"f2a5c0492caa4a321f2d2f8ec856ff2f5300a104598364c29e1cc0118d24e010","schema_version":"1.0","event_id":"sha256:f2a5c0492caa4a321f2d2f8ec856ff2f5300a104598364c29e1cc0118d24e010"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFW7Q54SEA3EZKXTHRWTWSU6H3/bundle.json","state_url":"https://pith.science/pith/VFW7Q54SEA3EZKXTHRWTWSU6H3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFW7Q54SEA3EZKXTHRWTWSU6H3/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":"2026-08-12T22:57:25Z","links":{"resolver":"https://pith.science/pith/VFW7Q54SEA3EZKXTHRWTWSU6H3","bundle":"https://pith.science/pith/VFW7Q54SEA3EZKXTHRWTWSU6H3/bundle.json","state":"https://pith.science/pith/VFW7Q54SEA3EZKXTHRWTWSU6H3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFW7Q54SEA3EZKXTHRWTWSU6H3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VFW7Q54SEA3EZKXTHRWTWSU6H3","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":"c89f740de8be017497a6f5331533e2269e1e4b009640ae8e5d9d91586b7917ae","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-20T14:05:04Z","title_canon_sha256":"6c13ef042b0cc7c9e27a371a3ab7e480e4cc38c575a4e8f86fdb761ee12d5e86"},"schema_version":"1.0","source":{"id":"2412.15913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15913","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15913v1","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15913","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"VFW7Q54SEA3E","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"pith_short_16","alias_value":"VFW7Q54SEA3EZKXT","created_at":"2026-07-05T09:52:31Z"},{"alias_kind":"pith_short_8","alias_value":"VFW7Q54S","created_at":"2026-07-05T09:52:31Z"}],"graph_snapshots":[{"event_id":"sha256:f2a5c0492caa4a321f2d2f8ec856ff2f5300a104598364c29e1cc0118d24e010","target":"graph","created_at":"2026-07-05T09:52:31Z","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/2412.15913/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that very general noncommutative projective planes do not admit phantom categories.","authors_text":"Koshiro Murai","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-20T14:05:04Z","title":"Nonexistence of phantom categories on very general noncommutative projective planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15913","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":"sha256:786db107d18f4408c453e1575a59a1385af9f83c4260229d9239bb2bf4fa9689","target":"record","created_at":"2026-07-05T09:52:31Z","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":"c89f740de8be017497a6f5331533e2269e1e4b009640ae8e5d9d91586b7917ae","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-20T14:05:04Z","title_canon_sha256":"6c13ef042b0cc7c9e27a371a3ab7e480e4cc38c575a4e8f86fdb761ee12d5e86"},"schema_version":"1.0","source":{"id":"2412.15913","kind":"arxiv","version":1}},"canonical_sha256":"a96df8779220364caaf33c6d3b4a9e3ef27c66860a2a256af2d3aa6e15bd1f53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a96df8779220364caaf33c6d3b4a9e3ef27c66860a2a256af2d3aa6e15bd1f53","first_computed_at":"2026-07-05T09:52:31.981326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:31.981326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G7UWcqrhUQ70WetSGr4K/CfRAUtyCaXrbEbPMnT7LvDF9wENOFD0FssWKqfAfh+b0BiJLuArKIGI7mP83gLZAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:31.981697Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.15913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:786db107d18f4408c453e1575a59a1385af9f83c4260229d9239bb2bf4fa9689","sha256:f2a5c0492caa4a321f2d2f8ec856ff2f5300a104598364c29e1cc0118d24e010"],"state_sha256":"6833ada74047e97e3c48abee87beb22871e24e10b457cb65b34f9d0a6715f1fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T1pbK6oP/vdEQNLdBVW31SG+Jgo14oK6GDxLDXo6eUICBXiSw62psXo6/SF2bpypifZvUyC3ZOMNqLjfYhjZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:57:25.605792Z","bundle_sha256":"d0fa57709034c78123469597190fb502764266697a5ca548771b298f0346342d"}}