{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3OKOOPS45YYCJGQYD3NB7EO4M3","short_pith_number":"pith:3OKOOPS4","canonical_record":{"source":{"id":"2505.21373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-05-27T16:04:35Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"88a13e922ced35422fd79438be44edba52b26afdab5b829c7f52ca5f25f28361","abstract_canon_sha256":"d4cf7237642ffbcfbb36890ee1ca6816f1e24d2dcb74f1feb8c40ccd74db999a"},"schema_version":"1.0"},"canonical_sha256":"db94e73e5cee30249a181eda1f91dc66e7d7c1b139e4896b73b584f8e92fbd0b","source":{"kind":"arxiv","id":"2505.21373","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21373","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21373v1","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21373","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"pith_short_12","alias_value":"3OKOOPS45YYC","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"pith_short_16","alias_value":"3OKOOPS45YYCJGQY","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"pith_short_8","alias_value":"3OKOOPS4","created_at":"2026-07-05T11:10:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3OKOOPS45YYCJGQYD3NB7EO4M3","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-05-27T16:04:35Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"88a13e922ced35422fd79438be44edba52b26afdab5b829c7f52ca5f25f28361","abstract_canon_sha256":"d4cf7237642ffbcfbb36890ee1ca6816f1e24d2dcb74f1feb8c40ccd74db999a"},"schema_version":"1.0"},"canonical_sha256":"db94e73e5cee30249a181eda1f91dc66e7d7c1b139e4896b73b584f8e92fbd0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:40.930643Z","signature_b64":"yDC6HnTUdU0IrRbecuG+TVntoxzcr5FrXcJvpkkJIdUrsTOVVkz2qaZLogOfCFrYSkSBUReP9SaEPJbSRq44DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db94e73e5cee30249a181eda1f91dc66e7d7c1b139e4896b73b584f8e92fbd0b","last_reissued_at":"2026-07-05T11:10:40.930139Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:40.930139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21373","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":"2026-07-05T11:10:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"20EAAN5Hmg6KiyZqqrS63aCYcdYnNCCpXTvjJtPh9K3VgRDWaR8ovlhaOS2zvg7UQJ+ZvdcV4RXQtXFqdzCwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:54:22.758599Z"},"content_sha256":"0e59a9511b32f0b6fd0a670fd57a2c77eaf36d4fc759c8837c2255365f7b1c38","schema_version":"1.0","event_id":"sha256:0e59a9511b32f0b6fd0a670fd57a2c77eaf36d4fc759c8837c2255365f7b1c38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3OKOOPS45YYCJGQYD3NB7EO4M3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Restricted (2+1)-TQFTs supported by thickened and solid tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.GT","authors_text":"Danica Kosanovi\\'c, Du\\v{s}an {\\DJ}or{\\dj}evi\\'c, Jovana Nikoli\\'c, Zoran Petri\\'c","submitted_at":"2025-05-27T16:04:35Z","abstract_excerpt":"A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distinguishable by quantum invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21373","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/2505.21373/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":"2026-07-05T11:10:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYeHoHn25igrAk2yA2D0Gm8eSv6cj8Lefy3kPQ1xd3fqL6PiAAuFEIt+O+2OPWaocXmV5vkYjfzUEA/TO6l8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:54:22.759909Z"},"content_sha256":"b4e41f57648d22f95fc10daaeb3494841811969533f7c31253b613ab3ec09fcc","schema_version":"1.0","event_id":"sha256:b4e41f57648d22f95fc10daaeb3494841811969533f7c31253b613ab3ec09fcc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3OKOOPS45YYCJGQYD3NB7EO4M3/bundle.json","state_url":"https://pith.science/pith/3OKOOPS45YYCJGQYD3NB7EO4M3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3OKOOPS45YYCJGQYD3NB7EO4M3/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":"2026-08-08T13:54:22Z","links":{"resolver":"https://pith.science/pith/3OKOOPS45YYCJGQYD3NB7EO4M3","bundle":"https://pith.science/pith/3OKOOPS45YYCJGQYD3NB7EO4M3/bundle.json","state":"https://pith.science/pith/3OKOOPS45YYCJGQYD3NB7EO4M3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3OKOOPS45YYCJGQYD3NB7EO4M3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3OKOOPS45YYCJGQYD3NB7EO4M3","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":"d4cf7237642ffbcfbb36890ee1ca6816f1e24d2dcb74f1feb8c40ccd74db999a","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-05-27T16:04:35Z","title_canon_sha256":"88a13e922ced35422fd79438be44edba52b26afdab5b829c7f52ca5f25f28361"},"schema_version":"1.0","source":{"id":"2505.21373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21373","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21373v1","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21373","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"pith_short_12","alias_value":"3OKOOPS45YYC","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"pith_short_16","alias_value":"3OKOOPS45YYCJGQY","created_at":"2026-07-05T11:10:40Z"},{"alias_kind":"pith_short_8","alias_value":"3OKOOPS4","created_at":"2026-07-05T11:10:40Z"}],"graph_snapshots":[{"event_id":"sha256:b4e41f57648d22f95fc10daaeb3494841811969533f7c31253b613ab3ec09fcc","target":"graph","created_at":"2026-07-05T11:10:40Z","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/2505.21373/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distinguishable by quantum invariants.","authors_text":"Danica Kosanovi\\'c, Du\\v{s}an {\\DJ}or{\\dj}evi\\'c, Jovana Nikoli\\'c, Zoran Petri\\'c","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-05-27T16:04:35Z","title":"Restricted (2+1)-TQFTs supported by thickened and solid tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21373","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":"sha256:0e59a9511b32f0b6fd0a670fd57a2c77eaf36d4fc759c8837c2255365f7b1c38","target":"record","created_at":"2026-07-05T11:10:40Z","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":"d4cf7237642ffbcfbb36890ee1ca6816f1e24d2dcb74f1feb8c40ccd74db999a","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-05-27T16:04:35Z","title_canon_sha256":"88a13e922ced35422fd79438be44edba52b26afdab5b829c7f52ca5f25f28361"},"schema_version":"1.0","source":{"id":"2505.21373","kind":"arxiv","version":1}},"canonical_sha256":"db94e73e5cee30249a181eda1f91dc66e7d7c1b139e4896b73b584f8e92fbd0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db94e73e5cee30249a181eda1f91dc66e7d7c1b139e4896b73b584f8e92fbd0b","first_computed_at":"2026-07-05T11:10:40.930139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:40.930139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yDC6HnTUdU0IrRbecuG+TVntoxzcr5FrXcJvpkkJIdUrsTOVVkz2qaZLogOfCFrYSkSBUReP9SaEPJbSRq44DA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:40.930643Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e59a9511b32f0b6fd0a670fd57a2c77eaf36d4fc759c8837c2255365f7b1c38","sha256:b4e41f57648d22f95fc10daaeb3494841811969533f7c31253b613ab3ec09fcc"],"state_sha256":"bd5dc2d037e15338ffb7cc61e5e41593ee087ba7dcf325f8e8af0768544c71c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lryEinkDtoTBKScqZnH51cSAnGIDSFJkFbP0KZQtQmdCSI8DQ9vMwslvCrXcFeCRqlRJsrPlSCoFa+xClgb/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:54:22.766454Z","bundle_sha256":"518b0893b4d15e405d87f71b8d20ba155e734f82b3e26ab14db2bfe67e949c92"}}