{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QTKA7NA662X7D5I2J5TZHM4OSQ","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":"2c6d046c82e9cc79692bd20dbeeb194a95c63c1f242b966a9b70832450006cbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-11-24T01:31:55Z","title_canon_sha256":"ee8d32379a31c5df294be2cee144449292516365fc5c13db91abd3579abcef18"},"schema_version":"1.0","source":{"id":"2411.15680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15680","created_at":"2026-07-05T09:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15680v1","created_at":"2026-07-05T09:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15680","created_at":"2026-07-05T09:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"QTKA7NA662X7","created_at":"2026-07-05T09:39:39Z"},{"alias_kind":"pith_short_16","alias_value":"QTKA7NA662X7D5I2","created_at":"2026-07-05T09:39:39Z"},{"alias_kind":"pith_short_8","alias_value":"QTKA7NA6","created_at":"2026-07-05T09:39:39Z"}],"graph_snapshots":[{"event_id":"sha256:354b32c7a2ac5d9513244c78371311d88f003802484b82eef8915c879e0afd1d","target":"graph","created_at":"2026-07-05T09:39:39Z","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/2411.15680/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Infinite families of 3-dimensional closed graph manifolds and closed Seifert fibered spaces are exhibited, each member of which contains an essential torus not detected by ideal points of the variety of $\\text{SL}_2(\\mathbb{F})$-characters over any algebraically closed field $\\mathbb{F}$.","authors_text":"Benjamin Martin, Grace S. Garden, Stephan Tillmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-11-24T01:31:55Z","title":"Essential tori in 3-manifolds not detected in any characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15680","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":"sha256:7b6d069b406033a96f2c8993e4314af1e72409c0d07f9666b343ca640e7f9864","target":"record","created_at":"2026-07-05T09:39:39Z","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":"2c6d046c82e9cc79692bd20dbeeb194a95c63c1f242b966a9b70832450006cbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-11-24T01:31:55Z","title_canon_sha256":"ee8d32379a31c5df294be2cee144449292516365fc5c13db91abd3579abcef18"},"schema_version":"1.0","source":{"id":"2411.15680","kind":"arxiv","version":1}},"canonical_sha256":"84d40fb41ef6aff1f51a4f6793b38e94043ff2522a6fc62f6ae0c020f55fb934","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84d40fb41ef6aff1f51a4f6793b38e94043ff2522a6fc62f6ae0c020f55fb934","first_computed_at":"2026-07-05T09:39:39.226240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:39.226240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SLo0ytEUt/h2YbQSeNegId9O9aHgsflh6m6IRtrabUAFqLi6hibWqBwiSrZ6UCQ8VlAwcTvNBSDttH9mNfobDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:39.226726Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b6d069b406033a96f2c8993e4314af1e72409c0d07f9666b343ca640e7f9864","sha256:354b32c7a2ac5d9513244c78371311d88f003802484b82eef8915c879e0afd1d"],"state_sha256":"0015102cbbaca62a55459cb763127c07819670aa8091c333d79c3e68c0755361"}