{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:2AQ4GUOLMFX2W2FQQCAPBDAJBS","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":"333918167fa17f8823414c01bbd54bd994ca281e5c52f75ffddc57d8b7521f14","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1998-09-28T01:59:48Z","title_canon_sha256":"97ac89b4f5855560bda93ffb1f6c73222922040d3f32a1f6d6e333332e938187"},"schema_version":"1.0","source":{"id":"math/9809155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9809155","created_at":"2026-07-04T14:40:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9809155v1","created_at":"2026-07-04T14:40:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9809155","created_at":"2026-07-04T14:40:48Z"},{"alias_kind":"pith_short_12","alias_value":"2AQ4GUOLMFX2","created_at":"2026-07-04T14:40:48Z"},{"alias_kind":"pith_short_16","alias_value":"2AQ4GUOLMFX2W2FQ","created_at":"2026-07-04T14:40:48Z"},{"alias_kind":"pith_short_8","alias_value":"2AQ4GUOL","created_at":"2026-07-04T14:40:48Z"}],"graph_snapshots":[{"event_id":"sha256:14e765b6b2ed863dc70fcf53649e2f2f7b2ba6d378a7b7f7ab0c8aa39a4e5812","target":"graph","created_at":"2026-07-04T14:40:48Z","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/math/9809155/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify groups generated by powers of 2 Dehn twists which are 1) free or 2) have no ``unexpected'' reducible elements. We give some sufficient conditions in the case of groups generated by powers of more than two twists.","authors_text":"Hessam Hamidi-Tehrani","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"1998-09-28T01:59:48Z","title":"Groups Generated by Powers of Dehn Twists"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9809155","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:ed1a0144f2cdbe926a4358e3d89b4a68c835bf07da7145ba25dbd5ae82926546","target":"record","created_at":"2026-07-04T14:40:48Z","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":"333918167fa17f8823414c01bbd54bd994ca281e5c52f75ffddc57d8b7521f14","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1998-09-28T01:59:48Z","title_canon_sha256":"97ac89b4f5855560bda93ffb1f6c73222922040d3f32a1f6d6e333332e938187"},"schema_version":"1.0","source":{"id":"math/9809155","kind":"arxiv","version":1}},"canonical_sha256":"d021c351cb616fab68b08080f08c090cb109f02fa382f6be42e792f1695837fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d021c351cb616fab68b08080f08c090cb109f02fa382f6be42e792f1695837fc","first_computed_at":"2026-07-04T14:40:48.180520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:48.180520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vYxipNCK3GURLWr0Zmuk6ew5L9L33+2jhkCoGdfewnk7YkNF/Qiz9/Ka/ZtwntGCkdiPUQTMbhdMk/vd7cjpBg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:48.180913Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9809155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed1a0144f2cdbe926a4358e3d89b4a68c835bf07da7145ba25dbd5ae82926546","sha256:14e765b6b2ed863dc70fcf53649e2f2f7b2ba6d378a7b7f7ab0c8aa39a4e5812"],"state_sha256":"6068c4f8482a52ace3a423e170024d2e7a89fcc41e2db9b837663e2eb9dcdcc0"}