{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MYAFB6M7QSGV7UI6VMNDM7A7I2","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":"944040353c7ef4ef513b93aa8f9503faa952244de4563230d19669119004e032","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-29T16:26:57Z","title_canon_sha256":"cf5a66723d5873207a31105010c6b7be9bb91fb67a4ba90fa40ba930ef932ea6"},"schema_version":"1.0","source":{"id":"1111.6877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6877","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6877v1","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6877","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"pith_short_12","alias_value":"MYAFB6M7QSGV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MYAFB6M7QSGV7UI6","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MYAFB6M7","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:8cec0016a446768e62cc6b84a9571014a9f8891e5e15d383bff7c13b670b378e","target":"graph","created_at":"2026-05-18T04:07:28Z","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":"Hedden defined two knots in each lens space that, through analogies with their knot Floer homology and doubly pointed Heegaard diagrams of genus one, may be viewed as generalizations of the two trefoils in S^3. Rasmussen shows that when the `left-handed' one is in the homology class of the dual to a Berge knot of type VII, it admits an L-space homology sphere surgery. In this note we give a simple proof that these L-space homology spheres are always the Poincar\\'e homology sphere.","authors_text":"Kenneth L. Baker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-29T16:26:57Z","title":"The Poincare homology sphere and almost simple knots in lens spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6877","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":"sha256:389ad9802cd097587d246bb2c654363dc1bb41606f91eefa85396a42911b5574","target":"record","created_at":"2026-05-18T04:07:28Z","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":"944040353c7ef4ef513b93aa8f9503faa952244de4563230d19669119004e032","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-29T16:26:57Z","title_canon_sha256":"cf5a66723d5873207a31105010c6b7be9bb91fb67a4ba90fa40ba930ef932ea6"},"schema_version":"1.0","source":{"id":"1111.6877","kind":"arxiv","version":1}},"canonical_sha256":"660050f99f848d5fd11eab1a367c1f46a8038211865aae1a497d9aedcfde5fe0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"660050f99f848d5fd11eab1a367c1f46a8038211865aae1a497d9aedcfde5fe0","first_computed_at":"2026-05-18T04:07:28.348408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:28.348408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zquHwYIDl545xV6U4uSNzY/yoCewqF0luTkTcdmDUyBc/eE4cEnQ8KO9r5rfRn7dLNGmWBtxshUL4wC4kHTsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:28.348863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:389ad9802cd097587d246bb2c654363dc1bb41606f91eefa85396a42911b5574","sha256:8cec0016a446768e62cc6b84a9571014a9f8891e5e15d383bff7c13b670b378e"],"state_sha256":"b0c9a7671949cbdf44021080f96217a88463eaf4d6ad74ccd7d2ea6b37b32c5f"}