{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VGM5P2TLCA6TOQO62BV6JAHKNR","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":"8e9d4ac46da664be07d8eb6b47e56acba083f703fcc42edd3f56ac79271ca593","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-23T21:19:51Z","title_canon_sha256":"5ec2012639508f3d7281c8e2d9d012d3e5c1d26b14d7c8a489593454be115978"},"schema_version":"1.0","source":{"id":"1105.4638","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4638","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4638v2","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4638","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"VGM5P2TLCA6T","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VGM5P2TLCA6TOQO6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VGM5P2TL","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:91d15f9c0344ac37de2eb5667f5fe48fa789d87e9188c3b4284a450c53d757e5","target":"graph","created_at":"2026-05-18T02:58:00Z","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":"Given two free homotopy classes $\\alpha_1, \\alpha_2$ of loops on an oriented surface, it is natural to ask how to compute the minimum number of intersection points $m(\\alpha_1, \\alpha_2)$ of loops in these two classes.\n  We show that for $\\alpha_1\\neq\\alpha_2$ the number of terms in the Andersen-Mattes-Reshetikhin Poisson bracket of $\\alpha_1$ and $\\alpha_2$ is equal to $m(\\alpha_1, \\alpha_2)$. Chas found examples showing that a similar statement does not, in general, hold for the Goldman Lie bracket of $\\alpha_1$ and $\\alpha_2$.\n  The main result of this paper in the case where $\\alpha_1, \\al","authors_text":"Patricia Cahn, Vladimir Chernov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-23T21:19:51Z","title":"Intersections of Loops and the Andersen-Mattes-Reshetikhin Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4638","kind":"arxiv","version":2},"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":"sha256:30d66c2742fca5a977f74f4f6f7a8fafd018915c4d77d930e57dbaad6c7bbc1f","target":"record","created_at":"2026-05-18T02:58:00Z","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":"8e9d4ac46da664be07d8eb6b47e56acba083f703fcc42edd3f56ac79271ca593","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-23T21:19:51Z","title_canon_sha256":"5ec2012639508f3d7281c8e2d9d012d3e5c1d26b14d7c8a489593454be115978"},"schema_version":"1.0","source":{"id":"1105.4638","kind":"arxiv","version":2}},"canonical_sha256":"a999d7ea6b103d3741ded06be480ea6c6d23fa7d3ba6ea688f73179d0b88226b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a999d7ea6b103d3741ded06be480ea6c6d23fa7d3ba6ea688f73179d0b88226b","first_computed_at":"2026-05-18T02:58:00.881578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.881578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mfvfwAkJczyayEH3/K+89jelL44JRsIyUaZ0w4hbaGB09TPEyO2sksowrONE9NJl7GkKWHinChkGvhah8Pm2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.882213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4638","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30d66c2742fca5a977f74f4f6f7a8fafd018915c4d77d930e57dbaad6c7bbc1f","sha256:91d15f9c0344ac37de2eb5667f5fe48fa789d87e9188c3b4284a450c53d757e5"],"state_sha256":"893be30c2d6372aed3b84685bfc75ce59a7d5540ec6b960c03ea2e027bcd173f"}