{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RS5ZCBKAMJ5VNSTUSXTPKLOMOP","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":"c850f6459d1b42bd885040a7cfd0b32ba201601fa201ed338dafe4d269f232f9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-15T22:53:18Z","title_canon_sha256":"d80322c96b4e62f41d6a86ad5a21b93d30a53facd022902d3bd41ca1ec3a0e86"},"schema_version":"1.0","source":{"id":"1106.3116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3116","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3116v1","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3116","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"pith_short_12","alias_value":"RS5ZCBKAMJ5V","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RS5ZCBKAMJ5VNSTU","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RS5ZCBKA","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:7a84695429c3651eda537be8ac11b41d0e48b5c5172037dded279742876919dd","target":"graph","created_at":"2026-05-18T01:23:10Z","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":"Let $M$ be a smooth closed orientable surface. Let $F$ be the space of Morse functions on $M$, and $\\mathbb{F}^1$ the space of framed Morse functions, both endowed with $C^\\infty$-topology. The space $\\mathbb{F}^0$ of special framed Morse functions is defined. We prove that the inclusion mapping $\\mathbb{F}^0\\hookrightarrow\\mathbb{F}^1$ is a homotopy equivalence. In the case when at least $\\chi(M)+1$ critical points of each function of $F$ are labeled, homotopy equivalences $\\mathbb{\\widetilde K}\\sim\\widetilde{\\cal M}$ and $F\\sim\\mathbb{F}^0\\sim{\\mathscr D}^0\\times\\mathbb{\\widetilde K}$ are pr","authors_text":"Elena A. Kudryavtseva","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-15T22:53:18Z","title":"Special framed Morse functions on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3116","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":"sha256:14a6b7db8888720b1fa2d2b7a15c9204dfdf2b32bae1bd793738983a8119a08e","target":"record","created_at":"2026-05-18T01:23:10Z","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":"c850f6459d1b42bd885040a7cfd0b32ba201601fa201ed338dafe4d269f232f9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-15T22:53:18Z","title_canon_sha256":"d80322c96b4e62f41d6a86ad5a21b93d30a53facd022902d3bd41ca1ec3a0e86"},"schema_version":"1.0","source":{"id":"1106.3116","kind":"arxiv","version":1}},"canonical_sha256":"8cbb910540627b56ca7495e6f52dcc73f9fb31a4e2b8fb07e81c725423304808","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cbb910540627b56ca7495e6f52dcc73f9fb31a4e2b8fb07e81c725423304808","first_computed_at":"2026-05-18T01:23:10.772355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:10.772355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jAOVJSLbmlOOTnofuSvDSFGpA2uX15U6VdxCM6NTW4zE4y7fAvHPeu5vC5SSBCHTEkdfQtgQDjiLcD9iNV2sAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:10.772954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14a6b7db8888720b1fa2d2b7a15c9204dfdf2b32bae1bd793738983a8119a08e","sha256:7a84695429c3651eda537be8ac11b41d0e48b5c5172037dded279742876919dd"],"state_sha256":"e03e38440e53de544faac3604c9e646a9938d76992e4d263553e30ac471a16b6"}