{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:SIHIROAQ2V272WEXDLNSF6IILM","short_pith_number":"pith:SIHIROAQ","canonical_record":{"source":{"id":"0710.4437","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-10-24T11:40:44Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"580d5dbe6446ad17f1c4e37f5651060ab433656fcff4b958cd456dc68b0ae6cc","abstract_canon_sha256":"cf8c18ff162755e508c0bf290c0b7470f4cf772ee6f6ad56b9fbffa0c67d27c1"},"schema_version":"1.0"},"canonical_sha256":"920e88b810d575fd58971adb22f9085b3891589cd8a314ba5039118be0e6cea6","source":{"kind":"arxiv","id":"0710.4437","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.4437","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"arxiv_version","alias_value":"0710.4437v3","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.4437","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"pith_short_12","alias_value":"SIHIROAQ2V27","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SIHIROAQ2V272WEX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SIHIROAQ","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:SIHIROAQ2V272WEXDLNSF6IILM","target":"record","payload":{"canonical_record":{"source":{"id":"0710.4437","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-10-24T11:40:44Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"580d5dbe6446ad17f1c4e37f5651060ab433656fcff4b958cd456dc68b0ae6cc","abstract_canon_sha256":"cf8c18ff162755e508c0bf290c0b7470f4cf772ee6f6ad56b9fbffa0c67d27c1"},"schema_version":"1.0"},"canonical_sha256":"920e88b810d575fd58971adb22f9085b3891589cd8a314ba5039118be0e6cea6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:48.597084Z","signature_b64":"1ey8CRQnBxGAoPNQF5zYpp0y/HlDnXH0t8Zz5FPqKqNE/nIGvmOqkIf7iAsR90JVyqEtxrF/p3Z0OpEbGmLGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"920e88b810d575fd58971adb22f9085b3891589cd8a314ba5039118be0e6cea6","last_reissued_at":"2026-05-18T01:23:48.596374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:48.596374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.4437","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ep3XEv7f8x7M5FphYVFiIgqTMHz1qCbMzEWvYgMxu2JOdwxrWaoo/iTQpwOIo1WGtcdceiSHrlwrpD4aHTRYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:39:54.227196Z"},"content_sha256":"51043f8ecef466b8babd169df0ad09c6d53defb26c7e17d01983bd14357c95ea","schema_version":"1.0","event_id":"sha256:51043f8ecef466b8babd169df0ad09c6d53defb26c7e17d01983bd14357c95ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:SIHIROAQ2V272WEXDLNSF6IILM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy dimension of orbits of Morse functions on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Sergiy Maksymenko","submitted_at":"2007-10-24T11:40:44Z","abstract_excerpt":"Let $f$ be a real- or circle-valued Morse function on a compact surface M having exactly $n>0$ critical points. Denote by $O$ the orbit of $f$ with respect to the right action of the group of diffeomorphisms of $M$. We show that the connected components of $O$ have the homotopy type of a finite-dimensional CW-complex. Actually, these connected components are homotopy equivalent to a certain covering space of the $n$-th configuration space of the interior of $M$. As a consequence we obtain that the fundamental group of $O$ is a subgroup of the $n$-th braid group of $M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.4437","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItKX2clY629jyfFm9Jtnyh6cl9aAJDXF4p2agxRLt+CSHb1qkKOcWw/1yKl7xEyQMSguzmeY33xOdITpZlpoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:39:54.227564Z"},"content_sha256":"19726dbb9b31c4005e1ac3ea492c73f93e7f99054a296f5ef3b4284057c8f594","schema_version":"1.0","event_id":"sha256:19726dbb9b31c4005e1ac3ea492c73f93e7f99054a296f5ef3b4284057c8f594"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SIHIROAQ2V272WEXDLNSF6IILM/bundle.json","state_url":"https://pith.science/pith/SIHIROAQ2V272WEXDLNSF6IILM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SIHIROAQ2V272WEXDLNSF6IILM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T19:39:54Z","links":{"resolver":"https://pith.science/pith/SIHIROAQ2V272WEXDLNSF6IILM","bundle":"https://pith.science/pith/SIHIROAQ2V272WEXDLNSF6IILM/bundle.json","state":"https://pith.science/pith/SIHIROAQ2V272WEXDLNSF6IILM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SIHIROAQ2V272WEXDLNSF6IILM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:SIHIROAQ2V272WEXDLNSF6IILM","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":"cf8c18ff162755e508c0bf290c0b7470f4cf772ee6f6ad56b9fbffa0c67d27c1","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-10-24T11:40:44Z","title_canon_sha256":"580d5dbe6446ad17f1c4e37f5651060ab433656fcff4b958cd456dc68b0ae6cc"},"schema_version":"1.0","source":{"id":"0710.4437","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.4437","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"arxiv_version","alias_value":"0710.4437v3","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.4437","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"pith_short_12","alias_value":"SIHIROAQ2V27","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SIHIROAQ2V272WEX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SIHIROAQ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:19726dbb9b31c4005e1ac3ea492c73f93e7f99054a296f5ef3b4284057c8f594","target":"graph","created_at":"2026-05-18T01:23:48Z","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"},"paper":{"abstract_excerpt":"Let $f$ be a real- or circle-valued Morse function on a compact surface M having exactly $n>0$ critical points. Denote by $O$ the orbit of $f$ with respect to the right action of the group of diffeomorphisms of $M$. We show that the connected components of $O$ have the homotopy type of a finite-dimensional CW-complex. Actually, these connected components are homotopy equivalent to a certain covering space of the $n$-th configuration space of the interior of $M$. As a consequence we obtain that the fundamental group of $O$ is a subgroup of the $n$-th braid group of $M$.","authors_text":"Sergiy Maksymenko","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-10-24T11:40:44Z","title":"Homotopy dimension of orbits of Morse functions on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.4437","kind":"arxiv","version":3},"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":"sha256:51043f8ecef466b8babd169df0ad09c6d53defb26c7e17d01983bd14357c95ea","target":"record","created_at":"2026-05-18T01:23:48Z","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":"cf8c18ff162755e508c0bf290c0b7470f4cf772ee6f6ad56b9fbffa0c67d27c1","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-10-24T11:40:44Z","title_canon_sha256":"580d5dbe6446ad17f1c4e37f5651060ab433656fcff4b958cd456dc68b0ae6cc"},"schema_version":"1.0","source":{"id":"0710.4437","kind":"arxiv","version":3}},"canonical_sha256":"920e88b810d575fd58971adb22f9085b3891589cd8a314ba5039118be0e6cea6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"920e88b810d575fd58971adb22f9085b3891589cd8a314ba5039118be0e6cea6","first_computed_at":"2026-05-18T01:23:48.596374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:48.596374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ey8CRQnBxGAoPNQF5zYpp0y/HlDnXH0t8Zz5FPqKqNE/nIGvmOqkIf7iAsR90JVyqEtxrF/p3Z0OpEbGmLGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:48.597084Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.4437","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51043f8ecef466b8babd169df0ad09c6d53defb26c7e17d01983bd14357c95ea","sha256:19726dbb9b31c4005e1ac3ea492c73f93e7f99054a296f5ef3b4284057c8f594"],"state_sha256":"4334dabe3cbf94ec3b1979fc9f9c4d1d623efa66b5a985a9707947ecc280acad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"60Fs5Pj/H6qdm1Gxf9HuFyuuJHxkPGoC+5Anbh+WJoLpQZqzfFG1Xb0BOR3ttmfPdTP/ScL+Z4V5qAvxSqFRDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:39:54.229595Z","bundle_sha256":"6d0bdacd163560a6718cd5534caee254de4a96e97b45e27bb2c270a325485311"}}