{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3CPMWPKPGKJX2NPTWFV5SGHB6T","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":"937f40d515c7d077b927af65ad3b20ee26fc26b4efb1f815bb046706701a5f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-05-19T02:09:24Z","title_canon_sha256":"ffed2440541341aaa1f15078cdcd58a3079994d83abff2faa09f210ffe2646f5"},"schema_version":"1.0","source":{"id":"1405.4579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4579","created_at":"2026-05-18T01:19:34Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4579v1","created_at":"2026-05-18T01:19:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4579","created_at":"2026-05-18T01:19:34Z"},{"alias_kind":"pith_short_12","alias_value":"3CPMWPKPGKJX","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3CPMWPKPGKJX2NPT","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3CPMWPKP","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:d5b3a542e15b3171ce85a21276aba2bb6b3d67d433b7b54d1dec745deb7243d2","target":"graph","created_at":"2026-05-18T01:19:34Z","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":"The Reeb graph $\\mathcal{R}(f) $ is one of the fundamental invariants of a smooth function $f\\colon M\\to \\mathbb{R} $ with isolated critical points. It is defined as the quotient space $M/_{\\!\\sim}$ of the closed manifold $M$ by a relation that depends on $f$. Here we construct a $1$-dimensional complex $\\Gamma(f)$ embedded into $M$ which is homotopy equivalent to $\\mathcal{R}(f)$. As a consequence we show that for every function $f$ on a manifold with finite fundamental group, the Reeb graph of $f$ is a tree. If $\\pi_1(M)$ is an abelian group, or more general, a discrete amenable group, then ","authors_text":"Marek Kaluba, Nelson Silva, Wac{\\l}aw Marzantowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-05-19T02:09:24Z","title":"On Representation of the Reeb Graph as a Sub-Complex of Manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4579","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":"sha256:31017f05cf21522606e179fb735809d40340051e6b0c4c4772a07b45847fc5d0","target":"record","created_at":"2026-05-18T01:19:34Z","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":"937f40d515c7d077b927af65ad3b20ee26fc26b4efb1f815bb046706701a5f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-05-19T02:09:24Z","title_canon_sha256":"ffed2440541341aaa1f15078cdcd58a3079994d83abff2faa09f210ffe2646f5"},"schema_version":"1.0","source":{"id":"1405.4579","kind":"arxiv","version":1}},"canonical_sha256":"d89ecb3d4f32937d35f3b16bd918e1f4d6e67a100a209bc84b16716cf2e86568","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d89ecb3d4f32937d35f3b16bd918e1f4d6e67a100a209bc84b16716cf2e86568","first_computed_at":"2026-05-18T01:19:34.594577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:34.594577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M1UCmuORfGjBCx185QQ5lHD+tDG/oNgdpjNJodwlL9HGhpUrMOC02E8NP9Ycv/W/1o74dZ+6BCI3Q0N0JjpfCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:34.595137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31017f05cf21522606e179fb735809d40340051e6b0c4c4772a07b45847fc5d0","sha256:d5b3a542e15b3171ce85a21276aba2bb6b3d67d433b7b54d1dec745deb7243d2"],"state_sha256":"a72f3e50ac6f4f3b49e8f5cd096ef99be85e568254e0f10c12b54b4646353c94"}