{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NDGVUCIUACMSHJ4EATCL3ZRQNF","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":"8784d293d6e17646c69445cb1c83aff407002a71613413f98600620a1f84d68d","cross_cats_sorted":["cs.CG","cs.DM","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-18T15:20:09Z","title_canon_sha256":"71f51363c89ef91af89210f304f04f0a218b874594e7a6e66be609c4f786b21c"},"schema_version":"1.0","source":{"id":"1408.4036","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4036","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4036v2","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4036","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"pith_short_12","alias_value":"NDGVUCIUACMS","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NDGVUCIUACMSHJ4E","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NDGVUCIU","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:2016bc96469881dc1f78ff23f030ee21995c2e74d590b3d4c067dda6d689b3a6","target":"graph","created_at":"2026-05-18T02:19:28Z","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":"How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given combinatorial map in triangulated combinatorial surfaces (or their dual cross-metric counterpart).\n  Our work builds upon Riemannian systolic inequalities, which bound the minimum length of non-trivial closed curves in terms of the genus and the area of the surface. We first describe a systematic way to translate Riemannian systolic inequalities to a discre","authors_text":"Alfredo Hubard, Arnaud de Mesmay, \\'Eric Colin de Verdi\\`ere","cross_cats":["cs.CG","cs.DM","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-18T15:20:09Z","title":"Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4036","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":"sha256:58bd940e929312517dc9b4ba559d5d14ec1a30f2c851a3ac00b7736622a5281d","target":"record","created_at":"2026-05-18T02:19:28Z","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":"8784d293d6e17646c69445cb1c83aff407002a71613413f98600620a1f84d68d","cross_cats_sorted":["cs.CG","cs.DM","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-18T15:20:09Z","title_canon_sha256":"71f51363c89ef91af89210f304f04f0a218b874594e7a6e66be609c4f786b21c"},"schema_version":"1.0","source":{"id":"1408.4036","kind":"arxiv","version":2}},"canonical_sha256":"68cd5a0914009923a78404c4bde6306950a87609a260e3e6d351855a7acf4dc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68cd5a0914009923a78404c4bde6306950a87609a260e3e6d351855a7acf4dc3","first_computed_at":"2026-05-18T02:19:28.408941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:28.408941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MiDpX6o92jfNHM3aUT/N4NfMTK3rUYnx9XNon/2DRs34gH6SUAQ84IMwlEkmnT25afOofLMi+aRnUGGlJGNLAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:28.409431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4036","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58bd940e929312517dc9b4ba559d5d14ec1a30f2c851a3ac00b7736622a5281d","sha256:2016bc96469881dc1f78ff23f030ee21995c2e74d590b3d4c067dda6d689b3a6"],"state_sha256":"cb0f7b44f6a78d588e48bda2cc628bbbfd7972ea3b9ebee5736ca385fb7b8b62"}