{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2AWAEFKR3TTEV52LP6SVJJFTGZ","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":"88f7c3bd7190dbd73b8c48972df3b1d44a0d83c7f0c5f4af923690cda9e282c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-04T17:11:11Z","title_canon_sha256":"7f375b3744bd621ee87bdcf28574aa947223651cd705d20aaf762cf1f3290187"},"schema_version":"1.0","source":{"id":"1111.1187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1187","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1187v1","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1187","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"pith_short_12","alias_value":"2AWAEFKR3TTE","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2AWAEFKR3TTEV52L","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2AWAEFKR","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:a01b71c06944be742d1e9e848ef39f16e7b14d3eda7c3d5695d5a87ba70fcd70","target":"graph","created_at":"2026-05-18T04:09:35Z","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":"We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph.","authors_text":"Cyril Lecuire, Hugo Parlier, Javier Aramayona, Kenneth J. Shackleton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-04T17:11:11Z","title":"Convexity of strata in diagonal pants graphs of surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1187","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:c5292cb3b4806364c5e2846cdfcafa75405c72931d2ee1cf0ae9620e63bf353c","target":"record","created_at":"2026-05-18T04:09:35Z","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":"88f7c3bd7190dbd73b8c48972df3b1d44a0d83c7f0c5f4af923690cda9e282c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-04T17:11:11Z","title_canon_sha256":"7f375b3744bd621ee87bdcf28574aa947223651cd705d20aaf762cf1f3290187"},"schema_version":"1.0","source":{"id":"1111.1187","kind":"arxiv","version":1}},"canonical_sha256":"d02c021551dce64af74b7fa554a4b33666f13f1715088293cc5ffa7de30327d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d02c021551dce64af74b7fa554a4b33666f13f1715088293cc5ffa7de30327d3","first_computed_at":"2026-05-18T04:09:35.570540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:35.570540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wrfFDaMRBwXooTPzXd5SilKYVWgONJPNMy3dPVdNhcxEtiqSJinP21bfzAp/CPBW8G/gpU6+2WsBKECvXDsTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:35.571078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5292cb3b4806364c5e2846cdfcafa75405c72931d2ee1cf0ae9620e63bf353c","sha256:a01b71c06944be742d1e9e848ef39f16e7b14d3eda7c3d5695d5a87ba70fcd70"],"state_sha256":"b622d4b3a162884dd116c0f9a6275d4b7f91d0af94ad78415b14039e40900a95"}