{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DJCOTW4JATRKY6Q7X2S3A4E437","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":"1a8dec3cb5128c483465b3af92a099333279084a1bc99d3141f9322a2aa91b68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-21T20:12:23Z","title_canon_sha256":"a06c8ccec74226db90a0a5b6911215a7808abeefef1a0f1ffdaaeae4cf12e9f2"},"schema_version":"1.0","source":{"id":"1803.08806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08806","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08806v1","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08806","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"DJCOTW4JATRK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DJCOTW4JATRKY6Q7","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DJCOTW4J","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:0fdf6c1d6a1667e2a17b9792355814cf954e10ae70a8749f71c4a202cf1d9b1c","target":"graph","created_at":"2026-05-18T00:20:18Z","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 $R$ be a compact, connected, orientable surface of genus $g$ with $n$ boundary components. Let $\\mathcal{C}(R)$ be the curve graph of $R$. We prove that if $g=0, n \\geq 5$ or $g=1, n \\geq 3$, and $\\lambda : \\mathcal{C}(R) \\rightarrow\\mathcal{C}(R)$ is an edge preserving map, then $\\lambda$ is induced by a homeomorphism of $R$, and this homeomorphism is unique up to isotopy.","authors_text":"Elmas Irmak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-21T20:12:23Z","title":"Edge Preserving Maps of the Curve Graphs in Low Genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08806","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":"sha256:2cec96b59a62b768c0aa21a9035418ed83d4a6b370bd8767d94ec219ed9e34d1","target":"record","created_at":"2026-05-18T00:20:18Z","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":"1a8dec3cb5128c483465b3af92a099333279084a1bc99d3141f9322a2aa91b68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-21T20:12:23Z","title_canon_sha256":"a06c8ccec74226db90a0a5b6911215a7808abeefef1a0f1ffdaaeae4cf12e9f2"},"schema_version":"1.0","source":{"id":"1803.08806","kind":"arxiv","version":1}},"canonical_sha256":"1a44e9db8904e2ac7a1fbea5b0709cdfd7730fccb3b7a9d046a170aa0b3e640d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a44e9db8904e2ac7a1fbea5b0709cdfd7730fccb3b7a9d046a170aa0b3e640d","first_computed_at":"2026-05-18T00:20:18.495648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:18.495648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wMI+Vvfef/oSjo35JRLNgvZc7XIN4jw81P8yAsN7B6+pkB/i1jFU0icNS5vr3X1KhGi8A5R9FePKW4cmgnsRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:18.496365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cec96b59a62b768c0aa21a9035418ed83d4a6b370bd8767d94ec219ed9e34d1","sha256:0fdf6c1d6a1667e2a17b9792355814cf954e10ae70a8749f71c4a202cf1d9b1c"],"state_sha256":"8b310bcf558cfec23d7f119d5027286b9700b2a73a858f39d908b92c7065cd69"}