{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TNPZQKTGIBBBHQ4P4DJID6EIT6","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":"a01939d9e42ea69be5fa666c91f8e8ee03867d8581d0ae3cd5a14bb8472a7388","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-11-30T03:30:54Z","title_canon_sha256":"90d93229a65f4e5d27ffdc14a3da730924193c62f0fcca2d397d47168ebf50dd"},"schema_version":"1.0","source":{"id":"1611.09986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09986","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09986v1","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09986","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"TNPZQKTGIBBB","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TNPZQKTGIBBBHQ4P","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TNPZQKTG","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:01eeaa3e85895d53607506013bbdcb40b8f351b1efe8c98438a94d0cfceb3636","target":"graph","created_at":"2026-05-18T00:36:47Z","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 $S_{1}$ and $S_{2}$ be connected orientable surfaces of genus $g_{1}, g_{2} \\geq 3$, $n_{1},n_{2} \\geq 0$ punctures, and empty boundary. Let also $\\varphi: \\mathcal{HT}(S_{1}) \\rightarrow \\mathcal{HT}(S_{2})$ be an edge-preserving alternating map between their Hatcher-Thurston graphs. We prove that $g_{1} \\leq g_{2}$ and that there is also a multicurve of cardinality $g_{2} - g_{1}$ contained in every element of the image. We also prove that if $n_{1} = 0$ and $g_{1} = g_{2}$, then the map $\\widetilde{\\varphi}$ obtained by filling the punctures of $S_{2}$, is induced by a homeomorphism of ","authors_text":"Jes\\'us Hern\\'andez Hern\\'andez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-11-30T03:30:54Z","title":"Alternating maps on Hatcher-Thurston graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09986","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:ec25b4c862597d5c144d62fb0f07ffcdb14b3dbfe9b4a31e79acbe8399ac0ded","target":"record","created_at":"2026-05-18T00:36:47Z","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":"a01939d9e42ea69be5fa666c91f8e8ee03867d8581d0ae3cd5a14bb8472a7388","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-11-30T03:30:54Z","title_canon_sha256":"90d93229a65f4e5d27ffdc14a3da730924193c62f0fcca2d397d47168ebf50dd"},"schema_version":"1.0","source":{"id":"1611.09986","kind":"arxiv","version":1}},"canonical_sha256":"9b5f982a66404213c38fe0d281f8889faf620dd12117af2b931ed9a8ede22b13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b5f982a66404213c38fe0d281f8889faf620dd12117af2b931ed9a8ede22b13","first_computed_at":"2026-05-18T00:36:47.755843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:47.755843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CmhKAJHXg4mjaSoKgx/ehwTnlu3y+SydeWKXFduSdThRDFZVIEqQ+tuHd4MaEe8yIPoSUstnhAz6S4xHqPIGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:47.756355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec25b4c862597d5c144d62fb0f07ffcdb14b3dbfe9b4a31e79acbe8399ac0ded","sha256:01eeaa3e85895d53607506013bbdcb40b8f351b1efe8c98438a94d0cfceb3636"],"state_sha256":"5fbfbb9c16de1170d66101284f87aca156ba3ffbcb56d0a8852cc879b2ebda26"}