{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TNPZQKTGIBBBHQ4P4DJID6EIT6","short_pith_number":"pith:TNPZQKTG","canonical_record":{"source":{"id":"1611.09986","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-11-30T03:30:54Z","cross_cats_sorted":[],"title_canon_sha256":"90d93229a65f4e5d27ffdc14a3da730924193c62f0fcca2d397d47168ebf50dd","abstract_canon_sha256":"a01939d9e42ea69be5fa666c91f8e8ee03867d8581d0ae3cd5a14bb8472a7388"},"schema_version":"1.0"},"canonical_sha256":"9b5f982a66404213c38fe0d281f8889faf620dd12117af2b931ed9a8ede22b13","source":{"kind":"arxiv","id":"1611.09986","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TNPZQKTGIBBBHQ4P4DJID6EIT6","target":"record","payload":{"canonical_record":{"source":{"id":"1611.09986","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-11-30T03:30:54Z","cross_cats_sorted":[],"title_canon_sha256":"90d93229a65f4e5d27ffdc14a3da730924193c62f0fcca2d397d47168ebf50dd","abstract_canon_sha256":"a01939d9e42ea69be5fa666c91f8e8ee03867d8581d0ae3cd5a14bb8472a7388"},"schema_version":"1.0"},"canonical_sha256":"9b5f982a66404213c38fe0d281f8889faf620dd12117af2b931ed9a8ede22b13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:47.756355Z","signature_b64":"CmhKAJHXg4mjaSoKgx/ehwTnlu3y+SydeWKXFduSdThRDFZVIEqQ+tuHd4MaEe8yIPoSUstnhAz6S4xHqPIGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b5f982a66404213c38fe0d281f8889faf620dd12117af2b931ed9a8ede22b13","last_reissued_at":"2026-05-18T00:36:47.755843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:47.755843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.09986","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0GCXG2Knj5OuHNzA3cqFQINYBV4rzTrC/U+knwf6s0E5WIMnKQl3yjqeO1EHlT1Jevv1MTV91i/RJG6vUnwBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:15:57.515562Z"},"content_sha256":"ec25b4c862597d5c144d62fb0f07ffcdb14b3dbfe9b4a31e79acbe8399ac0ded","schema_version":"1.0","event_id":"sha256:ec25b4c862597d5c144d62fb0f07ffcdb14b3dbfe9b4a31e79acbe8399ac0ded"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TNPZQKTGIBBBHQ4P4DJID6EIT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alternating maps on Hatcher-Thurston graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jes\\'us Hern\\'andez Hern\\'andez","submitted_at":"2016-11-30T03:30:54Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09986","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ITeSl6AsVv7N2Tu4A8aqqCy1lLtzdGUsRhVOnT6aUV77X50XDXC9oL5CLp5/H/i7/QgdkfMa36E24szHGI/oCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:15:57.516050Z"},"content_sha256":"01eeaa3e85895d53607506013bbdcb40b8f351b1efe8c98438a94d0cfceb3636","schema_version":"1.0","event_id":"sha256:01eeaa3e85895d53607506013bbdcb40b8f351b1efe8c98438a94d0cfceb3636"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNPZQKTGIBBBHQ4P4DJID6EIT6/bundle.json","state_url":"https://pith.science/pith/TNPZQKTGIBBBHQ4P4DJID6EIT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNPZQKTGIBBBHQ4P4DJID6EIT6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T06:15:57Z","links":{"resolver":"https://pith.science/pith/TNPZQKTGIBBBHQ4P4DJID6EIT6","bundle":"https://pith.science/pith/TNPZQKTGIBBBHQ4P4DJID6EIT6/bundle.json","state":"https://pith.science/pith/TNPZQKTGIBBBHQ4P4DJID6EIT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNPZQKTGIBBBHQ4P4DJID6EIT6/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZ/lREDdujIF4ptscy9aJHBMDJpLujdhXLVCEcQSs0xpheWd6XbgWxILHBEYaGpkEw8HxaBMFgiBGmovA5ztDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:15:57.518722Z","bundle_sha256":"dbdd653996b1c7e516d0a01614e1e33e6684c70c0c1145b0a895774f8d916b24"}}