{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KYLR2F65ZIUCGY4COIPPKYGIRD","short_pith_number":"pith:KYLR2F65","canonical_record":{"source":{"id":"1409.7046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-24T19:30:30Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1c7578c941bde7017acf78ecb23bc42f26a0abcd79162831233ea3ca6bdb1f72","abstract_canon_sha256":"3c4025ff98d5f8d223e39adbf76826ef261a3a32ff560bdb86efa2ef1856f798"},"schema_version":"1.0"},"canonical_sha256":"56171d17ddca28236382721ef560c888ef6c968a886568a7e99578aade755e29","source":{"kind":"arxiv","id":"1409.7046","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7046","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7046v2","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7046","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"pith_short_12","alias_value":"KYLR2F65ZIUC","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KYLR2F65ZIUCGY4C","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KYLR2F65","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KYLR2F65ZIUCGY4COIPPKYGIRD","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-24T19:30:30Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1c7578c941bde7017acf78ecb23bc42f26a0abcd79162831233ea3ca6bdb1f72","abstract_canon_sha256":"3c4025ff98d5f8d223e39adbf76826ef261a3a32ff560bdb86efa2ef1856f798"},"schema_version":"1.0"},"canonical_sha256":"56171d17ddca28236382721ef560c888ef6c968a886568a7e99578aade755e29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:38.389009Z","signature_b64":"G2c3pnltzl7gYu793LmBTDE5sq9JngcZF6b92mmU8tlH6z+vkB7X8A9WMhbwqZoGn0zuyIC3Orrv3NEA17kHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56171d17ddca28236382721ef560c888ef6c968a886568a7e99578aade755e29","last_reissued_at":"2026-05-18T02:32:38.388558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:38.388558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7046","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nRQccYUuL+tUFmXWb4k4L0KKm9pvddaBCBgEcvjuJIpkf6ytqmsmp41kTwQ2z4EuDtFJ0KHhjUreRiUneEwACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:08:34.427829Z"},"content_sha256":"025b5093b4a98b534809a5aa7bb68c2c83548fca2fef04393bf5b2ab71e82932","schema_version":"1.0","event_id":"sha256:025b5093b4a98b534809a5aa7bb68c2c83548fca2fef04393bf5b2ab71e82932"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KYLR2F65ZIUCGY4COIPPKYGIRD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Injective maps between flip graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Hugo Parlier, Javier Aramayona, Thomas Koberda","submitted_at":"2014-09-24T19:30:30Z","abstract_excerpt":"We prove that every injective simplicial map $\\mathcal{F}(S) \\to \\mathcal{F}(S')$ between flip graphs is induced by a subsurface inclusion $S\\to S'$, except in finitely many cases. This extends a result of Korkmaz--Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is induced by a surface homeomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7046","kind":"arxiv","version":2},"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":"2026-05-18T02:32:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q+hZ7UZu20t7Pa8+xkhr973+qa7B0Udhm8bSG8S0zGoogm2HoCPM/g781wzhghIChHtL7xq5kN+J+EQ7fYFHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:08:34.428514Z"},"content_sha256":"4201507486785471ff1e851d930f9671ed4b1e0fc1a62231b394382f281d4364","schema_version":"1.0","event_id":"sha256:4201507486785471ff1e851d930f9671ed4b1e0fc1a62231b394382f281d4364"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KYLR2F65ZIUCGY4COIPPKYGIRD/bundle.json","state_url":"https://pith.science/pith/KYLR2F65ZIUCGY4COIPPKYGIRD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KYLR2F65ZIUCGY4COIPPKYGIRD/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":"2026-05-26T01:08:34Z","links":{"resolver":"https://pith.science/pith/KYLR2F65ZIUCGY4COIPPKYGIRD","bundle":"https://pith.science/pith/KYLR2F65ZIUCGY4COIPPKYGIRD/bundle.json","state":"https://pith.science/pith/KYLR2F65ZIUCGY4COIPPKYGIRD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KYLR2F65ZIUCGY4COIPPKYGIRD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KYLR2F65ZIUCGY4COIPPKYGIRD","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":"3c4025ff98d5f8d223e39adbf76826ef261a3a32ff560bdb86efa2ef1856f798","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-24T19:30:30Z","title_canon_sha256":"1c7578c941bde7017acf78ecb23bc42f26a0abcd79162831233ea3ca6bdb1f72"},"schema_version":"1.0","source":{"id":"1409.7046","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7046","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7046v2","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7046","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"pith_short_12","alias_value":"KYLR2F65ZIUC","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KYLR2F65ZIUCGY4C","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KYLR2F65","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:4201507486785471ff1e851d930f9671ed4b1e0fc1a62231b394382f281d4364","target":"graph","created_at":"2026-05-18T02:32:38Z","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 that every injective simplicial map $\\mathcal{F}(S) \\to \\mathcal{F}(S')$ between flip graphs is induced by a subsurface inclusion $S\\to S'$, except in finitely many cases. This extends a result of Korkmaz--Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is induced by a surface homeomorphism.","authors_text":"Hugo Parlier, Javier Aramayona, Thomas Koberda","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-24T19:30:30Z","title":"Injective maps between flip graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7046","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":"sha256:025b5093b4a98b534809a5aa7bb68c2c83548fca2fef04393bf5b2ab71e82932","target":"record","created_at":"2026-05-18T02:32:38Z","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":"3c4025ff98d5f8d223e39adbf76826ef261a3a32ff560bdb86efa2ef1856f798","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-24T19:30:30Z","title_canon_sha256":"1c7578c941bde7017acf78ecb23bc42f26a0abcd79162831233ea3ca6bdb1f72"},"schema_version":"1.0","source":{"id":"1409.7046","kind":"arxiv","version":2}},"canonical_sha256":"56171d17ddca28236382721ef560c888ef6c968a886568a7e99578aade755e29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56171d17ddca28236382721ef560c888ef6c968a886568a7e99578aade755e29","first_computed_at":"2026-05-18T02:32:38.388558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:38.388558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G2c3pnltzl7gYu793LmBTDE5sq9JngcZF6b92mmU8tlH6z+vkB7X8A9WMhbwqZoGn0zuyIC3Orrv3NEA17kHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:38.389009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7046","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:025b5093b4a98b534809a5aa7bb68c2c83548fca2fef04393bf5b2ab71e82932","sha256:4201507486785471ff1e851d930f9671ed4b1e0fc1a62231b394382f281d4364"],"state_sha256":"bbb5430832687faaccbd24176b0800ccaecf6b81b155f5ac21367edc45cbc0be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LN6m43G3Fs7ZMHROsDmNbzPfktfkw5m0oiS/8aNah3QtHLfuDv5rTKizO4zrn4SkvH13ADPx2LygNj/VBL1UDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:08:34.432063Z","bundle_sha256":"107efacdd868aace94cfc25496d26794fba32a41bb1b5ce6600420f6440e8e19"}}