{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:A7WFW7HIJE7YWC5QM2DSAZKP2M","short_pith_number":"pith:A7WFW7HI","canonical_record":{"source":{"id":"1301.5577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-23T17:21:51Z","cross_cats_sorted":[],"title_canon_sha256":"629a887e80d180b9156c6e8fe1f544389c8d6581a7f5906606360d4d2181ab14","abstract_canon_sha256":"50c05c933eeaee1f1618d9705502532bc0f38b0ad5eef7270be2b3cc468b207a"},"schema_version":"1.0"},"canonical_sha256":"07ec5b7ce8493f8b0bb0668720654fd33ef5057b0d9f99da290a5a99739f6764","source":{"kind":"arxiv","id":"1301.5577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5577","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5577v1","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5577","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"pith_short_12","alias_value":"A7WFW7HIJE7Y","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A7WFW7HIJE7YWC5Q","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A7WFW7HI","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:A7WFW7HIJE7YWC5QM2DSAZKP2M","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-23T17:21:51Z","cross_cats_sorted":[],"title_canon_sha256":"629a887e80d180b9156c6e8fe1f544389c8d6581a7f5906606360d4d2181ab14","abstract_canon_sha256":"50c05c933eeaee1f1618d9705502532bc0f38b0ad5eef7270be2b3cc468b207a"},"schema_version":"1.0"},"canonical_sha256":"07ec5b7ce8493f8b0bb0668720654fd33ef5057b0d9f99da290a5a99739f6764","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:39.368988Z","signature_b64":"P+umUb4pZLzCiQM9D2XuH9CQC5IczI0hGRuFBEz2jSNVsX0gAFbm159hptjE2HGPHbtSHjJG3l1EjQiLClk1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07ec5b7ce8493f8b0bb0668720654fd33ef5057b0d9f99da290a5a99739f6764","last_reissued_at":"2026-05-18T03:35:39.368180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:39.368180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5577","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":"2026-05-18T03:35:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DFjdPu6A1jkU+LcP0PbeQ5YHguoJe93Lg05yc4LinbGbzUhIAAO1DsSBOOcZuxHr7YPdDzw8cIi3graEnHcfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:57:25.646034Z"},"content_sha256":"a14c78700144f58f9952caead0e7c973ce3824c48d62e87050d64e6369885840","schema_version":"1.0","event_id":"sha256:a14c78700144f58f9952caead0e7c973ce3824c48d62e87050d64e6369885840"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:A7WFW7HIJE7YWC5QM2DSAZKP2M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Piotr Przytycki, Richard C. H. Webb, Sebastian Hensel","submitted_at":"2013-01-23T17:21:51Z","abstract_excerpt":"We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5577","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":"2026-05-18T03:35:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xi2PIcWe2FZAwihq3OE9+YCUu40AAXrhOXB3y9ZZFD9bbQmmlzTguHpUpMlLx0lYldx82S60GHf8IuxjvMA4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:57:25.646527Z"},"content_sha256":"153333e32066882f0a72b6b42fe57d267768a34a33bde87b9fe1069e230932ad","schema_version":"1.0","event_id":"sha256:153333e32066882f0a72b6b42fe57d267768a34a33bde87b9fe1069e230932ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7WFW7HIJE7YWC5QM2DSAZKP2M/bundle.json","state_url":"https://pith.science/pith/A7WFW7HIJE7YWC5QM2DSAZKP2M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7WFW7HIJE7YWC5QM2DSAZKP2M/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":"2026-05-27T11:57:25Z","links":{"resolver":"https://pith.science/pith/A7WFW7HIJE7YWC5QM2DSAZKP2M","bundle":"https://pith.science/pith/A7WFW7HIJE7YWC5QM2DSAZKP2M/bundle.json","state":"https://pith.science/pith/A7WFW7HIJE7YWC5QM2DSAZKP2M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7WFW7HIJE7YWC5QM2DSAZKP2M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:A7WFW7HIJE7YWC5QM2DSAZKP2M","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":"50c05c933eeaee1f1618d9705502532bc0f38b0ad5eef7270be2b3cc468b207a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-23T17:21:51Z","title_canon_sha256":"629a887e80d180b9156c6e8fe1f544389c8d6581a7f5906606360d4d2181ab14"},"schema_version":"1.0","source":{"id":"1301.5577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5577","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5577v1","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5577","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"pith_short_12","alias_value":"A7WFW7HIJE7Y","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A7WFW7HIJE7YWC5Q","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A7WFW7HI","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:153333e32066882f0a72b6b42fe57d267768a34a33bde87b9fe1069e230932ad","target":"graph","created_at":"2026-05-18T03:35:39Z","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 describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.","authors_text":"Piotr Przytycki, Richard C. H. Webb, Sebastian Hensel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-23T17:21:51Z","title":"Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5577","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:a14c78700144f58f9952caead0e7c973ce3824c48d62e87050d64e6369885840","target":"record","created_at":"2026-05-18T03:35:39Z","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":"50c05c933eeaee1f1618d9705502532bc0f38b0ad5eef7270be2b3cc468b207a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-23T17:21:51Z","title_canon_sha256":"629a887e80d180b9156c6e8fe1f544389c8d6581a7f5906606360d4d2181ab14"},"schema_version":"1.0","source":{"id":"1301.5577","kind":"arxiv","version":1}},"canonical_sha256":"07ec5b7ce8493f8b0bb0668720654fd33ef5057b0d9f99da290a5a99739f6764","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07ec5b7ce8493f8b0bb0668720654fd33ef5057b0d9f99da290a5a99739f6764","first_computed_at":"2026-05-18T03:35:39.368180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:39.368180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P+umUb4pZLzCiQM9D2XuH9CQC5IczI0hGRuFBEz2jSNVsX0gAFbm159hptjE2HGPHbtSHjJG3l1EjQiLClk1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:39.368988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a14c78700144f58f9952caead0e7c973ce3824c48d62e87050d64e6369885840","sha256:153333e32066882f0a72b6b42fe57d267768a34a33bde87b9fe1069e230932ad"],"state_sha256":"40035da701856e30f87cba201e352e51a317749436430377e40506ac6cfe5dce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5oGQweV0b92pXDHOWijpgNuZ59DsAMfBIEuV5k4a8E6tcRU8DrdASgCZArBOXEepvrIWU0HDQR093WC2GqUmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:57:25.648970Z","bundle_sha256":"95b6f4a506fc52bea11a76aa1898982da1ad9ce04e2bc4da62f5955f43269abf"}}