{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VY3YJQDDS253LAPZBXHUZ3XBX4","short_pith_number":"pith:VY3YJQDD","canonical_record":{"source":{"id":"1309.4884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-19T07:32:07Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"3f46c7739fb9a00f39e7a19aa5d35b3d8804d508d3d9568e68734b0f4cc42310","abstract_canon_sha256":"10a3d2dfae62bc2cde2c1326fb85f5c2760fa6a4fa4d4cfede94ab2766b06a5a"},"schema_version":"1.0"},"canonical_sha256":"ae3784c06396bbb581f90dcf4ceee1bf21fb2565d16f3809446e45d8542ab201","source":{"kind":"arxiv","id":"1309.4884","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4884","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4884v1","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4884","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"VY3YJQDDS253","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VY3YJQDDS253LAPZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VY3YJQDD","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VY3YJQDDS253LAPZBXHUZ3XBX4","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-19T07:32:07Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"3f46c7739fb9a00f39e7a19aa5d35b3d8804d508d3d9568e68734b0f4cc42310","abstract_canon_sha256":"10a3d2dfae62bc2cde2c1326fb85f5c2760fa6a4fa4d4cfede94ab2766b06a5a"},"schema_version":"1.0"},"canonical_sha256":"ae3784c06396bbb581f90dcf4ceee1bf21fb2565d16f3809446e45d8542ab201","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:35.926639Z","signature_b64":"RXFHpB9HKrgUKIjehdggtEPDks3BASYQOZs0WYqejcDhvAtRfZsANv590EKdl7ZF/0G1kNHjSPPW+rwqheUABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae3784c06396bbb581f90dcf4ceee1bf21fb2565d16f3809446e45d8542ab201","last_reissued_at":"2026-05-18T01:34:35.925991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:35.925991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4884","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":"2026-05-18T01:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWc1slLrlae5ufNwGQr3kc3m/z+XwNJA+6Mkhhrq45IHhUk2bcl+Id36NubZEwZxkCAdyKaQoB3o3asTfVqJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:59:52.911668Z"},"content_sha256":"3d5fe7c063b12a2c844b6c8a05d057f5754782e091af6b96135b1c49d6c91781","schema_version":"1.0","event_id":"sha256:3d5fe7c063b12a2c844b6c8a05d057f5754782e091af6b96135b1c49d6c91781"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VY3YJQDDS253LAPZBXHUZ3XBX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On typical leaves of a measured foliated 2-complex of thin type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.GT","authors_text":"Alexandra Skripchenko, Ivan Dynnikov","submitted_at":"2013-09-19T07:32:07Z","abstract_excerpt":"It is known that all but finitely many leaves of a measured foliated 2-complex of thin type are quasi-isometric to an infinite tree with at most two topological ends. We show that if the foliation is cooriented, and the associated R-tree is self-similar, then a typical leaf has exactly one topological end. We also construct the first example of a foliated 2-complex of thin type whose typical leaf has exactly two topological ends. `Typical' means that the property holds with probability one in a natural sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4884","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":"2026-05-18T01:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8Xh9sqYWzxzHj0yyEChceL3d0jya/+BMAhGSqYM6GqFsZ82a+Bv3z0zTvvUh9IWzoxfAC4uHJwzsMGdBV4HDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:59:52.912006Z"},"content_sha256":"1d552972179e1d597169b326bef2daaba37d9bcf5f8b1f7a78ad84839b76f897","schema_version":"1.0","event_id":"sha256:1d552972179e1d597169b326bef2daaba37d9bcf5f8b1f7a78ad84839b76f897"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VY3YJQDDS253LAPZBXHUZ3XBX4/bundle.json","state_url":"https://pith.science/pith/VY3YJQDDS253LAPZBXHUZ3XBX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VY3YJQDDS253LAPZBXHUZ3XBX4/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":"2026-06-24T16:59:52Z","links":{"resolver":"https://pith.science/pith/VY3YJQDDS253LAPZBXHUZ3XBX4","bundle":"https://pith.science/pith/VY3YJQDDS253LAPZBXHUZ3XBX4/bundle.json","state":"https://pith.science/pith/VY3YJQDDS253LAPZBXHUZ3XBX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VY3YJQDDS253LAPZBXHUZ3XBX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VY3YJQDDS253LAPZBXHUZ3XBX4","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":"10a3d2dfae62bc2cde2c1326fb85f5c2760fa6a4fa4d4cfede94ab2766b06a5a","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-19T07:32:07Z","title_canon_sha256":"3f46c7739fb9a00f39e7a19aa5d35b3d8804d508d3d9568e68734b0f4cc42310"},"schema_version":"1.0","source":{"id":"1309.4884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4884","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4884v1","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4884","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"VY3YJQDDS253","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VY3YJQDDS253LAPZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VY3YJQDD","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:1d552972179e1d597169b326bef2daaba37d9bcf5f8b1f7a78ad84839b76f897","target":"graph","created_at":"2026-05-18T01:34:35Z","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":"It is known that all but finitely many leaves of a measured foliated 2-complex of thin type are quasi-isometric to an infinite tree with at most two topological ends. We show that if the foliation is cooriented, and the associated R-tree is self-similar, then a typical leaf has exactly one topological end. We also construct the first example of a foliated 2-complex of thin type whose typical leaf has exactly two topological ends. `Typical' means that the property holds with probability one in a natural sense.","authors_text":"Alexandra Skripchenko, Ivan Dynnikov","cross_cats":["math.DS","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-19T07:32:07Z","title":"On typical leaves of a measured foliated 2-complex of thin type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4884","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":"sha256:3d5fe7c063b12a2c844b6c8a05d057f5754782e091af6b96135b1c49d6c91781","target":"record","created_at":"2026-05-18T01:34:35Z","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":"10a3d2dfae62bc2cde2c1326fb85f5c2760fa6a4fa4d4cfede94ab2766b06a5a","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-19T07:32:07Z","title_canon_sha256":"3f46c7739fb9a00f39e7a19aa5d35b3d8804d508d3d9568e68734b0f4cc42310"},"schema_version":"1.0","source":{"id":"1309.4884","kind":"arxiv","version":1}},"canonical_sha256":"ae3784c06396bbb581f90dcf4ceee1bf21fb2565d16f3809446e45d8542ab201","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae3784c06396bbb581f90dcf4ceee1bf21fb2565d16f3809446e45d8542ab201","first_computed_at":"2026-05-18T01:34:35.925991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:35.925991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RXFHpB9HKrgUKIjehdggtEPDks3BASYQOZs0WYqejcDhvAtRfZsANv590EKdl7ZF/0G1kNHjSPPW+rwqheUABw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:35.926639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d5fe7c063b12a2c844b6c8a05d057f5754782e091af6b96135b1c49d6c91781","sha256:1d552972179e1d597169b326bef2daaba37d9bcf5f8b1f7a78ad84839b76f897"],"state_sha256":"50e5dc6fc84a7ee0255b7a0ff99fc782877d41b6984bf7b4eaafdbb673d07481"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yANVXuJgx236jdmpmKOMm51OwhqhuJjYMjZalFpO4EKc58C3wOZezmUnnVA4I1H+cxOj7MooFhjRoBmDqh3GDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:59:52.913813Z","bundle_sha256":"3a9d2707d5392eaf0712b75dcba485dcbd70647fbced017b5a59f8ba81f5cd52"}}