{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CQH6CFCI7KR5JDFECI5QJOTEN3","short_pith_number":"pith:CQH6CFCI","canonical_record":{"source":{"id":"1608.04475","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-16T04:12:02Z","cross_cats_sorted":[],"title_canon_sha256":"ec79bf89856e44fba06942e40232e2a440a3013db3f337f9bfb52152c703718f","abstract_canon_sha256":"e87a4a01c19065651e2f47fd1c25736b5a365b9d62b7eb37a478081fac565e30"},"schema_version":"1.0"},"canonical_sha256":"140fe11448faa3d48ca4123b04ba646eea4e0fff39ad661ff0c358fb9e166e69","source":{"kind":"arxiv","id":"1608.04475","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04475","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04475v2","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04475","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"CQH6CFCI7KR5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CQH6CFCI7KR5JDFE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CQH6CFCI","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CQH6CFCI7KR5JDFECI5QJOTEN3","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04475","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-16T04:12:02Z","cross_cats_sorted":[],"title_canon_sha256":"ec79bf89856e44fba06942e40232e2a440a3013db3f337f9bfb52152c703718f","abstract_canon_sha256":"e87a4a01c19065651e2f47fd1c25736b5a365b9d62b7eb37a478081fac565e30"},"schema_version":"1.0"},"canonical_sha256":"140fe11448faa3d48ca4123b04ba646eea4e0fff39ad661ff0c358fb9e166e69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:12.550464Z","signature_b64":"AVhfk3/+zKIMHdDQZrfK8NosK5bo4It/DKphhH0JFTsLMgHYObhPvocpP+asr4gysPdcPOUiDyZsIvZEtiYYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"140fe11448faa3d48ca4123b04ba646eea4e0fff39ad661ff0c358fb9e166e69","last_reissued_at":"2026-05-18T00:07:12.549863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:12.549863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04475","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":"2026-05-18T00:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FOlYj/8acnRY2447v5U/dBTeEZf8m/cQSWW2/0EMxk5NIF5EuycKUbA/SkeLsidShTVr+ZBe1OGXyz8CQwGdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:33:57.129263Z"},"content_sha256":"1d658a21653a7e040efc283dc98e2d774c3c4702bce993c924d61b8674937e81","schema_version":"1.0","event_id":"sha256:1d658a21653a7e040efc283dc98e2d774c3c4702bce993c924d61b8674937e81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CQH6CFCI7KR5JDFECI5QJOTEN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Gromov boundary of the ray graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alden Walker, Juliette Bavard","submitted_at":"2016-08-16T04:12:02Z","abstract_excerpt":"The ray graph is a Gromov hyperbolic graph on which the mapping class group of the plane minus a Cantor set acts by isometries. We give a description of the Gromov boundary of the ray graph in terms of cliques of long rays on the plane minus a Cantor set. As a consequence, we prove that the Gromov boundary of the ray graph is homeomorphic to a quotient of a subset of the circle.\n  This version contains some updates and corrections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04475","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":"2026-05-18T00:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yA1DaZGBFdBlfuDTUNh6ii9ynep8SAOMNHC2TYZxNgdeLUkZv+aQEJUIjNXB44M4bkySCR6lr5Yipx6wOKlqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:33:57.129626Z"},"content_sha256":"c08592e4c762fda9d90dcbb5a7daaff92ef9e28777ec6972c00500c2982170ff","schema_version":"1.0","event_id":"sha256:c08592e4c762fda9d90dcbb5a7daaff92ef9e28777ec6972c00500c2982170ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQH6CFCI7KR5JDFECI5QJOTEN3/bundle.json","state_url":"https://pith.science/pith/CQH6CFCI7KR5JDFECI5QJOTEN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQH6CFCI7KR5JDFECI5QJOTEN3/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":"2026-06-24T20:33:57Z","links":{"resolver":"https://pith.science/pith/CQH6CFCI7KR5JDFECI5QJOTEN3","bundle":"https://pith.science/pith/CQH6CFCI7KR5JDFECI5QJOTEN3/bundle.json","state":"https://pith.science/pith/CQH6CFCI7KR5JDFECI5QJOTEN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQH6CFCI7KR5JDFECI5QJOTEN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CQH6CFCI7KR5JDFECI5QJOTEN3","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":"e87a4a01c19065651e2f47fd1c25736b5a365b9d62b7eb37a478081fac565e30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-16T04:12:02Z","title_canon_sha256":"ec79bf89856e44fba06942e40232e2a440a3013db3f337f9bfb52152c703718f"},"schema_version":"1.0","source":{"id":"1608.04475","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04475","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04475v2","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04475","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"CQH6CFCI7KR5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CQH6CFCI7KR5JDFE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CQH6CFCI","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:c08592e4c762fda9d90dcbb5a7daaff92ef9e28777ec6972c00500c2982170ff","target":"graph","created_at":"2026-05-18T00:07:12Z","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":"The ray graph is a Gromov hyperbolic graph on which the mapping class group of the plane minus a Cantor set acts by isometries. We give a description of the Gromov boundary of the ray graph in terms of cliques of long rays on the plane minus a Cantor set. As a consequence, we prove that the Gromov boundary of the ray graph is homeomorphic to a quotient of a subset of the circle.\n  This version contains some updates and corrections.","authors_text":"Alden Walker, Juliette Bavard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-16T04:12:02Z","title":"The Gromov boundary of the ray graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04475","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":"sha256:1d658a21653a7e040efc283dc98e2d774c3c4702bce993c924d61b8674937e81","target":"record","created_at":"2026-05-18T00:07:12Z","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":"e87a4a01c19065651e2f47fd1c25736b5a365b9d62b7eb37a478081fac565e30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-16T04:12:02Z","title_canon_sha256":"ec79bf89856e44fba06942e40232e2a440a3013db3f337f9bfb52152c703718f"},"schema_version":"1.0","source":{"id":"1608.04475","kind":"arxiv","version":2}},"canonical_sha256":"140fe11448faa3d48ca4123b04ba646eea4e0fff39ad661ff0c358fb9e166e69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"140fe11448faa3d48ca4123b04ba646eea4e0fff39ad661ff0c358fb9e166e69","first_computed_at":"2026-05-18T00:07:12.549863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:12.549863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVhfk3/+zKIMHdDQZrfK8NosK5bo4It/DKphhH0JFTsLMgHYObhPvocpP+asr4gysPdcPOUiDyZsIvZEtiYYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:12.550464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04475","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d658a21653a7e040efc283dc98e2d774c3c4702bce993c924d61b8674937e81","sha256:c08592e4c762fda9d90dcbb5a7daaff92ef9e28777ec6972c00500c2982170ff"],"state_sha256":"19ddee8e2f4ce1b223dcdb227deca7a67eaeefca2e74cb6d7da06b2cc9777f9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vdll6UWWLBVqipEgsAZmb2fQrAkSSW0yhcYDVxZOcYu7XuPSzqpqSEKCs48kE/kj6d1dEQ4W8rlROGw8krfeCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:33:57.131565Z","bundle_sha256":"4c49afa778b11b3eee7f4ad661e87997066c0a8f497787595f57ccdc624e655a"}}