{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:H3UHGY4CAVDSXILIGAOV37HPYV","short_pith_number":"pith:H3UHGY4C","canonical_record":{"source":{"id":"1106.0200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-01T15:07:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"04081bfa926774e614dbcc2e5d303cf85e9861afcbc3864e72171a5efc363177","abstract_canon_sha256":"837cc7078dd5b12a29db12c2ff899ecf2e9ca8da6399ba1d2cc8d4e810bf5505"},"schema_version":"1.0"},"canonical_sha256":"3ee873638205472ba168301d5dfcefc56708239d931c80b640a836b31d0b6939","source":{"kind":"arxiv","id":"1106.0200","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0200","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0200v2","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0200","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"H3UHGY4CAVDS","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H3UHGY4CAVDSXILI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H3UHGY4C","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:H3UHGY4CAVDSXILIGAOV37HPYV","target":"record","payload":{"canonical_record":{"source":{"id":"1106.0200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-01T15:07:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"04081bfa926774e614dbcc2e5d303cf85e9861afcbc3864e72171a5efc363177","abstract_canon_sha256":"837cc7078dd5b12a29db12c2ff899ecf2e9ca8da6399ba1d2cc8d4e810bf5505"},"schema_version":"1.0"},"canonical_sha256":"3ee873638205472ba168301d5dfcefc56708239d931c80b640a836b31d0b6939","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:18.052212Z","signature_b64":"Ii9ptIxPBUhOPJP9cv7LpWY1LveO28Tm/HRji1b079Jr5veEGagL8Gt9BszgdFy73nJTgn2y6BQMBPKuXxMWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ee873638205472ba168301d5dfcefc56708239d931c80b640a836b31d0b6939","last_reissued_at":"2026-05-18T02:48:18.051775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:18.051775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.0200","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":"2026-05-18T02:48:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7r8hG0Y8VwQMcte5RXKTwqH413Ssx8vjfhLtDnb2NedTw2yx7aeeAQD8Y0zXrbMXswFcJ7JhssoZUtmCJucEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:12:51.832404Z"},"content_sha256":"f903b919827fb5a0951c8a38d149c893ef1fb52ddd3d8b7edd785ab16f50622b","schema_version":"1.0","event_id":"sha256:f903b919827fb5a0951c8a38d149c893ef1fb52ddd3d8b7edd785ab16f50622b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:H3UHGY4CAVDSXILIGAOV37HPYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hausdorff dimension of visibility sets for well-behaved continuum percolation in the hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christoph Thaele","submitted_at":"2011-06-01T15:07:33Z","abstract_excerpt":"Let Z be a so-called well-behaved percolation, i.e. a certain random closed set in the hyperbolic plane, whose law is invariant under all isometries; for example the covered region in a Poisson Boolean model. The Hausdorff-dimension of the set of directions is determined in terms of the $\\alpha$-value of Z in which visibility from a fixed point to the ideal boundary of the hyperbolic plane is possible within Z. Moreover, the Hausdorff-dimension of the set of (hyperbolic) lines through a fixed point contained in Z is calculated. Thereby several conjectures raised by Benjamini, Jonasson, Schramm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0200","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":"2026-05-18T02:48:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sTrb6E42wlWqhCDRz/nbVgCs01YUPNh8uP8GdOBNeG1P1ry6hWBOkLI/qOZoBvk7YzhYCK0rGWBte4yYS/2xDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:12:51.832758Z"},"content_sha256":"e33bba99d49959e1bade005a8672414d6b92c9d29e72e4a4560d13d85fe5f4ec","schema_version":"1.0","event_id":"sha256:e33bba99d49959e1bade005a8672414d6b92c9d29e72e4a4560d13d85fe5f4ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3UHGY4CAVDSXILIGAOV37HPYV/bundle.json","state_url":"https://pith.science/pith/H3UHGY4CAVDSXILIGAOV37HPYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3UHGY4CAVDSXILIGAOV37HPYV/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":"2026-06-24T04:12:51Z","links":{"resolver":"https://pith.science/pith/H3UHGY4CAVDSXILIGAOV37HPYV","bundle":"https://pith.science/pith/H3UHGY4CAVDSXILIGAOV37HPYV/bundle.json","state":"https://pith.science/pith/H3UHGY4CAVDSXILIGAOV37HPYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3UHGY4CAVDSXILIGAOV37HPYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:H3UHGY4CAVDSXILIGAOV37HPYV","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":"837cc7078dd5b12a29db12c2ff899ecf2e9ca8da6399ba1d2cc8d4e810bf5505","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-01T15:07:33Z","title_canon_sha256":"04081bfa926774e614dbcc2e5d303cf85e9861afcbc3864e72171a5efc363177"},"schema_version":"1.0","source":{"id":"1106.0200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0200","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0200v2","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0200","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"H3UHGY4CAVDS","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H3UHGY4CAVDSXILI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H3UHGY4C","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:e33bba99d49959e1bade005a8672414d6b92c9d29e72e4a4560d13d85fe5f4ec","target":"graph","created_at":"2026-05-18T02:48:18Z","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 Z be a so-called well-behaved percolation, i.e. a certain random closed set in the hyperbolic plane, whose law is invariant under all isometries; for example the covered region in a Poisson Boolean model. The Hausdorff-dimension of the set of directions is determined in terms of the $\\alpha$-value of Z in which visibility from a fixed point to the ideal boundary of the hyperbolic plane is possible within Z. Moreover, the Hausdorff-dimension of the set of (hyperbolic) lines through a fixed point contained in Z is calculated. Thereby several conjectures raised by Benjamini, Jonasson, Schramm","authors_text":"Christoph Thaele","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-01T15:07:33Z","title":"Hausdorff dimension of visibility sets for well-behaved continuum percolation in the hyperbolic plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0200","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:f903b919827fb5a0951c8a38d149c893ef1fb52ddd3d8b7edd785ab16f50622b","target":"record","created_at":"2026-05-18T02:48:18Z","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":"837cc7078dd5b12a29db12c2ff899ecf2e9ca8da6399ba1d2cc8d4e810bf5505","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-01T15:07:33Z","title_canon_sha256":"04081bfa926774e614dbcc2e5d303cf85e9861afcbc3864e72171a5efc363177"},"schema_version":"1.0","source":{"id":"1106.0200","kind":"arxiv","version":2}},"canonical_sha256":"3ee873638205472ba168301d5dfcefc56708239d931c80b640a836b31d0b6939","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ee873638205472ba168301d5dfcefc56708239d931c80b640a836b31d0b6939","first_computed_at":"2026-05-18T02:48:18.051775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:18.051775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ii9ptIxPBUhOPJP9cv7LpWY1LveO28Tm/HRji1b079Jr5veEGagL8Gt9BszgdFy73nJTgn2y6BQMBPKuXxMWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:18.052212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f903b919827fb5a0951c8a38d149c893ef1fb52ddd3d8b7edd785ab16f50622b","sha256:e33bba99d49959e1bade005a8672414d6b92c9d29e72e4a4560d13d85fe5f4ec"],"state_sha256":"4132117bf9d94058b11ba9f7d76bb7631f8cbeabeb729c31105093d2692fc440"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"czdZss65XZBYIVQvJEFRPw8xIb20HdDkM9l93SrLJfPdRGJa87NX7qe4qclt+fdSLo3IcRPCzH49gNQXgJ+BCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:12:51.834933Z","bundle_sha256":"030316eb005a14a16d28046c2ad2f375d4ba2392a9cc7db067189b0a8f5ff7d6"}}