{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TLFOS2FGEOZCLGWR34ZBBJUPK7","short_pith_number":"pith:TLFOS2FG","canonical_record":{"source":{"id":"1011.5822","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-26T15:27:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a50b5424f3479381ef1cd3a758459df5321a75fcbec5dc538cc308de78039ddc","abstract_canon_sha256":"e71100e45a91259e448d497555dd25a3dfd1675883a9b9a84f73ea3befb13935"},"schema_version":"1.0"},"canonical_sha256":"9acae968a623b2259ad1df3210a68f57c0fa2e53708588041fcac0ab3b4e492e","source":{"kind":"arxiv","id":"1011.5822","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5822","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5822v3","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5822","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"TLFOS2FGEOZC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TLFOS2FGEOZCLGWR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TLFOS2FG","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TLFOS2FGEOZCLGWR34ZBBJUPK7","target":"record","payload":{"canonical_record":{"source":{"id":"1011.5822","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-26T15:27:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a50b5424f3479381ef1cd3a758459df5321a75fcbec5dc538cc308de78039ddc","abstract_canon_sha256":"e71100e45a91259e448d497555dd25a3dfd1675883a9b9a84f73ea3befb13935"},"schema_version":"1.0"},"canonical_sha256":"9acae968a623b2259ad1df3210a68f57c0fa2e53708588041fcac0ab3b4e492e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:34.487919Z","signature_b64":"UksAFqY/UtiaFkJl0UD6Y4X2kls7yJL+iW38zeN6R/1CvfqIi8qY5s+Bqv0Qzu0QkHT6kdwf75wZPWNKHWLEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9acae968a623b2259ad1df3210a68f57c0fa2e53708588041fcac0ab3b4e492e","last_reissued_at":"2026-05-18T04:10:34.487296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:34.487296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.5822","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CL9qJHXQQBoaRmRDeD+gl76wnwiy4a/zXZ3/pk7tbY7VoV/VndNZc7R542IiOr1+y91GVrAWhEgcP3dS1wMOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:16:44.427825Z"},"content_sha256":"f345586a6ae3bc109b603df0279054e32d0f3f31d32e7a8114ca655c72c2fe4f","schema_version":"1.0","event_id":"sha256:f345586a6ae3bc109b603df0279054e32d0f3f31d32e7a8114ca655c72c2fe4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TLFOS2FGEOZCLGWR34ZBBJUPK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A proof of factorization formula for critical percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Dmitry Beliaev, Konstantin Izyurov","submitted_at":"2010-11-26T15:27:34Z","abstract_excerpt":"We give mathematical proofs to a number of statements which appeared in the series of papers by Kleban, Simmons and Ziff where they computed the probabilities of several percolation crossing events."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5822","kind":"arxiv","version":3},"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":"2026-05-18T04:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bnm1mxM1879McLI2KVDn9ovn5kcQq0tvCGg1jyx8CtIQJ/81GzPyJDsLlBLL4m46z7CD7xZoWOMr763YKGocCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:16:44.428467Z"},"content_sha256":"4c1127341d5efbd7672da46e4506cc2701647f13b738c3f5b4ac5662a3e6a125","schema_version":"1.0","event_id":"sha256:4c1127341d5efbd7672da46e4506cc2701647f13b738c3f5b4ac5662a3e6a125"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLFOS2FGEOZCLGWR34ZBBJUPK7/bundle.json","state_url":"https://pith.science/pith/TLFOS2FGEOZCLGWR34ZBBJUPK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLFOS2FGEOZCLGWR34ZBBJUPK7/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":"2026-06-03T11:16:44Z","links":{"resolver":"https://pith.science/pith/TLFOS2FGEOZCLGWR34ZBBJUPK7","bundle":"https://pith.science/pith/TLFOS2FGEOZCLGWR34ZBBJUPK7/bundle.json","state":"https://pith.science/pith/TLFOS2FGEOZCLGWR34ZBBJUPK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLFOS2FGEOZCLGWR34ZBBJUPK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TLFOS2FGEOZCLGWR34ZBBJUPK7","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":"e71100e45a91259e448d497555dd25a3dfd1675883a9b9a84f73ea3befb13935","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-26T15:27:34Z","title_canon_sha256":"a50b5424f3479381ef1cd3a758459df5321a75fcbec5dc538cc308de78039ddc"},"schema_version":"1.0","source":{"id":"1011.5822","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5822","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5822v3","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5822","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"TLFOS2FGEOZC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TLFOS2FGEOZCLGWR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TLFOS2FG","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:4c1127341d5efbd7672da46e4506cc2701647f13b738c3f5b4ac5662a3e6a125","target":"graph","created_at":"2026-05-18T04:10:34Z","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 give mathematical proofs to a number of statements which appeared in the series of papers by Kleban, Simmons and Ziff where they computed the probabilities of several percolation crossing events.","authors_text":"Dmitry Beliaev, Konstantin Izyurov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-26T15:27:34Z","title":"A proof of factorization formula for critical percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5822","kind":"arxiv","version":3},"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:f345586a6ae3bc109b603df0279054e32d0f3f31d32e7a8114ca655c72c2fe4f","target":"record","created_at":"2026-05-18T04:10:34Z","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":"e71100e45a91259e448d497555dd25a3dfd1675883a9b9a84f73ea3befb13935","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-26T15:27:34Z","title_canon_sha256":"a50b5424f3479381ef1cd3a758459df5321a75fcbec5dc538cc308de78039ddc"},"schema_version":"1.0","source":{"id":"1011.5822","kind":"arxiv","version":3}},"canonical_sha256":"9acae968a623b2259ad1df3210a68f57c0fa2e53708588041fcac0ab3b4e492e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9acae968a623b2259ad1df3210a68f57c0fa2e53708588041fcac0ab3b4e492e","first_computed_at":"2026-05-18T04:10:34.487296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:34.487296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UksAFqY/UtiaFkJl0UD6Y4X2kls7yJL+iW38zeN6R/1CvfqIi8qY5s+Bqv0Qzu0QkHT6kdwf75wZPWNKHWLEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:34.487919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5822","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f345586a6ae3bc109b603df0279054e32d0f3f31d32e7a8114ca655c72c2fe4f","sha256:4c1127341d5efbd7672da46e4506cc2701647f13b738c3f5b4ac5662a3e6a125"],"state_sha256":"1b94d1288626499fe84aebde80ad9cbdae725b11ab2b987cbbb5ad8d2169df1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HVN8WD88coiMPjegbPy9tSS7CqK0eO/4NRM8fNq6XoAz5pQxOD75qCpw8+yoPFe1v1nduWwyLd5wEKlWbOzxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:16:44.431804Z","bundle_sha256":"49699be0a833f2082c64819e7f1535520be92fe02317a284f7681d9c8f021ed4"}}