{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6HTN5GPB5WZID4JATOGDFKRVQB","short_pith_number":"pith:6HTN5GPB","canonical_record":{"source":{"id":"1011.1101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-11-04T10:27:36Z","cross_cats_sorted":["hep-lat","math-ph","math.MP"],"title_canon_sha256":"632c308ad3a8df638c7b8274953733a579cf745125d98691744515255367800d","abstract_canon_sha256":"31713ec58a6cf1ee9183877932866141a4e0174b2e838f3083c62eb4963fdbdc"},"schema_version":"1.0"},"canonical_sha256":"f1e6de99e1edb281f1209b8c32aa35807b96b1839939bd5b635b9f03b4de9b48","source":{"kind":"arxiv","id":"1011.1101","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1101","created_at":"2026-05-18T02:23:37Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1101v2","created_at":"2026-05-18T02:23:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1101","created_at":"2026-05-18T02:23:37Z"},{"alias_kind":"pith_short_12","alias_value":"6HTN5GPB5WZI","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6HTN5GPB5WZID4JA","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6HTN5GPB","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6HTN5GPB5WZID4JATOGDFKRVQB","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-11-04T10:27:36Z","cross_cats_sorted":["hep-lat","math-ph","math.MP"],"title_canon_sha256":"632c308ad3a8df638c7b8274953733a579cf745125d98691744515255367800d","abstract_canon_sha256":"31713ec58a6cf1ee9183877932866141a4e0174b2e838f3083c62eb4963fdbdc"},"schema_version":"1.0"},"canonical_sha256":"f1e6de99e1edb281f1209b8c32aa35807b96b1839939bd5b635b9f03b4de9b48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:37.633093Z","signature_b64":"Ohpn4IUZD2AzAd1LygprEFJ3YnP2vYuyRAQm3ESixBzQBCrM+Q4VSkusrjArbffVOacovCzhltRyyyy7cQ2uCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1e6de99e1edb281f1209b8c32aa35807b96b1839939bd5b635b9f03b4de9b48","last_reissued_at":"2026-05-18T02:23:37.632420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:37.632420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1101","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":"2026-05-18T02:23:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r3kOroq/rpb0DlOp9qmWntmpuRWJEU0qoDo/k+PlxDYjPJPz2UQvSul+JhMGk4ulzwxU4qPHksGQPJa5+eR0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:57:17.745953Z"},"content_sha256":"b8555d30e4536638cd42228a99de286b65f54d73cf90eab7747c317d222ab186","schema_version":"1.0","event_id":"sha256:b8555d30e4536638cd42228a99de286b65f54d73cf90eab7747c317d222ab186"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6HTN5GPB5WZID4JATOGDFKRVQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factorization of correlations in two-dimensional percolation on the plane and torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math-ph","math.MP"],"primary_cat":"cond-mat.dis-nn","authors_text":"Jacob J. H. Simmons, Peter Kleban, Robert M. Ziff","submitted_at":"2010-11-04T10:27:36Z","abstract_excerpt":"Recently, Delfino and Viti have examined the factorization of the three-point density correlation function P_3 at the percolation point in terms of the two-point density correlation functions P_2. According to conformal invariance, this factorization is exact on the infinite plane, such that the ratio R(z_1, z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2, z_3)]^{1/2} is not only universal but also a constant, independent of the z_i, and in fact an operator product expansion (OPE) coefficient. Delfino and Viti analytically calculate its value (1.022013...) for percolation, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1101","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":"2026-05-18T02:23:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cKJzp3/6oOoJv7My02N/dflr0jnGsuhM9ZpLLLCglqAOUZhoWov3V5xKFcVr2nKSBnGZSv0bWn1ABDOySn8LBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:57:17.746300Z"},"content_sha256":"568ef3222ad13bdf5d4c54f28f8d4fd0fb6aeb175c681e2f33aaa16dce71ecfe","schema_version":"1.0","event_id":"sha256:568ef3222ad13bdf5d4c54f28f8d4fd0fb6aeb175c681e2f33aaa16dce71ecfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HTN5GPB5WZID4JATOGDFKRVQB/bundle.json","state_url":"https://pith.science/pith/6HTN5GPB5WZID4JATOGDFKRVQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HTN5GPB5WZID4JATOGDFKRVQB/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":"2026-06-24T06:57:17Z","links":{"resolver":"https://pith.science/pith/6HTN5GPB5WZID4JATOGDFKRVQB","bundle":"https://pith.science/pith/6HTN5GPB5WZID4JATOGDFKRVQB/bundle.json","state":"https://pith.science/pith/6HTN5GPB5WZID4JATOGDFKRVQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HTN5GPB5WZID4JATOGDFKRVQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6HTN5GPB5WZID4JATOGDFKRVQB","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":"31713ec58a6cf1ee9183877932866141a4e0174b2e838f3083c62eb4963fdbdc","cross_cats_sorted":["hep-lat","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-11-04T10:27:36Z","title_canon_sha256":"632c308ad3a8df638c7b8274953733a579cf745125d98691744515255367800d"},"schema_version":"1.0","source":{"id":"1011.1101","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1101","created_at":"2026-05-18T02:23:37Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1101v2","created_at":"2026-05-18T02:23:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1101","created_at":"2026-05-18T02:23:37Z"},{"alias_kind":"pith_short_12","alias_value":"6HTN5GPB5WZI","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6HTN5GPB5WZID4JA","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6HTN5GPB","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:568ef3222ad13bdf5d4c54f28f8d4fd0fb6aeb175c681e2f33aaa16dce71ecfe","target":"graph","created_at":"2026-05-18T02:23:37Z","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":"Recently, Delfino and Viti have examined the factorization of the three-point density correlation function P_3 at the percolation point in terms of the two-point density correlation functions P_2. According to conformal invariance, this factorization is exact on the infinite plane, such that the ratio R(z_1, z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2, z_3)]^{1/2} is not only universal but also a constant, independent of the z_i, and in fact an operator product expansion (OPE) coefficient. Delfino and Viti analytically calculate its value (1.022013...) for percolation, ","authors_text":"Jacob J. H. Simmons, Peter Kleban, Robert M. Ziff","cross_cats":["hep-lat","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-11-04T10:27:36Z","title":"Factorization of correlations in two-dimensional percolation on the plane and torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1101","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:b8555d30e4536638cd42228a99de286b65f54d73cf90eab7747c317d222ab186","target":"record","created_at":"2026-05-18T02:23:37Z","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":"31713ec58a6cf1ee9183877932866141a4e0174b2e838f3083c62eb4963fdbdc","cross_cats_sorted":["hep-lat","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-11-04T10:27:36Z","title_canon_sha256":"632c308ad3a8df638c7b8274953733a579cf745125d98691744515255367800d"},"schema_version":"1.0","source":{"id":"1011.1101","kind":"arxiv","version":2}},"canonical_sha256":"f1e6de99e1edb281f1209b8c32aa35807b96b1839939bd5b635b9f03b4de9b48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1e6de99e1edb281f1209b8c32aa35807b96b1839939bd5b635b9f03b4de9b48","first_computed_at":"2026-05-18T02:23:37.632420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:37.632420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ohpn4IUZD2AzAd1LygprEFJ3YnP2vYuyRAQm3ESixBzQBCrM+Q4VSkusrjArbffVOacovCzhltRyyyy7cQ2uCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:37.633093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1101","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8555d30e4536638cd42228a99de286b65f54d73cf90eab7747c317d222ab186","sha256:568ef3222ad13bdf5d4c54f28f8d4fd0fb6aeb175c681e2f33aaa16dce71ecfe"],"state_sha256":"29416c994bbf8ebda702dc0b555e9b14faa8d1e3c0c2e127a43e58765c83398d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b31in71nEx/KBDZ6X6MfgQDBa7wHaaxgo2Ku9O1UryEStOEN2GFEmxN4WKkqfBZLt46M+gvA+l60hoXuDAFxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:57:17.748294Z","bundle_sha256":"0f8c30ecf95c61b5a5015b0574ad8df125554f58bf1afaa73a48abdc5c824666"}}