{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UOYEHBZB3ISGGFDTWNVXP4X2UC","short_pith_number":"pith:UOYEHBZB","canonical_record":{"source":{"id":"1010.3075","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-15T05:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"f34ae769b087a33c0d9fc78b547bdbb0519411d5a7b56d528439d36b6b85fed1","abstract_canon_sha256":"52fc0ba198cc602effe9b2b418173ec383e1ab2e2a91597cb1bf463ccca36786"},"schema_version":"1.0"},"canonical_sha256":"a3b0438721da24631473b36b77f2faa0bc804b9584d2c99d02bf58cee3b13f7b","source":{"kind":"arxiv","id":"1010.3075","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3075","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3075v1","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3075","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"UOYEHBZB3ISG","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UOYEHBZB3ISGGFDT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UOYEHBZB","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UOYEHBZB3ISGGFDTWNVXP4X2UC","target":"record","payload":{"canonical_record":{"source":{"id":"1010.3075","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-15T05:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"f34ae769b087a33c0d9fc78b547bdbb0519411d5a7b56d528439d36b6b85fed1","abstract_canon_sha256":"52fc0ba198cc602effe9b2b418173ec383e1ab2e2a91597cb1bf463ccca36786"},"schema_version":"1.0"},"canonical_sha256":"a3b0438721da24631473b36b77f2faa0bc804b9584d2c99d02bf58cee3b13f7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:56.652088Z","signature_b64":"2vimPLcnsY+7Q64tWH+Ak2mBQ2KMAtvPLjG8BK5xaJDeApiZuQTtehEpy9BwPuOWIITLcdzJaXv7PLwOcmPICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3b0438721da24631473b36b77f2faa0bc804b9584d2c99d02bf58cee3b13f7b","last_reissued_at":"2026-05-18T04:28:56.651387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:56.651387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.3075","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":"2026-05-18T04:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0I+3q7t33JdpruAAm8tyCdrD2960SSuEgcDtwbvHeJcDIPFfTsWoldu68d+wjhWg2WnHNTqC6dvl0e+pYrt9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:13:41.385363Z"},"content_sha256":"9e10c40fcff0d1a0007db69165cd97ede4df510d2b588e3d1b20b2fc37a3a9ba","schema_version":"1.0","event_id":"sha256:9e10c40fcff0d1a0007db69165cd97ede4df510d2b588e3d1b20b2fc37a3a9ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UOYEHBZB3ISGGFDTWNVXP4X2UC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Berezinskii-Kosterlitz-Thouless-like percolation transitions in the two-dimensional XY model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Hao Hu, Henk W. J. Bl\\\"ote, Youjin Deng","submitted_at":"2010-10-15T05:33:36Z","abstract_excerpt":"We study a percolation problem on a substrate formed by two-dimensional XY spin configurations, using Monte Carlo methods. For a given spin configuration we construct percolation clusters by randomly choosing a direction $x$ in the spin vector space, and then placing a percolation bond between nearest-neighbor sites $i$ and $j$ with probability $p_{ij} = \\max (0,1-e^{-2K s^x_i s^x_j})$, where $K > 0$ governs the percolation process. A line of percolation thresholds $K_{\\rm c} (J)$ is found in the low-temperature range $J \\geq J_{\\rm c}$, where $J > 0$ is the XY coupling strength. Analysis of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3075","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":"2026-05-18T04:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9TXM7pOcP+kkolrtA+0CWB8LbnzjIEu+nKHXBcTn25w3sWzM3Dv8wVn3oaFECeKslmBU0fQdO1SWDoxcdw75Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:13:41.386074Z"},"content_sha256":"8ec6fcf938ff12f3c4de52b9c9f49cc38f88b95a9ff1e90836918a1cf13b92b2","schema_version":"1.0","event_id":"sha256:8ec6fcf938ff12f3c4de52b9c9f49cc38f88b95a9ff1e90836918a1cf13b92b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOYEHBZB3ISGGFDTWNVXP4X2UC/bundle.json","state_url":"https://pith.science/pith/UOYEHBZB3ISGGFDTWNVXP4X2UC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOYEHBZB3ISGGFDTWNVXP4X2UC/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":"2026-05-28T18:13:41Z","links":{"resolver":"https://pith.science/pith/UOYEHBZB3ISGGFDTWNVXP4X2UC","bundle":"https://pith.science/pith/UOYEHBZB3ISGGFDTWNVXP4X2UC/bundle.json","state":"https://pith.science/pith/UOYEHBZB3ISGGFDTWNVXP4X2UC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOYEHBZB3ISGGFDTWNVXP4X2UC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UOYEHBZB3ISGGFDTWNVXP4X2UC","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":"52fc0ba198cc602effe9b2b418173ec383e1ab2e2a91597cb1bf463ccca36786","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-15T05:33:36Z","title_canon_sha256":"f34ae769b087a33c0d9fc78b547bdbb0519411d5a7b56d528439d36b6b85fed1"},"schema_version":"1.0","source":{"id":"1010.3075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3075","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3075v1","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3075","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"UOYEHBZB3ISG","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UOYEHBZB3ISGGFDT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UOYEHBZB","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:8ec6fcf938ff12f3c4de52b9c9f49cc38f88b95a9ff1e90836918a1cf13b92b2","target":"graph","created_at":"2026-05-18T04:28:56Z","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 study a percolation problem on a substrate formed by two-dimensional XY spin configurations, using Monte Carlo methods. For a given spin configuration we construct percolation clusters by randomly choosing a direction $x$ in the spin vector space, and then placing a percolation bond between nearest-neighbor sites $i$ and $j$ with probability $p_{ij} = \\max (0,1-e^{-2K s^x_i s^x_j})$, where $K > 0$ governs the percolation process. A line of percolation thresholds $K_{\\rm c} (J)$ is found in the low-temperature range $J \\geq J_{\\rm c}$, where $J > 0$ is the XY coupling strength. Analysis of t","authors_text":"Hao Hu, Henk W. J. Bl\\\"ote, Youjin Deng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-15T05:33:36Z","title":"Berezinskii-Kosterlitz-Thouless-like percolation transitions in the two-dimensional XY model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3075","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":"sha256:9e10c40fcff0d1a0007db69165cd97ede4df510d2b588e3d1b20b2fc37a3a9ba","target":"record","created_at":"2026-05-18T04:28:56Z","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":"52fc0ba198cc602effe9b2b418173ec383e1ab2e2a91597cb1bf463ccca36786","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-15T05:33:36Z","title_canon_sha256":"f34ae769b087a33c0d9fc78b547bdbb0519411d5a7b56d528439d36b6b85fed1"},"schema_version":"1.0","source":{"id":"1010.3075","kind":"arxiv","version":1}},"canonical_sha256":"a3b0438721da24631473b36b77f2faa0bc804b9584d2c99d02bf58cee3b13f7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3b0438721da24631473b36b77f2faa0bc804b9584d2c99d02bf58cee3b13f7b","first_computed_at":"2026-05-18T04:28:56.651387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:56.651387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2vimPLcnsY+7Q64tWH+Ak2mBQ2KMAtvPLjG8BK5xaJDeApiZuQTtehEpy9BwPuOWIITLcdzJaXv7PLwOcmPICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:56.652088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e10c40fcff0d1a0007db69165cd97ede4df510d2b588e3d1b20b2fc37a3a9ba","sha256:8ec6fcf938ff12f3c4de52b9c9f49cc38f88b95a9ff1e90836918a1cf13b92b2"],"state_sha256":"866e263d0ee7cf248c0cc17950a537f36121f00a2be203badb04438c98bb8e67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ybk5/hHTu8DC8MdkZDrUBKt8xujor56hQUGZk6KVjaqita9ebRAVfPv+a26cLFnFqi+91CdtEeopD5Gb3AxvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:13:41.390034Z","bundle_sha256":"ae272aa8efa83d8f3177c946cfa98242ab8e29670b8c87589072e4b5639fefc6"}}