{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:M4IAB775AXBVLJEREWHAFTSWIV","short_pith_number":"pith:M4IAB775","schema_version":"1.0","canonical_sha256":"671000fffd05c355a491258e02ce56457cb4c95248c379ca0bac2b030378b4ba","source":{"kind":"arxiv","id":"0906.1554","version":2},"attestation_state":"computed","paper":{"title":"Three-leg correlations in the two component spanning tree on the upper half-plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"S.Y. Grigorev, V.B. Priezzhev, V.S. Poghosyan","submitted_at":"2009-06-08T18:19:38Z","abstract_excerpt":"We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\\gg s \\gg 1$ and $s \\gg r \\gg 1$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0906.1554","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-06-08T18:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"1a71f00ecd2f43358e6cc7d30161417a5fe653bf38642d5fffdbaaed7d5b7985","abstract_canon_sha256":"f6bb5af7d093627c0a6fac88d70d8e4b4dc07bb33f3736e833149ed26ca5d4b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:44.177352Z","signature_b64":"Nx6FjU6Zge99KrelTTbpyGmLv6fgVCa8XhuJvl3ftXu0O8EuDpWzKQtJZsqZprG50noK8TXf1bsjZG+iactRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"671000fffd05c355a491258e02ce56457cb4c95248c379ca0bac2b030378b4ba","last_reissued_at":"2026-05-18T03:15:44.176872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:44.176872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three-leg correlations in the two component spanning tree on the upper half-plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"S.Y. Grigorev, V.B. Priezzhev, V.S. Poghosyan","submitted_at":"2009-06-08T18:19:38Z","abstract_excerpt":"We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\\gg s \\gg 1$ and $s \\gg r \\gg 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.1554","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0906.1554","created_at":"2026-05-18T03:15:44.176950+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.1554v2","created_at":"2026-05-18T03:15:44.176950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.1554","created_at":"2026-05-18T03:15:44.176950+00:00"},{"alias_kind":"pith_short_12","alias_value":"M4IAB775AXBV","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"M4IAB775AXBVLJER","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"M4IAB775","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV","json":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV.json","graph_json":"https://pith.science/api/pith-number/M4IAB775AXBVLJEREWHAFTSWIV/graph.json","events_json":"https://pith.science/api/pith-number/M4IAB775AXBVLJEREWHAFTSWIV/events.json","paper":"https://pith.science/paper/M4IAB775"},"agent_actions":{"view_html":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV","download_json":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV.json","view_paper":"https://pith.science/paper/M4IAB775","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.1554&json=true","fetch_graph":"https://pith.science/api/pith-number/M4IAB775AXBVLJEREWHAFTSWIV/graph.json","fetch_events":"https://pith.science/api/pith-number/M4IAB775AXBVLJEREWHAFTSWIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV/action/storage_attestation","attest_author":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV/action/author_attestation","sign_citation":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV/action/citation_signature","submit_replication":"https://pith.science/pith/M4IAB775AXBVLJEREWHAFTSWIV/action/replication_record"}},"created_at":"2026-05-18T03:15:44.176950+00:00","updated_at":"2026-05-18T03:15:44.176950+00:00"}