{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AD4LYB3XE7JGNXHFNC6SDPMSIQ","short_pith_number":"pith:AD4LYB3X","schema_version":"1.0","canonical_sha256":"00f8bc077727d266dce568bd21bd92441676ae32e6e25a4194775f032453b3a8","source":{"kind":"arxiv","id":"1208.1223","version":2},"attestation_state":"computed","paper":{"title":"Continuum percolation for Gibbsian point processes with attractive interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sabine Jansen","submitted_at":"2012-08-06T17:58:24Z","abstract_excerpt":"We study the problem of continuum percolation in infinite volume Gibbs measures for particles with an attractive pair potential, with a focus on low temperatures (large $\\beta$). The main results are bounds on percolation thresholds $\\rho_\\pm(\\beta)$ in terms of the density rather than the chemical potential or activity. In addition, we prove a variational formula for a large deviations rate function for cluster size distributions. This formula establishes a link with the Gibbs variational principle and a form of equivalence of ensembles, and allows us to combine knowledge on finite volume, ca"},"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":"1208.1223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-06T17:58:24Z","cross_cats_sorted":[],"title_canon_sha256":"86cae69959c5b80f8b0e4126909d804d4ef8ca3749ddc41748769727999c2a66","abstract_canon_sha256":"12bc2b56a14d1c0df20a762f384fc994781273d0b85c40e7de3625a6aa41bf89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:46.941179Z","signature_b64":"Si/9HCAY+Zuc7S6OIpHq9vanbvrJbVdDJd9bCdGxv2zAVYwsgadxNMfIspk8cyAeRe2RRuNhoPHVyMOqhYqhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00f8bc077727d266dce568bd21bd92441676ae32e6e25a4194775f032453b3a8","last_reissued_at":"2026-05-18T03:46:46.940223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:46.940223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuum percolation for Gibbsian point processes with attractive interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sabine Jansen","submitted_at":"2012-08-06T17:58:24Z","abstract_excerpt":"We study the problem of continuum percolation in infinite volume Gibbs measures for particles with an attractive pair potential, with a focus on low temperatures (large $\\beta$). The main results are bounds on percolation thresholds $\\rho_\\pm(\\beta)$ in terms of the density rather than the chemical potential or activity. In addition, we prove a variational formula for a large deviations rate function for cluster size distributions. This formula establishes a link with the Gibbs variational principle and a form of equivalence of ensembles, and allows us to combine knowledge on finite volume, ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1223","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":"1208.1223","created_at":"2026-05-18T03:46:46.940391+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.1223v2","created_at":"2026-05-18T03:46:46.940391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1223","created_at":"2026-05-18T03:46:46.940391+00:00"},{"alias_kind":"pith_short_12","alias_value":"AD4LYB3XE7JG","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AD4LYB3XE7JGNXHF","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AD4LYB3X","created_at":"2026-05-18T12:26:58.693483+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/AD4LYB3XE7JGNXHFNC6SDPMSIQ","json":"https://pith.science/pith/AD4LYB3XE7JGNXHFNC6SDPMSIQ.json","graph_json":"https://pith.science/api/pith-number/AD4LYB3XE7JGNXHFNC6SDPMSIQ/graph.json","events_json":"https://pith.science/api/pith-number/AD4LYB3XE7JGNXHFNC6SDPMSIQ/events.json","paper":"https://pith.science/paper/AD4LYB3X"},"agent_actions":{"view_html":"https://pith.science/pith/AD4LYB3XE7JGNXHFNC6SDPMSIQ","download_json":"https://pith.science/pith/AD4LYB3XE7JGNXHFNC6SDPMSIQ.json","view_paper":"https://pith.science/paper/AD4LYB3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.1223&json=true","fetch_graph":"https://pith.science/api/pith-number/AD4LYB3XE7JGNXHFNC6SDPMSIQ/graph.json","fetch_events":"https://pith.science/api/pith-number/AD4LYB3XE7JGNXHFNC6SDPMSIQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AD4LYB3XE7JGNXHFNC6SDPMSIQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AD4LYB3XE7JGNXHFNC6SDPMSIQ/action/storage_attestation","attest_author":"https://pith.science/pith/AD4LYB3XE7JGNXHFNC6SDPMSIQ/action/author_attestation","sign_citation":"https://pith.science/pith/AD4LYB3XE7JGNXHFNC6SDPMSIQ/action/citation_signature","submit_replication":"https://pith.science/pith/AD4LYB3XE7JGNXHFNC6SDPMSIQ/action/replication_record"}},"created_at":"2026-05-18T03:46:46.940391+00:00","updated_at":"2026-05-18T03:46:46.940391+00:00"}