{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:C4BLUMPHPNRFPZKF4HKJAZ2HAC","short_pith_number":"pith:C4BLUMPH","schema_version":"1.0","canonical_sha256":"1702ba31e77b6257e545e1d4906747008034e37ba8889b25e4ca19c90df36536","source":{"kind":"arxiv","id":"2605.18312","version":1},"attestation_state":"computed","paper":{"title":"Energy-Weighted Site Percolation in Two Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Bond energy shifts the percolation threshold smoothly and changes the correlation-length exponent continuously in two dimensions.","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Kabir Ramola, Sayan Sircar","submitted_at":"2026-05-18T12:30:51Z","abstract_excerpt":"We study a generalization of two-dimensional site percolation by assigning an energy cost $\\varepsilon$ to bonds between nearest-neighbor occupied sites. This leads to a competition between entropy-driven cluster growth and energetic suppression (or enhancement) of connectivity. Varying $\\varepsilon$ continuously interpolates between dense ferromagnetic-like clusters, ordinary classical percolation, and a dilute regime of minimally connected isolated clusters. Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation thresh"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.18312","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-18T12:30:51Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"66d0abc3c176b044f2e36524e9b7c2c2f6ce18e154a1b23fba504e3324012bac","abstract_canon_sha256":"3d76627c954c44d41b7599c00c4468051ed2233d1fa58956eaf174378b51363a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:54.552808Z","signature_b64":"YXU+KnZttznx5lkb+hvnk85B4YYvghZLDLx63YpzObdt6KxOD7eLC7eaGimFViq6xqYr2bmZrj+0OXubqJ2MAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1702ba31e77b6257e545e1d4906747008034e37ba8889b25e4ca19c90df36536","last_reissued_at":"2026-05-20T00:05:54.552113Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:54.552113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy-Weighted Site Percolation in Two Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Bond energy shifts the percolation threshold smoothly and changes the correlation-length exponent continuously in two dimensions.","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Kabir Ramola, Sayan Sircar","submitted_at":"2026-05-18T12:30:51Z","abstract_excerpt":"We study a generalization of two-dimensional site percolation by assigning an energy cost $\\varepsilon$ to bonds between nearest-neighbor occupied sites. This leads to a competition between entropy-driven cluster growth and energetic suppression (or enhancement) of connectivity. Varying $\\varepsilon$ continuously interpolates between dense ferromagnetic-like clusters, ordinary classical percolation, and a dilute regime of minimally connected isolated clusters. Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation thresh"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation threshold smoothly. We define an energy-weighted correlation length that remains finite at the classical site occupation threshold (p_c(ε=0)) and shrinks with increasing ε, capturing the energetic suppression of large-scale connectivity.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The real-space RG with Kadanoff block recursions accurately tracks the continuous evolution of the correlation-length exponent ν from 1/2 to 4/3 to 1 and matches Coulomb-gas predictions for loop models without requiring additional parameters or post-hoc adjustments specific to the energy term.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Adding a continuous bond energy ε to 2D site percolation shifts the threshold smoothly and drives the correlation-length exponent ν from 1/2 through 4/3 to 1, as shown by Monte Carlo simulations and real-space RG that also reveal an energy-weighted correlation length and antiferromagnetic ordering,","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Bond energy shifts the percolation threshold smoothly and changes the correlation-length exponent continuously in two dimensions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1279c42dd0ac5f664bbef9799d4a97e3f95815f0337beb077339299fc42ff1cd"},"source":{"id":"2605.18312","kind":"arxiv","version":1},"verdict":{"id":"305f7100-a8fd-44ed-aef5-218f825a5f58","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:55:21.666710Z","strongest_claim":"Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation threshold smoothly. We define an energy-weighted correlation length that remains finite at the classical site occupation threshold (p_c(ε=0)) and shrinks with increasing ε, capturing the energetic suppression of large-scale connectivity.","one_line_summary":"Adding a continuous bond energy ε to 2D site percolation shifts the threshold smoothly and drives the correlation-length exponent ν from 1/2 through 4/3 to 1, as shown by Monte Carlo simulations and real-space RG that also reveal an energy-weighted correlation length and antiferromagnetic ordering,","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The real-space RG with Kadanoff block recursions accurately tracks the continuous evolution of the correlation-length exponent ν from 1/2 to 4/3 to 1 and matches Coulomb-gas predictions for loop models without requiring additional parameters or post-hoc adjustments specific to the energy term.","pith_extraction_headline":"Bond energy shifts the percolation threshold smoothly and changes the correlation-length exponent continuously in two dimensions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18312/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T00:02:52.399518Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:20.476096Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.197702Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:21:58.879228Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b23c5e551f0fafdace6d90db6cc6161b85da431b5b7e260b5a5c0b2574caabbf"},"references":{"count":85,"sample":[{"doi":"","year":null,"title":"In the dense cluster limit, asεapproaches−∞, loops become abundant with a loop fugacity ofn= 2","work_id":"531bbfb9-58af-411c-a361-4de6580f4d9b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"D. Stauffer and A. Aharony,Introduction to Percolation Theory(Taylor & Francis, 1994)","work_id":"7ea51201-081f-407b-986b-d540c279bf07","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"Bollob´ as and O","work_id":"4f1bbe07-a097-42e3-a117-5dc17592b066","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1982,"title":"Kesten,Percolation Theory for Mathematicians (Birkh¨ auser, 1982)","work_id":"bd9b64eb-8699-4210-bcb0-71af902ba74e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"Sahimi,Applications of Percolation Theory(Taylor & Francis, 1994)","work_id":"2eb5df91-a32c-42d3-8ee8-031800a42fb1","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":85,"snapshot_sha256":"cb69b004ba0d983979582f2f0a2664d5ec5925f1cf8978291fb19d21f876ccc0","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5f3bee70bfd959c90f4513cf45f26f48a4269866e0e20cff1847ecf79f838198"},"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":"2605.18312","created_at":"2026-05-20T00:05:54.552230+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.18312v1","created_at":"2026-05-20T00:05:54.552230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18312","created_at":"2026-05-20T00:05:54.552230+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4BLUMPHPNRF","created_at":"2026-05-20T00:05:54.552230+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4BLUMPHPNRFPZKF","created_at":"2026-05-20T00:05:54.552230+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4BLUMPH","created_at":"2026-05-20T00:05:54.552230+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC","json":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC.json","graph_json":"https://pith.science/api/pith-number/C4BLUMPHPNRFPZKF4HKJAZ2HAC/graph.json","events_json":"https://pith.science/api/pith-number/C4BLUMPHPNRFPZKF4HKJAZ2HAC/events.json","paper":"https://pith.science/paper/C4BLUMPH"},"agent_actions":{"view_html":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC","download_json":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC.json","view_paper":"https://pith.science/paper/C4BLUMPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.18312&json=true","fetch_graph":"https://pith.science/api/pith-number/C4BLUMPHPNRFPZKF4HKJAZ2HAC/graph.json","fetch_events":"https://pith.science/api/pith-number/C4BLUMPHPNRFPZKF4HKJAZ2HAC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC/action/storage_attestation","attest_author":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC/action/author_attestation","sign_citation":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC/action/citation_signature","submit_replication":"https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC/action/replication_record"}},"created_at":"2026-05-20T00:05:54.552230+00:00","updated_at":"2026-05-20T00:05:54.552230+00:00"}