{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VLPQA6L4ORPYN326UFUBX7BPTK","short_pith_number":"pith:VLPQA6L4","schema_version":"1.0","canonical_sha256":"aadf00797c745f86ef5ea1681bfc2f9ab4ecd4ab78a23a3bb9abe2c9e13f232b","source":{"kind":"arxiv","id":"1109.0719","version":1},"attestation_state":"computed","paper":{"title":"Combinatorial models of rigidity and renormalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Julien Barr\\'e","submitted_at":"2011-09-04T14:41:34Z","abstract_excerpt":"We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation ph"},"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":"1109.0719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-04T14:41:34Z","cross_cats_sorted":[],"title_canon_sha256":"8e95b2279eb55ac84ac44a72c79cf521972d27172ced699daefe9b7e27235c1c","abstract_canon_sha256":"a5fb9c0d15773db71a90b08aaea4dd314cc068ede7096353d6f8cb51dffe7a93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:40.178627Z","signature_b64":"Nk4vFGQnH47hLwTUg/LWM1v1cTFcLj36jxqYXVV25h8ibc7OWQspgomoUaM36EOxjhMxPA33/m4GIk8nsvdhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aadf00797c745f86ef5ea1681bfc2f9ab4ecd4ab78a23a3bb9abe2c9e13f232b","last_reissued_at":"2026-05-18T02:00:40.177877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:40.177877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial models of rigidity and renormalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Julien Barr\\'e","submitted_at":"2011-09-04T14:41:34Z","abstract_excerpt":"We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation ph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0719","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.0719","created_at":"2026-05-18T02:00:40.177983+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.0719v1","created_at":"2026-05-18T02:00:40.177983+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0719","created_at":"2026-05-18T02:00:40.177983+00:00"},{"alias_kind":"pith_short_12","alias_value":"VLPQA6L4ORPY","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VLPQA6L4ORPYN326","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VLPQA6L4","created_at":"2026-05-18T12:26:44.992195+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/VLPQA6L4ORPYN326UFUBX7BPTK","json":"https://pith.science/pith/VLPQA6L4ORPYN326UFUBX7BPTK.json","graph_json":"https://pith.science/api/pith-number/VLPQA6L4ORPYN326UFUBX7BPTK/graph.json","events_json":"https://pith.science/api/pith-number/VLPQA6L4ORPYN326UFUBX7BPTK/events.json","paper":"https://pith.science/paper/VLPQA6L4"},"agent_actions":{"view_html":"https://pith.science/pith/VLPQA6L4ORPYN326UFUBX7BPTK","download_json":"https://pith.science/pith/VLPQA6L4ORPYN326UFUBX7BPTK.json","view_paper":"https://pith.science/paper/VLPQA6L4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.0719&json=true","fetch_graph":"https://pith.science/api/pith-number/VLPQA6L4ORPYN326UFUBX7BPTK/graph.json","fetch_events":"https://pith.science/api/pith-number/VLPQA6L4ORPYN326UFUBX7BPTK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VLPQA6L4ORPYN326UFUBX7BPTK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VLPQA6L4ORPYN326UFUBX7BPTK/action/storage_attestation","attest_author":"https://pith.science/pith/VLPQA6L4ORPYN326UFUBX7BPTK/action/author_attestation","sign_citation":"https://pith.science/pith/VLPQA6L4ORPYN326UFUBX7BPTK/action/citation_signature","submit_replication":"https://pith.science/pith/VLPQA6L4ORPYN326UFUBX7BPTK/action/replication_record"}},"created_at":"2026-05-18T02:00:40.177983+00:00","updated_at":"2026-05-18T02:00:40.177983+00:00"}