{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:DHNE2MB7AIQ3BKDMTFXICZ2JJV","short_pith_number":"pith:DHNE2MB7","schema_version":"1.0","canonical_sha256":"19da4d303f0221b0a86c996e8167494d4fe5fad231e233fdefa829b624fb1bbf","source":{"kind":"arxiv","id":"2202.09436","version":1},"attestation_state":"computed","paper":{"title":"Renormalization Group Approach to Percolation in Hierarchical Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Abraham Levitan","submitted_at":"2022-02-18T21:40:47Z","abstract_excerpt":"Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most percolative systems undergo a phase transition from a disconnected state with many disjoint clusters to a state where a finite fraction of the lattice sites are connected to a single cluster. As in the case of thermodynamic phase transitions, power law dependencies generically near the critical percolation threshold. The origin of these dependencies can be u"},"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":"2202.09436","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2022-02-18T21:40:47Z","cross_cats_sorted":[],"title_canon_sha256":"8445f58f7dd18c2906fb0b5cbd6b708e77794ba92ceef18c5bffc3e95c512c81","abstract_canon_sha256":"faf72fe9569dfef8ca67da73d345a4cce64afa9c8bd62d94e4c51138908a8736"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:58:22.155927Z","signature_b64":"Rbq7P67B5WBdX6iAjGzk26Oiili7+KTcprJewc0R5gTQz36kNlhSP7ZDB8fCJuS72fEjktdD8o4sSvVmIZsrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19da4d303f0221b0a86c996e8167494d4fe5fad231e233fdefa829b624fb1bbf","last_reissued_at":"2026-07-05T03:58:22.155501Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:58:22.155501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renormalization Group Approach to Percolation in Hierarchical Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Abraham Levitan","submitted_at":"2022-02-18T21:40:47Z","abstract_excerpt":"Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most percolative systems undergo a phase transition from a disconnected state with many disjoint clusters to a state where a finite fraction of the lattice sites are connected to a single cluster. As in the case of thermodynamic phase transitions, power law dependencies generically near the critical percolation threshold. The origin of these dependencies can be u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.09436","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.09436/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2202.09436","created_at":"2026-07-05T03:58:22.155562+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.09436v1","created_at":"2026-07-05T03:58:22.155562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.09436","created_at":"2026-07-05T03:58:22.155562+00:00"},{"alias_kind":"pith_short_12","alias_value":"DHNE2MB7AIQ3","created_at":"2026-07-05T03:58:22.155562+00:00"},{"alias_kind":"pith_short_16","alias_value":"DHNE2MB7AIQ3BKDM","created_at":"2026-07-05T03:58:22.155562+00:00"},{"alias_kind":"pith_short_8","alias_value":"DHNE2MB7","created_at":"2026-07-05T03:58:22.155562+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2506.18073","citing_title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV","json":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV.json","graph_json":"https://pith.science/api/pith-number/DHNE2MB7AIQ3BKDMTFXICZ2JJV/graph.json","events_json":"https://pith.science/api/pith-number/DHNE2MB7AIQ3BKDMTFXICZ2JJV/events.json","paper":"https://pith.science/paper/DHNE2MB7"},"agent_actions":{"view_html":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV","download_json":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV.json","view_paper":"https://pith.science/paper/DHNE2MB7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.09436&json=true","fetch_graph":"https://pith.science/api/pith-number/DHNE2MB7AIQ3BKDMTFXICZ2JJV/graph.json","fetch_events":"https://pith.science/api/pith-number/DHNE2MB7AIQ3BKDMTFXICZ2JJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV/action/storage_attestation","attest_author":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV/action/author_attestation","sign_citation":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV/action/citation_signature","submit_replication":"https://pith.science/pith/DHNE2MB7AIQ3BKDMTFXICZ2JJV/action/replication_record"}},"created_at":"2026-07-05T03:58:22.155562+00:00","updated_at":"2026-07-05T03:58:22.155562+00:00"}