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A lattice of $N$ sites has $O(\\sqrt{N})$ zero-frequency floppy modes that convert to finite-frequency anomalous modes when next-nearest-neighbor ($NNN$) springs are added. We use the coherent potential approximation (CPA) to study the mode structure and mechanical properties of the kagome lattice in which $NNN$ springs with spring constant $\\kappa$ are added with probability $\\Prob= \\Delta z/4$, where $\\Delta z= z-4$ and $z$ is the average "},"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":"1008.2037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-08-12T03:50:09Z","cross_cats_sorted":["cond-mat.soft","cond-mat.stat-mech"],"title_canon_sha256":"790ac0141d99f01b5260266eabf08b6df045133f3ff1add49e0a6ce1ba53cf20","abstract_canon_sha256":"60b6fc0656d3dfb0540aac73426bbc3c0bf4fa43f79f1b7f4f762c0ca57cefaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:06.783423Z","signature_b64":"0wlIdS+K2BoRCIjovJLAimmcGsv+dx1Oyt/BXt3CZMPOEti+/gB2vQd+jhsK3bpZAWORJBY/x9Y2KDRqgswxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74fe7130934812b263180112edf5ca393808bafb729e4fdcfce3d0576a02a9d6","last_reissued_at":"2026-05-18T04:07:06.782798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:06.782798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coherent potential approximation of random nearly isostatic kagome lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"T. 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We use the coherent potential approximation (CPA) to study the mode structure and mechanical properties of the kagome lattice in which $NNN$ springs with spring constant $\\kappa$ are added with probability $\\Prob= \\Delta z/4$, where $\\Delta z= z-4$ and $z$ is the average "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2037","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":"1008.2037","created_at":"2026-05-18T04:07:06.782879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.2037v1","created_at":"2026-05-18T04:07:06.782879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2037","created_at":"2026-05-18T04:07:06.782879+00:00"},{"alias_kind":"pith_short_12","alias_value":"OT7HCMETJAJL","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OT7HCMETJAJLEYYY","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OT7HCMET","created_at":"2026-05-18T12:26:12.377268+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/OT7HCMETJAJLEYYYAEJO35OKHE","json":"https://pith.science/pith/OT7HCMETJAJLEYYYAEJO35OKHE.json","graph_json":"https://pith.science/api/pith-number/OT7HCMETJAJLEYYYAEJO35OKHE/graph.json","events_json":"https://pith.science/api/pith-number/OT7HCMETJAJLEYYYAEJO35OKHE/events.json","paper":"https://pith.science/paper/OT7HCMET"},"agent_actions":{"view_html":"https://pith.science/pith/OT7HCMETJAJLEYYYAEJO35OKHE","download_json":"https://pith.science/pith/OT7HCMETJAJLEYYYAEJO35OKHE.json","view_paper":"https://pith.science/paper/OT7HCMET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.2037&json=true","fetch_graph":"https://pith.science/api/pith-number/OT7HCMETJAJLEYYYAEJO35OKHE/graph.json","fetch_events":"https://pith.science/api/pith-number/OT7HCMETJAJLEYYYAEJO35OKHE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OT7HCMETJAJLEYYYAEJO35OKHE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OT7HCMETJAJLEYYYAEJO35OKHE/action/storage_attestation","attest_author":"https://pith.science/pith/OT7HCMETJAJLEYYYAEJO35OKHE/action/author_attestation","sign_citation":"https://pith.science/pith/OT7HCMETJAJLEYYYAEJO35OKHE/action/citation_signature","submit_replication":"https://pith.science/pith/OT7HCMETJAJLEYYYAEJO35OKHE/action/replication_record"}},"created_at":"2026-05-18T04:07:06.782879+00:00","updated_at":"2026-05-18T04:07:06.782879+00:00"}