{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:L4FGLKLEWVH6VT2KOGPVVW2VUL","short_pith_number":"pith:L4FGLKLE","schema_version":"1.0","canonical_sha256":"5f0a65a964b54feacf4a719f5adb55a2d14a2f9a57518ea695239392724685cb","source":{"kind":"arxiv","id":"1104.5637","version":2},"attestation_state":"computed","paper":{"title":"Lifshitz tails on the Bethe lattice: a combinatorial approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.dis-nn","authors_text":"Guilhem Semerjian, Victor Bapst","submitted_at":"2011-04-29T14:33:16Z","abstract_excerpt":"The density of states of disordered hopping models generically exhibits an essential singularity around the edges of its support, known as a Lifshitz tail. We study this phenomenon on the Bethe lattice, i.e. for the large-size limit of random regular graphs, converging locally to the infinite regular tree, for both diagonal and off-diagonal disorder. The exponential growth of the volume and surface of balls on these lattices is an obstacle for the techniques used to characterize the Lifshitz tails in the finite-dimensional case. We circumvent this difficulty by computing bounds on the moments "},"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":"1104.5637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2011-04-29T14:33:16Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"title_canon_sha256":"154b9c64e3ede4ef341ba76daa87a7a9401be836faceba05921e7bffcf144b87","abstract_canon_sha256":"3e6678bb63dd0c8ede2b720d6ca7e57ede1d791e2ff03687f566e535e8c2def5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:11.801221Z","signature_b64":"ckzoI0Yt2Psg46jd/67v5SkcvSWpxVcrKBkCN10TYHcNAm/lMq0Qfnyu6DvUYV51O+FqvTMPu6HGrpVGKIzqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f0a65a964b54feacf4a719f5adb55a2d14a2f9a57518ea695239392724685cb","last_reissued_at":"2026-05-18T04:12:11.800628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:11.800628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifshitz tails on the Bethe lattice: a combinatorial approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.dis-nn","authors_text":"Guilhem Semerjian, Victor Bapst","submitted_at":"2011-04-29T14:33:16Z","abstract_excerpt":"The density of states of disordered hopping models generically exhibits an essential singularity around the edges of its support, known as a Lifshitz tail. We study this phenomenon on the Bethe lattice, i.e. for the large-size limit of random regular graphs, converging locally to the infinite regular tree, for both diagonal and off-diagonal disorder. The exponential growth of the volume and surface of balls on these lattices is an obstacle for the techniques used to characterize the Lifshitz tails in the finite-dimensional case. We circumvent this difficulty by computing bounds on the moments "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5637","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":"1104.5637","created_at":"2026-05-18T04:12:11.800728+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.5637v2","created_at":"2026-05-18T04:12:11.800728+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5637","created_at":"2026-05-18T04:12:11.800728+00:00"},{"alias_kind":"pith_short_12","alias_value":"L4FGLKLEWVH6","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"L4FGLKLEWVH6VT2K","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"L4FGLKLE","created_at":"2026-05-18T12:26:34.985390+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/L4FGLKLEWVH6VT2KOGPVVW2VUL","json":"https://pith.science/pith/L4FGLKLEWVH6VT2KOGPVVW2VUL.json","graph_json":"https://pith.science/api/pith-number/L4FGLKLEWVH6VT2KOGPVVW2VUL/graph.json","events_json":"https://pith.science/api/pith-number/L4FGLKLEWVH6VT2KOGPVVW2VUL/events.json","paper":"https://pith.science/paper/L4FGLKLE"},"agent_actions":{"view_html":"https://pith.science/pith/L4FGLKLEWVH6VT2KOGPVVW2VUL","download_json":"https://pith.science/pith/L4FGLKLEWVH6VT2KOGPVVW2VUL.json","view_paper":"https://pith.science/paper/L4FGLKLE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.5637&json=true","fetch_graph":"https://pith.science/api/pith-number/L4FGLKLEWVH6VT2KOGPVVW2VUL/graph.json","fetch_events":"https://pith.science/api/pith-number/L4FGLKLEWVH6VT2KOGPVVW2VUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L4FGLKLEWVH6VT2KOGPVVW2VUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L4FGLKLEWVH6VT2KOGPVVW2VUL/action/storage_attestation","attest_author":"https://pith.science/pith/L4FGLKLEWVH6VT2KOGPVVW2VUL/action/author_attestation","sign_citation":"https://pith.science/pith/L4FGLKLEWVH6VT2KOGPVVW2VUL/action/citation_signature","submit_replication":"https://pith.science/pith/L4FGLKLEWVH6VT2KOGPVVW2VUL/action/replication_record"}},"created_at":"2026-05-18T04:12:11.800728+00:00","updated_at":"2026-05-18T04:12:11.800728+00:00"}