{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BDXO55JONG4W2T2AZQK3J5USSB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"de93fa37f5a19fbba274116bd12d592caa8312cb5d252aa9f5f3ed0320ea0eea","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-18T14:01:13Z","title_canon_sha256":"8e140ea1f17772ddc5a91873c6cd82c01f96d3eb404ae187cee4ea6213677859"},"schema_version":"1.0","source":{"id":"1011.4192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4192","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4192v1","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4192","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"pith_short_12","alias_value":"BDXO55JONG4W","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BDXO55JONG4W2T2A","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BDXO55JO","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:8c6fde299dfea9a83bd43695532f8efefcd951caf64fb0def59329a19906e57d","target":"graph","created_at":"2026-05-18T04:35:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (IDS) or spectral distribution function can be approximated uniformly in the energy variable. Using this, we are able to characterise the set of discontinuities of the IDS.","authors_text":"Fabian Schwarzenberger","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-18T14:01:13Z","title":"Uniform approximation of the integrated density of states for long-range percolation Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4192","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ad94a4ad1477d068460cc89eb0cc2c6ced7939f2ea94ca22b69b8480228ee9e4","target":"record","created_at":"2026-05-18T04:35:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"de93fa37f5a19fbba274116bd12d592caa8312cb5d252aa9f5f3ed0320ea0eea","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-18T14:01:13Z","title_canon_sha256":"8e140ea1f17772ddc5a91873c6cd82c01f96d3eb404ae187cee4ea6213677859"},"schema_version":"1.0","source":{"id":"1011.4192","kind":"arxiv","version":1}},"canonical_sha256":"08eeeef52e69b96d4f40cc15b4f6929073e95e43931e84074ea1c22e990710af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08eeeef52e69b96d4f40cc15b4f6929073e95e43931e84074ea1c22e990710af","first_computed_at":"2026-05-18T04:35:46.463134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:46.463134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cPNVuoSH632fzgCj2eOOLVtH1jPa7wh/a5fi21yLmr3pHTfjfQOaMQj1cVBlEYR415gDMXSH1ylfsXF6MkYHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:46.463752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad94a4ad1477d068460cc89eb0cc2c6ced7939f2ea94ca22b69b8480228ee9e4","sha256:8c6fde299dfea9a83bd43695532f8efefcd951caf64fb0def59329a19906e57d"],"state_sha256":"c0524227b8b2b38a7c03d8c3d49ea606f8099cb699d326e323f16062bbf560bf"}