{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BDXO55JONG4W2T2AZQK3J5USSB","short_pith_number":"pith:BDXO55JO","canonical_record":{"source":{"id":"1011.4192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-18T14:01:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8e140ea1f17772ddc5a91873c6cd82c01f96d3eb404ae187cee4ea6213677859","abstract_canon_sha256":"de93fa37f5a19fbba274116bd12d592caa8312cb5d252aa9f5f3ed0320ea0eea"},"schema_version":"1.0"},"canonical_sha256":"08eeeef52e69b96d4f40cc15b4f6929073e95e43931e84074ea1c22e990710af","source":{"kind":"arxiv","id":"1011.4192","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BDXO55JONG4W2T2AZQK3J5USSB","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-18T14:01:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8e140ea1f17772ddc5a91873c6cd82c01f96d3eb404ae187cee4ea6213677859","abstract_canon_sha256":"de93fa37f5a19fbba274116bd12d592caa8312cb5d252aa9f5f3ed0320ea0eea"},"schema_version":"1.0"},"canonical_sha256":"08eeeef52e69b96d4f40cc15b4f6929073e95e43931e84074ea1c22e990710af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:46.463752Z","signature_b64":"cPNVuoSH632fzgCj2eOOLVtH1jPa7wh/a5fi21yLmr3pHTfjfQOaMQj1cVBlEYR415gDMXSH1ylfsXF6MkYHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08eeeef52e69b96d4f40cc15b4f6929073e95e43931e84074ea1c22e990710af","last_reissued_at":"2026-05-18T04:35:46.463134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:46.463134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4192","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DudhD4lmtvEfufPPvXSZ1GKUkwaSaqiJtcNr7d50Ux9nnXTNdB1lmyxrwoRzk82pdR2RAPk45G+UXAi0bxulCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:23:36.739690Z"},"content_sha256":"ad94a4ad1477d068460cc89eb0cc2c6ced7939f2ea94ca22b69b8480228ee9e4","schema_version":"1.0","event_id":"sha256:ad94a4ad1477d068460cc89eb0cc2c6ced7939f2ea94ca22b69b8480228ee9e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BDXO55JONG4W2T2AZQK3J5USSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform approximation of the integrated density of states for long-range percolation Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fabian Schwarzenberger","submitted_at":"2010-11-18T14:01:13Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4192","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tVwUeRU8PeDi+fxfoP/3nlacYDIc48ZHQCmAtIbOXzvBWPHMlRIK++3oGWXY2Y6vIao54ItPtzX2vVq07T5NDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:23:36.740462Z"},"content_sha256":"8c6fde299dfea9a83bd43695532f8efefcd951caf64fb0def59329a19906e57d","schema_version":"1.0","event_id":"sha256:8c6fde299dfea9a83bd43695532f8efefcd951caf64fb0def59329a19906e57d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDXO55JONG4W2T2AZQK3J5USSB/bundle.json","state_url":"https://pith.science/pith/BDXO55JONG4W2T2AZQK3J5USSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDXO55JONG4W2T2AZQK3J5USSB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T03:23:36Z","links":{"resolver":"https://pith.science/pith/BDXO55JONG4W2T2AZQK3J5USSB","bundle":"https://pith.science/pith/BDXO55JONG4W2T2AZQK3J5USSB/bundle.json","state":"https://pith.science/pith/BDXO55JONG4W2T2AZQK3J5USSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDXO55JONG4W2T2AZQK3J5USSB/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MoZOYxeh4Pz/oWRV83R8xoZr9ZE34PdUY1/zCJYlJEW7CJdGJvCzZbCb+ZxshDQIQ8FrD9TpIGDiaolivrpnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T03:23:36.744328Z","bundle_sha256":"fb5633c1e03883c8ae610e7a0261558df9da2b0497225a7ef25d2aa6745e3f96"}}