{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TARAPQBKVBXTCDWDZZ542UCBSU","short_pith_number":"pith:TARAPQBK","canonical_record":{"source":{"id":"1207.2445","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-10T19:25:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"56c9560757fc53d403e0b3116ea17d83f3cd9e538d02c3ba70fbb6b9774f0d76","abstract_canon_sha256":"2af384570657147703982bc04fd82386d21b66bdb77f3402d2e397df5248243e"},"schema_version":"1.0"},"canonical_sha256":"982207c02aa86f310ec3ce7bcd50419534d0996b98fab7667c314ec23cf3cf55","source":{"kind":"arxiv","id":"1207.2445","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2445","created_at":"2026-05-18T01:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2445v2","created_at":"2026-05-18T01:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2445","created_at":"2026-05-18T01:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"TARAPQBKVBXT","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TARAPQBKVBXTCDWD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TARAPQBK","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TARAPQBKVBXTCDWDZZ542UCBSU","target":"record","payload":{"canonical_record":{"source":{"id":"1207.2445","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-10T19:25:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"56c9560757fc53d403e0b3116ea17d83f3cd9e538d02c3ba70fbb6b9774f0d76","abstract_canon_sha256":"2af384570657147703982bc04fd82386d21b66bdb77f3402d2e397df5248243e"},"schema_version":"1.0"},"canonical_sha256":"982207c02aa86f310ec3ce7bcd50419534d0996b98fab7667c314ec23cf3cf55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:25.723558Z","signature_b64":"K1PAIKb2TJP3oSEg/sz1RtRlpyl51B5Nfjl/Bsd1LQGyVWw1aJDJMhKbve5DqK8aNFCrtb5BfWsU8DU04ickCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"982207c02aa86f310ec3ce7bcd50419534d0996b98fab7667c314ec23cf3cf55","last_reissued_at":"2026-05-18T01:56:25.722818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:25.722818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.2445","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TGIudh88Zan4GIGAF3svq05yd7u7zfEzeQwU5VXpl/K7IdrSX8ivb3G2qJgTdrW7BqC1Fz+ROiag0IwpJwkCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:16:59.824249Z"},"content_sha256":"12ebfbcc37a6e454af5c9aac66d08e8c6dff5e3049f09631a4e84327ee87a900","schema_version":"1.0","event_id":"sha256:12ebfbcc37a6e454af5c9aac66d08e8c6dff5e3049f09631a4e84327ee87a900"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TARAPQBKVBXTCDWDZZ542UCBSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fabian Schwarzenberger, Ivan Veselic, Slim Ayadi","submitted_at":"2012-07-10T19:25:51Z","abstract_excerpt":"In this paper we consider random Hamiltonians defined on long-range percolation graphs over $\\ZZ^d$. The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2445","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KPqbYWQmLxSG2a4hTL1LTcOspliu8zOb+LxR/HtBbW5vKH0TBGs1SMhsi2eBm4+HLltZpeNoMnC/NLXDGqqTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:16:59.824983Z"},"content_sha256":"dcbbe9763cf919483a3b334b80b071d5d873fd350aafae6c2e8a5494a4fa1cd1","schema_version":"1.0","event_id":"sha256:dcbbe9763cf919483a3b334b80b071d5d873fd350aafae6c2e8a5494a4fa1cd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TARAPQBKVBXTCDWDZZ542UCBSU/bundle.json","state_url":"https://pith.science/pith/TARAPQBKVBXTCDWDZZ542UCBSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TARAPQBKVBXTCDWDZZ542UCBSU/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":"2026-06-08T21:16:59Z","links":{"resolver":"https://pith.science/pith/TARAPQBKVBXTCDWDZZ542UCBSU","bundle":"https://pith.science/pith/TARAPQBKVBXTCDWDZZ542UCBSU/bundle.json","state":"https://pith.science/pith/TARAPQBKVBXTCDWDZZ542UCBSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TARAPQBKVBXTCDWDZZ542UCBSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TARAPQBKVBXTCDWDZZ542UCBSU","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":"2af384570657147703982bc04fd82386d21b66bdb77f3402d2e397df5248243e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-10T19:25:51Z","title_canon_sha256":"56c9560757fc53d403e0b3116ea17d83f3cd9e538d02c3ba70fbb6b9774f0d76"},"schema_version":"1.0","source":{"id":"1207.2445","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2445","created_at":"2026-05-18T01:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2445v2","created_at":"2026-05-18T01:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2445","created_at":"2026-05-18T01:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"TARAPQBKVBXT","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TARAPQBKVBXTCDWD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TARAPQBK","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:dcbbe9763cf919483a3b334b80b071d5d873fd350aafae6c2e8a5494a4fa1cd1","target":"graph","created_at":"2026-05-18T01:56:25Z","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 consider random Hamiltonians defined on long-range percolation graphs over $\\ZZ^d$. The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula.","authors_text":"Fabian Schwarzenberger, Ivan Veselic, Slim Ayadi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-10T19:25:51Z","title":"Uniform existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2445","kind":"arxiv","version":2},"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":"sha256:12ebfbcc37a6e454af5c9aac66d08e8c6dff5e3049f09631a4e84327ee87a900","target":"record","created_at":"2026-05-18T01:56:25Z","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":"2af384570657147703982bc04fd82386d21b66bdb77f3402d2e397df5248243e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-10T19:25:51Z","title_canon_sha256":"56c9560757fc53d403e0b3116ea17d83f3cd9e538d02c3ba70fbb6b9774f0d76"},"schema_version":"1.0","source":{"id":"1207.2445","kind":"arxiv","version":2}},"canonical_sha256":"982207c02aa86f310ec3ce7bcd50419534d0996b98fab7667c314ec23cf3cf55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"982207c02aa86f310ec3ce7bcd50419534d0996b98fab7667c314ec23cf3cf55","first_computed_at":"2026-05-18T01:56:25.722818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:25.722818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K1PAIKb2TJP3oSEg/sz1RtRlpyl51B5Nfjl/Bsd1LQGyVWw1aJDJMhKbve5DqK8aNFCrtb5BfWsU8DU04ickCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:25.723558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2445","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12ebfbcc37a6e454af5c9aac66d08e8c6dff5e3049f09631a4e84327ee87a900","sha256:dcbbe9763cf919483a3b334b80b071d5d873fd350aafae6c2e8a5494a4fa1cd1"],"state_sha256":"04c7219d270e0028f8b4aa54a7e9f9185a618f6bfe99680c27d829752f5c8aed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JplgM7YjbNkWodOp3a6Zfrm8QyNjH3tAfdO58gy40JvLyWaYSY/JwKZpW260HJe1viwciNkfWyrbuzzR4/dTCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:16:59.828994Z","bundle_sha256":"b22f46e13caf54d7e0097a153aab85a1cc8eb69a1ae3776282e9baff3b86f25b"}}