{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SUMOXHAKD4VUKBN3OSQV3OCIT3","short_pith_number":"pith:SUMOXHAK","canonical_record":{"source":{"id":"1509.03368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-11T00:55:45Z","cross_cats_sorted":[],"title_canon_sha256":"75f1742d2d0d2d950498a0e04df9937fe953ba2950625c40872d4223c5ccbd5f","abstract_canon_sha256":"fe965a908c2219d113201de22565bda86ec7d50b21cfbc2ca808f59e75bd7f0d"},"schema_version":"1.0"},"canonical_sha256":"9518eb9c0a1f2b4505bb74a15db8489eee1b37c7a60da1980bac5ae177eebb09","source":{"kind":"arxiv","id":"1509.03368","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03368","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03368v1","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03368","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"SUMOXHAKD4VU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SUMOXHAKD4VUKBN3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SUMOXHAK","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SUMOXHAKD4VUKBN3OSQV3OCIT3","target":"record","payload":{"canonical_record":{"source":{"id":"1509.03368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-11T00:55:45Z","cross_cats_sorted":[],"title_canon_sha256":"75f1742d2d0d2d950498a0e04df9937fe953ba2950625c40872d4223c5ccbd5f","abstract_canon_sha256":"fe965a908c2219d113201de22565bda86ec7d50b21cfbc2ca808f59e75bd7f0d"},"schema_version":"1.0"},"canonical_sha256":"9518eb9c0a1f2b4505bb74a15db8489eee1b37c7a60da1980bac5ae177eebb09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:23.491440Z","signature_b64":"9Wkfo2wB8elhQamBoNfaALII3gBJ1fiYtLdJAdfh5zFcfTwpBhiDkK3jUOiaCDAAQamXgl6zz1Gj4lNNJO54Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9518eb9c0a1f2b4505bb74a15db8489eee1b37c7a60da1980bac5ae177eebb09","last_reissued_at":"2026-05-18T01:33:23.490750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:23.490750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.03368","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":"2026-05-18T01:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6+SRsevw4miWaKpl1ML14f1FIuqEuSGsc+sfj6W62OCBkhw9D5jOMJxoD4DS8hXIpV5RxWZr+B8jbsQrIYm6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:01:11.085497Z"},"content_sha256":"e8ab3f6fe79a94bc90fa97bf0f1aa3d3904ef15ef289565b4519fca1f32c03ea","schema_version":"1.0","event_id":"sha256:e8ab3f6fe79a94bc90fa97bf0f1aa3d3904ef15ef289565b4519fca1f32c03ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SUMOXHAKD4VUKBN3OSQV3OCIT3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Statistics of Sparse Random Graphs with a General Degree Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ben Adlam, Ziliang Che","submitted_at":"2015-09-11T00:55:45Z","abstract_excerpt":"We consider the adjacency matrices of sparse random graphs from the Chung-Lu model, where edges are added independently between the $N$ vertices with varying probabilities $p_{ij}$. The rank of the matrix $(p_{ij})$ is some fixed positive integer. We prove that the distribution of eigenvalues is given by the solution of a functional self-consistent equation. We prove a local law down to the optimal scale and prove bulk universality. The results are parallel to \\cite{Erdos2013b} and \\cite{Landon2015}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03368","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":"2026-05-18T01:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a+EN7YVaFoNLSdRW3v+avZwtpf5p0TlmsByNZx09+eghhGZVcvQUx7A4AyQGkKmUXBPJwZgM8UEr+MPhWynjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:01:11.086088Z"},"content_sha256":"4b7b917c7763c0fc8b0fffe3e3b0c9b838aceb90c293f2f98440081cfab67136","schema_version":"1.0","event_id":"sha256:4b7b917c7763c0fc8b0fffe3e3b0c9b838aceb90c293f2f98440081cfab67136"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUMOXHAKD4VUKBN3OSQV3OCIT3/bundle.json","state_url":"https://pith.science/pith/SUMOXHAKD4VUKBN3OSQV3OCIT3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUMOXHAKD4VUKBN3OSQV3OCIT3/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":"2026-08-16T15:01:11Z","links":{"resolver":"https://pith.science/pith/SUMOXHAKD4VUKBN3OSQV3OCIT3","bundle":"https://pith.science/pith/SUMOXHAKD4VUKBN3OSQV3OCIT3/bundle.json","state":"https://pith.science/pith/SUMOXHAKD4VUKBN3OSQV3OCIT3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUMOXHAKD4VUKBN3OSQV3OCIT3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SUMOXHAKD4VUKBN3OSQV3OCIT3","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":"fe965a908c2219d113201de22565bda86ec7d50b21cfbc2ca808f59e75bd7f0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-11T00:55:45Z","title_canon_sha256":"75f1742d2d0d2d950498a0e04df9937fe953ba2950625c40872d4223c5ccbd5f"},"schema_version":"1.0","source":{"id":"1509.03368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03368","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03368v1","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03368","created_at":"2026-05-18T01:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"SUMOXHAKD4VU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SUMOXHAKD4VUKBN3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SUMOXHAK","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:4b7b917c7763c0fc8b0fffe3e3b0c9b838aceb90c293f2f98440081cfab67136","target":"graph","created_at":"2026-05-18T01:33:23Z","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":"We consider the adjacency matrices of sparse random graphs from the Chung-Lu model, where edges are added independently between the $N$ vertices with varying probabilities $p_{ij}$. The rank of the matrix $(p_{ij})$ is some fixed positive integer. We prove that the distribution of eigenvalues is given by the solution of a functional self-consistent equation. We prove a local law down to the optimal scale and prove bulk universality. The results are parallel to \\cite{Erdos2013b} and \\cite{Landon2015}.","authors_text":"Ben Adlam, Ziliang Che","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-11T00:55:45Z","title":"Spectral Statistics of Sparse Random Graphs with a General Degree Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03368","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:e8ab3f6fe79a94bc90fa97bf0f1aa3d3904ef15ef289565b4519fca1f32c03ea","target":"record","created_at":"2026-05-18T01:33:23Z","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":"fe965a908c2219d113201de22565bda86ec7d50b21cfbc2ca808f59e75bd7f0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-11T00:55:45Z","title_canon_sha256":"75f1742d2d0d2d950498a0e04df9937fe953ba2950625c40872d4223c5ccbd5f"},"schema_version":"1.0","source":{"id":"1509.03368","kind":"arxiv","version":1}},"canonical_sha256":"9518eb9c0a1f2b4505bb74a15db8489eee1b37c7a60da1980bac5ae177eebb09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9518eb9c0a1f2b4505bb74a15db8489eee1b37c7a60da1980bac5ae177eebb09","first_computed_at":"2026-05-18T01:33:23.490750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:23.490750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Wkfo2wB8elhQamBoNfaALII3gBJ1fiYtLdJAdfh5zFcfTwpBhiDkK3jUOiaCDAAQamXgl6zz1Gj4lNNJO54Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:23.491440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8ab3f6fe79a94bc90fa97bf0f1aa3d3904ef15ef289565b4519fca1f32c03ea","sha256:4b7b917c7763c0fc8b0fffe3e3b0c9b838aceb90c293f2f98440081cfab67136"],"state_sha256":"17c55bd0fb0cbdeb7a1ba945939e9871c150ee83f850985ea7abbf26c87f3804"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mINnxNXHdSTVMHd4gcWl4NrDywyTNx95nrdc9Y3T3Et7A7NCYQnYuHwzGYS2ptPxyigyWorh75gEkSoHUeXOAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:01:11.091674Z","bundle_sha256":"37e3b47cd169998a25fe50f939a74e884e6b17c3f15f88c2302ed9e65e84dc67"}}