{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DNHTJUZLJURUIL7EVBMS4X4M5T","short_pith_number":"pith:DNHTJUZL","canonical_record":{"source":{"id":"1503.00137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-28T15:09:11Z","cross_cats_sorted":[],"title_canon_sha256":"7a04ad0ca468334dd98ec8a48907e31d2af3c8df01aaf512b10443422d315ab3","abstract_canon_sha256":"b069a16fc1075e1a4222158630cfe9e626e2d6cb13077a7f2b750dd5e46db3ce"},"schema_version":"1.0"},"canonical_sha256":"1b4f34d32b4d23442fe4a8592e5f8cece4390945a8d4c798e7f3832365806571","source":{"kind":"arxiv","id":"1503.00137","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00137","created_at":"2026-05-18T01:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00137v1","created_at":"2026-05-18T01:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00137","created_at":"2026-05-18T01:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"DNHTJUZLJURU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DNHTJUZLJURUIL7E","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DNHTJUZL","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DNHTJUZLJURUIL7EVBMS4X4M5T","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-28T15:09:11Z","cross_cats_sorted":[],"title_canon_sha256":"7a04ad0ca468334dd98ec8a48907e31d2af3c8df01aaf512b10443422d315ab3","abstract_canon_sha256":"b069a16fc1075e1a4222158630cfe9e626e2d6cb13077a7f2b750dd5e46db3ce"},"schema_version":"1.0"},"canonical_sha256":"1b4f34d32b4d23442fe4a8592e5f8cece4390945a8d4c798e7f3832365806571","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:54.015803Z","signature_b64":"bnxpL6Z2iRDvaoeCLz0N3QclCauQ9bXKxwvsxlncqIckvKXqgd400LOb+2I5ZptW1oJ/Yfrgw/8yrdsrsTjCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b4f34d32b4d23442fe4a8592e5f8cece4390945a8d4c798e7f3832365806571","last_reissued_at":"2026-05-18T01:40:54.014845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:54.014845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00137","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":"2026-05-18T01:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lUG7YwZkOQcJuBkLVjJIpcGPvkvZB/VnsvNNfWcUMLpxjzU/HYGNPR4juCl7cve5h286JA5hMcRBaj2r2i9DDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:14:37.617423Z"},"content_sha256":"baac444ee646693b5b1e75f9fa4e01b51646c6a58dc4fb0571146ad34630054f","schema_version":"1.0","event_id":"sha256:baac444ee646693b5b1e75f9fa4e01b51646c6a58dc4fb0571146ad34630054f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DNHTJUZLJURUIL7EVBMS4X4M5T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality in the spectral and eigenfunction properties of random networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"A. Alcazar-Lopez, A. J. Martinez-Mendoza, Francisco A. Rodrigues, J. A. Mendez-Bermudez, Thomas K. DM. Peron","submitted_at":"2015-02-28T15:09:11Z","abstract_excerpt":"By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length of the adjacency matrices of Erd\\H{o}s-R\\'enyi (ER) {\\it fully} random networks are universal for fixed average degree $\\xi\\equiv \\alpha N$ ($\\alpha$ and $N$ being the average network connectivity and the network size, respectively). We also demonstrate that Brody distribution characterizes well $P(s)$ in the transition from $\\alpha=0$, when the vertices in the network are isolated, to $\\alpha=1$, when the network is fully c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00137","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":"2026-05-18T01:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBLFz4XuTvNKrHRn3qxMo9od80OQYl+Tl/ng6AiwAYltdTBdwL11WzFVrmdugceQKcmVTRzgZjvDr3F0/RQVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:14:37.617782Z"},"content_sha256":"72dcef82511df0e6189885b47b4255610a6bfbf541e51fec069c923ee01aeaae","schema_version":"1.0","event_id":"sha256:72dcef82511df0e6189885b47b4255610a6bfbf541e51fec069c923ee01aeaae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNHTJUZLJURUIL7EVBMS4X4M5T/bundle.json","state_url":"https://pith.science/pith/DNHTJUZLJURUIL7EVBMS4X4M5T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNHTJUZLJURUIL7EVBMS4X4M5T/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":"2026-06-20T18:14:37Z","links":{"resolver":"https://pith.science/pith/DNHTJUZLJURUIL7EVBMS4X4M5T","bundle":"https://pith.science/pith/DNHTJUZLJURUIL7EVBMS4X4M5T/bundle.json","state":"https://pith.science/pith/DNHTJUZLJURUIL7EVBMS4X4M5T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNHTJUZLJURUIL7EVBMS4X4M5T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DNHTJUZLJURUIL7EVBMS4X4M5T","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":"b069a16fc1075e1a4222158630cfe9e626e2d6cb13077a7f2b750dd5e46db3ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-28T15:09:11Z","title_canon_sha256":"7a04ad0ca468334dd98ec8a48907e31d2af3c8df01aaf512b10443422d315ab3"},"schema_version":"1.0","source":{"id":"1503.00137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00137","created_at":"2026-05-18T01:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00137v1","created_at":"2026-05-18T01:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00137","created_at":"2026-05-18T01:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"DNHTJUZLJURU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DNHTJUZLJURUIL7E","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DNHTJUZL","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:72dcef82511df0e6189885b47b4255610a6bfbf541e51fec069c923ee01aeaae","target":"graph","created_at":"2026-05-18T01:40:54Z","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":"By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length of the adjacency matrices of Erd\\H{o}s-R\\'enyi (ER) {\\it fully} random networks are universal for fixed average degree $\\xi\\equiv \\alpha N$ ($\\alpha$ and $N$ being the average network connectivity and the network size, respectively). We also demonstrate that Brody distribution characterizes well $P(s)$ in the transition from $\\alpha=0$, when the vertices in the network are isolated, to $\\alpha=1$, when the network is fully c","authors_text":"A. Alcazar-Lopez, A. J. Martinez-Mendoza, Francisco A. Rodrigues, J. A. Mendez-Bermudez, Thomas K. DM. Peron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-28T15:09:11Z","title":"Universality in the spectral and eigenfunction properties of random networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00137","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:baac444ee646693b5b1e75f9fa4e01b51646c6a58dc4fb0571146ad34630054f","target":"record","created_at":"2026-05-18T01:40:54Z","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":"b069a16fc1075e1a4222158630cfe9e626e2d6cb13077a7f2b750dd5e46db3ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-28T15:09:11Z","title_canon_sha256":"7a04ad0ca468334dd98ec8a48907e31d2af3c8df01aaf512b10443422d315ab3"},"schema_version":"1.0","source":{"id":"1503.00137","kind":"arxiv","version":1}},"canonical_sha256":"1b4f34d32b4d23442fe4a8592e5f8cece4390945a8d4c798e7f3832365806571","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b4f34d32b4d23442fe4a8592e5f8cece4390945a8d4c798e7f3832365806571","first_computed_at":"2026-05-18T01:40:54.014845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:54.014845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bnxpL6Z2iRDvaoeCLz0N3QclCauQ9bXKxwvsxlncqIckvKXqgd400LOb+2I5ZptW1oJ/Yfrgw/8yrdsrsTjCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:54.015803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baac444ee646693b5b1e75f9fa4e01b51646c6a58dc4fb0571146ad34630054f","sha256:72dcef82511df0e6189885b47b4255610a6bfbf541e51fec069c923ee01aeaae"],"state_sha256":"6bb6c15670270ffe9190750cbd9f447d2e5aab4cdfe20297fcb8f1360538f420"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ypaY4U+eJeBW0cAFTz0cw03EiMlyN+vHBFole5o13NHQD4LDbqsIe+rFLuI0RJiGl2Nn5MoFXr7ZjYlHXIQTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:14:37.619806Z","bundle_sha256":"279792bf5334743b49f086de40c875698b39cf287ceb0a916507ce56feb7b79c"}}