{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DVICHFI5KGWP5MDRSDYZEYSEB2","short_pith_number":"pith:DVICHFI5","canonical_record":{"source":{"id":"1502.00584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-02T19:16:46Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"9c7236c731c84d730b5d9463eba4e05c6ea4c50b9b756b31b689846d51948f5b","abstract_canon_sha256":"1f93ace403b5d7fa4c7c18f5ce5bbe9ba3ca276ef1ba4027fb8cbf31f34dcfe9"},"schema_version":"1.0"},"canonical_sha256":"1d5023951d51acfeb07190f19262440e86324a9507be9afa91221acf907da29d","source":{"kind":"arxiv","id":"1502.00584","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00584","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00584v1","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00584","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"DVICHFI5KGWP","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DVICHFI5KGWP5MDR","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DVICHFI5","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DVICHFI5KGWP5MDRSDYZEYSEB2","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-02T19:16:46Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"9c7236c731c84d730b5d9463eba4e05c6ea4c50b9b756b31b689846d51948f5b","abstract_canon_sha256":"1f93ace403b5d7fa4c7c18f5ce5bbe9ba3ca276ef1ba4027fb8cbf31f34dcfe9"},"schema_version":"1.0"},"canonical_sha256":"1d5023951d51acfeb07190f19262440e86324a9507be9afa91221acf907da29d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:13.388070Z","signature_b64":"mU5ISmbtkKH5gnc0way48o9t9qnMbubXLdeHNQEempdjl1rhIpzT0Qe2uUtTctZLq1BQt1rJ/dUGxB7TioE/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d5023951d51acfeb07190f19262440e86324a9507be9afa91221acf907da29d","last_reissued_at":"2026-05-18T01:29:13.387400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:13.387400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00584","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":"2026-05-18T01:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+wQKtoik/x6c5E0nXI4f5nPlqVg+NLHyJLjsuwvPVTU67nxDsnjhd/+0ADH1oyQKGOoF1fxpLO+EpnL6B8EKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:49:22.189994Z"},"content_sha256":"8f2152f00f94d475c5aa17a619822a59d48921bba4756f8aa08d6918f4be63e3","schema_version":"1.0","event_id":"sha256:8f2152f00f94d475c5aa17a619822a59d48921bba4756f8aa08d6918f4be63e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DVICHFI5KGWP5MDRSDYZEYSEB2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anderson transition for Google matrix eigenstates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"D.L.Shepelyansky, O.V.Zhirov","submitted_at":"2015-02-02T19:16:46Z","abstract_excerpt":"We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and a broad distribution of eigenvalues in the complex plain. The eigenstates of G are characterized by the Anderson transition from localized to delocalized states and a mobility edge curve in the complex p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00584","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":"2026-05-18T01:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kX4jwSpUXSJIovrZxPkz84McY4GITlUGsznQemnYHLrGDgu+QRQyj5LwC9aVxYeIN1ZNA5v/fD4ecJpB5TWEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:49:22.190359Z"},"content_sha256":"ce12be7390fac6864adb71f89f137a19424eefb4a1f8f35174381969ba79b76f","schema_version":"1.0","event_id":"sha256:ce12be7390fac6864adb71f89f137a19424eefb4a1f8f35174381969ba79b76f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVICHFI5KGWP5MDRSDYZEYSEB2/bundle.json","state_url":"https://pith.science/pith/DVICHFI5KGWP5MDRSDYZEYSEB2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVICHFI5KGWP5MDRSDYZEYSEB2/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":"2026-06-01T07:49:22Z","links":{"resolver":"https://pith.science/pith/DVICHFI5KGWP5MDRSDYZEYSEB2","bundle":"https://pith.science/pith/DVICHFI5KGWP5MDRSDYZEYSEB2/bundle.json","state":"https://pith.science/pith/DVICHFI5KGWP5MDRSDYZEYSEB2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVICHFI5KGWP5MDRSDYZEYSEB2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DVICHFI5KGWP5MDRSDYZEYSEB2","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":"1f93ace403b5d7fa4c7c18f5ce5bbe9ba3ca276ef1ba4027fb8cbf31f34dcfe9","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-02T19:16:46Z","title_canon_sha256":"9c7236c731c84d730b5d9463eba4e05c6ea4c50b9b756b31b689846d51948f5b"},"schema_version":"1.0","source":{"id":"1502.00584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00584","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00584v1","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00584","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"DVICHFI5KGWP","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DVICHFI5KGWP5MDR","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DVICHFI5","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:ce12be7390fac6864adb71f89f137a19424eefb4a1f8f35174381969ba79b76f","target":"graph","created_at":"2026-05-18T01:29:13Z","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 introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and a broad distribution of eigenvalues in the complex plain. The eigenstates of G are characterized by the Anderson transition from localized to delocalized states and a mobility edge curve in the complex p","authors_text":"D.L.Shepelyansky, O.V.Zhirov","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-02T19:16:46Z","title":"Anderson transition for Google matrix eigenstates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00584","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":"sha256:8f2152f00f94d475c5aa17a619822a59d48921bba4756f8aa08d6918f4be63e3","target":"record","created_at":"2026-05-18T01:29:13Z","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":"1f93ace403b5d7fa4c7c18f5ce5bbe9ba3ca276ef1ba4027fb8cbf31f34dcfe9","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-02T19:16:46Z","title_canon_sha256":"9c7236c731c84d730b5d9463eba4e05c6ea4c50b9b756b31b689846d51948f5b"},"schema_version":"1.0","source":{"id":"1502.00584","kind":"arxiv","version":1}},"canonical_sha256":"1d5023951d51acfeb07190f19262440e86324a9507be9afa91221acf907da29d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d5023951d51acfeb07190f19262440e86324a9507be9afa91221acf907da29d","first_computed_at":"2026-05-18T01:29:13.387400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:13.387400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mU5ISmbtkKH5gnc0way48o9t9qnMbubXLdeHNQEempdjl1rhIpzT0Qe2uUtTctZLq1BQt1rJ/dUGxB7TioE/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:13.388070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f2152f00f94d475c5aa17a619822a59d48921bba4756f8aa08d6918f4be63e3","sha256:ce12be7390fac6864adb71f89f137a19424eefb4a1f8f35174381969ba79b76f"],"state_sha256":"7b16504b239e3eebe18e126cd98b903111d794c4083fe219125123ddbaaea5c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMnsbSi8nmiIzL8FYkydrkSOanNBnQ2xhPxOKGElmA9EBhE2Wy3xXaL2RHlGo7UQz05L/qVcopGM0iFVhMihAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:49:22.192354Z","bundle_sha256":"77c2d7ed6289007808474210d68fe8591dcd2247169a7aa4cf74ffe1cc3108dd"}}