{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:F53EBMGDDABLFO2SNE3FCCXNR2","short_pith_number":"pith:F53EBMGD","canonical_record":{"source":{"id":"1908.08924","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-08-23T17:48:54Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"f84319e34097ba9ec13d47edfc3837bacfbbc31d0f0ff55f6a3d81802aa5e24a","abstract_canon_sha256":"eab11fae9348f5dac28e2c2b428c7da564287e94c4772c7d5ebfb2cc5b85a0ad"},"schema_version":"1.0"},"canonical_sha256":"2f7640b0c31802b2bb526936510aed8ea820826cb06fdfd909c02965e7b7b418","source":{"kind":"arxiv","id":"1908.08924","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08924","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08924v1","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08924","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"F53EBMGDDABL","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"pith_short_16","alias_value":"F53EBMGDDABLFO2S","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"pith_short_8","alias_value":"F53EBMGD","created_at":"2026-07-04T23:59:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:F53EBMGDDABLFO2SNE3FCCXNR2","target":"record","payload":{"canonical_record":{"source":{"id":"1908.08924","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-08-23T17:48:54Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"f84319e34097ba9ec13d47edfc3837bacfbbc31d0f0ff55f6a3d81802aa5e24a","abstract_canon_sha256":"eab11fae9348f5dac28e2c2b428c7da564287e94c4772c7d5ebfb2cc5b85a0ad"},"schema_version":"1.0"},"canonical_sha256":"2f7640b0c31802b2bb526936510aed8ea820826cb06fdfd909c02965e7b7b418","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:25.275697Z","signature_b64":"bH4oRX/M8Zy/tmFxvRSIemcb6iOUjEKWcJ6Hc96X9YtwkocRVdBUnc4OdtCa0NiUZEdkUJcYGUSku1fCsw4NCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f7640b0c31802b2bb526936510aed8ea820826cb06fdfd909c02965e7b7b418","last_reissued_at":"2026-07-04T23:59:25.275262Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:25.275262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.08924","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":"2026-07-04T23:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XArm9lgKyI/RhoT6buf/WZM3+DRXyuUqz56ZjJKX1+ciWfzOPdZq0QvgoAp9m3LBocFymmtGK8vuckMhTEIhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:13:06.036681Z"},"content_sha256":"46845972fb06488369dac129eaa3c8fc367e7c7fe233ccf17e84dfd12b5fca3e","schema_version":"1.0","event_id":"sha256:46845972fb06488369dac129eaa3c8fc367e7c7fe233ccf17e84dfd12b5fca3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:F53EBMGDDABLFO2SNE3FCCXNR2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear response theory for Google matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Dima L. Shepelyansky, Klaus M. Frahm","submitted_at":"2019-08-23T17:48:54Z","abstract_excerpt":"We develop the linear response theory for the Google matrix PageRank algorithm with respect to a general weak perturbation and a numerical efficient and accurate algorithm, called LIRGOMAX algorithm, to compute the linear response of the PageRank with respect to this perturbation. We illustrate its efficiency on the example of the English Wikipedia network with more than 5 millions of articles (nodes). For a group of initial nodes (or simply a pair of nodes) this algorithm allows to identify the effective pathway between initial nodes thus selecting a particular subset of nodes which are most "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08924","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08924/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ZLKPpUTRlxBSTXPJwUqDfzxcUdmpg62jY3BM3K3hg/zjmihu5jGqYSAk8k1w47JCMuyrTt+jkLx+xwQHGvJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:13:06.037555Z"},"content_sha256":"40bdc7bd1f1f9f2c3a9e6178678afb7b7947e3db5f55468589f94d723356c38c","schema_version":"1.0","event_id":"sha256:40bdc7bd1f1f9f2c3a9e6178678afb7b7947e3db5f55468589f94d723356c38c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F53EBMGDDABLFO2SNE3FCCXNR2/bundle.json","state_url":"https://pith.science/pith/F53EBMGDDABLFO2SNE3FCCXNR2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F53EBMGDDABLFO2SNE3FCCXNR2/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":"2026-08-16T13:13:06Z","links":{"resolver":"https://pith.science/pith/F53EBMGDDABLFO2SNE3FCCXNR2","bundle":"https://pith.science/pith/F53EBMGDDABLFO2SNE3FCCXNR2/bundle.json","state":"https://pith.science/pith/F53EBMGDDABLFO2SNE3FCCXNR2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F53EBMGDDABLFO2SNE3FCCXNR2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F53EBMGDDABLFO2SNE3FCCXNR2","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":"eab11fae9348f5dac28e2c2b428c7da564287e94c4772c7d5ebfb2cc5b85a0ad","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-08-23T17:48:54Z","title_canon_sha256":"f84319e34097ba9ec13d47edfc3837bacfbbc31d0f0ff55f6a3d81802aa5e24a"},"schema_version":"1.0","source":{"id":"1908.08924","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08924","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08924v1","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08924","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"F53EBMGDDABL","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"pith_short_16","alias_value":"F53EBMGDDABLFO2S","created_at":"2026-07-04T23:59:25Z"},{"alias_kind":"pith_short_8","alias_value":"F53EBMGD","created_at":"2026-07-04T23:59:25Z"}],"graph_snapshots":[{"event_id":"sha256:40bdc7bd1f1f9f2c3a9e6178678afb7b7947e3db5f55468589f94d723356c38c","target":"graph","created_at":"2026-07-04T23:59:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.08924/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the linear response theory for the Google matrix PageRank algorithm with respect to a general weak perturbation and a numerical efficient and accurate algorithm, called LIRGOMAX algorithm, to compute the linear response of the PageRank with respect to this perturbation. We illustrate its efficiency on the example of the English Wikipedia network with more than 5 millions of articles (nodes). For a group of initial nodes (or simply a pair of nodes) this algorithm allows to identify the effective pathway between initial nodes thus selecting a particular subset of nodes which are most ","authors_text":"Dima L. Shepelyansky, Klaus M. Frahm","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-08-23T17:48:54Z","title":"Linear response theory for Google matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08924","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":"sha256:46845972fb06488369dac129eaa3c8fc367e7c7fe233ccf17e84dfd12b5fca3e","target":"record","created_at":"2026-07-04T23:59:25Z","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":"eab11fae9348f5dac28e2c2b428c7da564287e94c4772c7d5ebfb2cc5b85a0ad","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-08-23T17:48:54Z","title_canon_sha256":"f84319e34097ba9ec13d47edfc3837bacfbbc31d0f0ff55f6a3d81802aa5e24a"},"schema_version":"1.0","source":{"id":"1908.08924","kind":"arxiv","version":1}},"canonical_sha256":"2f7640b0c31802b2bb526936510aed8ea820826cb06fdfd909c02965e7b7b418","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f7640b0c31802b2bb526936510aed8ea820826cb06fdfd909c02965e7b7b418","first_computed_at":"2026-07-04T23:59:25.275262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:25.275262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bH4oRX/M8Zy/tmFxvRSIemcb6iOUjEKWcJ6Hc96X9YtwkocRVdBUnc4OdtCa0NiUZEdkUJcYGUSku1fCsw4NCA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:25.275697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08924","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46845972fb06488369dac129eaa3c8fc367e7c7fe233ccf17e84dfd12b5fca3e","sha256:40bdc7bd1f1f9f2c3a9e6178678afb7b7947e3db5f55468589f94d723356c38c"],"state_sha256":"a94dcdf77b4c2371ff760694fa58b481ddbfda860bc7192c29bf41841c9e090b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4P1+/FEPaG616q2wYShkaeB0a4nFxGjw/fqVz3DJFwDMb5Ziq6ElEwNwiW182ZCQiiipB9XzUnHZkiazcNGwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:13:06.046042Z","bundle_sha256":"c8f9d3eb43e883ca5b0aac3c9b3db01693aed0433ec3d02e214843ce6cd32ad8"}}