{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4PFRYKDLNHQLROFFGDHVR32RWP","short_pith_number":"pith:4PFRYKDL","canonical_record":{"source":{"id":"1804.09820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-04-25T22:20:39Z","cross_cats_sorted":["math.NA","physics.data-an"],"title_canon_sha256":"96bd9f2bc23e6cc05edb3d4ac3137013c52a36e95d543ae345fa832a9ef75d60","abstract_canon_sha256":"a322b94e433a1af31b8e92a8265ec1979f618785060d142aced524c8032cf603"},"schema_version":"1.0"},"canonical_sha256":"e3cb1c286b69e0b8b8a530cf58ef51b3f899aea064869c7a3134e8e5ed93752a","source":{"kind":"arxiv","id":"1804.09820","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09820","created_at":"2026-05-17T23:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09820v2","created_at":"2026-05-17T23:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09820","created_at":"2026-05-17T23:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"4PFRYKDLNHQL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4PFRYKDLNHQLROFF","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4PFRYKDL","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4PFRYKDLNHQLROFFGDHVR32RWP","target":"record","payload":{"canonical_record":{"source":{"id":"1804.09820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-04-25T22:20:39Z","cross_cats_sorted":["math.NA","physics.data-an"],"title_canon_sha256":"96bd9f2bc23e6cc05edb3d4ac3137013c52a36e95d543ae345fa832a9ef75d60","abstract_canon_sha256":"a322b94e433a1af31b8e92a8265ec1979f618785060d142aced524c8032cf603"},"schema_version":"1.0"},"canonical_sha256":"e3cb1c286b69e0b8b8a530cf58ef51b3f899aea064869c7a3134e8e5ed93752a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:25.125980Z","signature_b64":"+d0uPD0y+hUl3Z5t1doWDxNNCtsIVntK9LOmnIz7Lo5Xv+I0S7FNmmyLBVG9UH+xk0YvV2Hb1U5IJvUfFRkKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3cb1c286b69e0b8b8a530cf58ef51b3f899aea064869c7a3134e8e5ed93752a","last_reissued_at":"2026-05-17T23:54:25.125214Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:25.125214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.09820","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":"2026-05-17T23:54:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AgvhfxtajC6hXK2SdMhPrWQW3pklYPWdMZlGvSWw0FGLoF4acOj+B+ExRNy/cYR2MsqLtg3frLC7HsftTPfTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:05:39.481651Z"},"content_sha256":"8c35cde197564f8ef3914699ad4dda781231859417e94a0ffc01192054620b93","schema_version":"1.0","event_id":"sha256:8c35cde197564f8ef3914699ad4dda781231859417e94a0ffc01192054620b93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4PFRYKDLNHQLROFFGDHVR32RWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Nonlinear Spectral Method for Core--Periphery Detection in Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.data-an"],"primary_cat":"cs.SI","authors_text":"Desmond J. Higham, Francesco Tudisco","submitted_at":"2018-04-25T22:20:39Z","abstract_excerpt":"We derive and analyse a new iterative algorithm for detecting network core--periphery structure. Using techniques in nonlinear Perron-Frobenius theory, we prove global convergence to the unique solution of a relaxed version of a natural discrete optimization problem. On sparse networks, the cost of each iteration scales linearly with the number of nodes, making the algorithm feasible for large-scale problems. We give an alternative interpretation of the algorithm from the perspective of maximum likelihood reordering of a new logistic core--periphery random graph model. This viewpoint also give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09820","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":"2026-05-17T23:54:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WcwN/h/ZTQJWXmeggFcOVXomGyTlsMgaIVKjAjnEmwI3QVewDLcb6uAs/oW00B5xr2fw/wT2ExLja0iwkBT2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:05:39.481999Z"},"content_sha256":"b4f750f63bd89d7fa313eab502c8b3b35d48ad63fc7c42ba846a56b7d5f44933","schema_version":"1.0","event_id":"sha256:b4f750f63bd89d7fa313eab502c8b3b35d48ad63fc7c42ba846a56b7d5f44933"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4PFRYKDLNHQLROFFGDHVR32RWP/bundle.json","state_url":"https://pith.science/pith/4PFRYKDLNHQLROFFGDHVR32RWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4PFRYKDLNHQLROFFGDHVR32RWP/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":"2026-06-12T10:05:39Z","links":{"resolver":"https://pith.science/pith/4PFRYKDLNHQLROFFGDHVR32RWP","bundle":"https://pith.science/pith/4PFRYKDLNHQLROFFGDHVR32RWP/bundle.json","state":"https://pith.science/pith/4PFRYKDLNHQLROFFGDHVR32RWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4PFRYKDLNHQLROFFGDHVR32RWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4PFRYKDLNHQLROFFGDHVR32RWP","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":"a322b94e433a1af31b8e92a8265ec1979f618785060d142aced524c8032cf603","cross_cats_sorted":["math.NA","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-04-25T22:20:39Z","title_canon_sha256":"96bd9f2bc23e6cc05edb3d4ac3137013c52a36e95d543ae345fa832a9ef75d60"},"schema_version":"1.0","source":{"id":"1804.09820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09820","created_at":"2026-05-17T23:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09820v2","created_at":"2026-05-17T23:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09820","created_at":"2026-05-17T23:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"4PFRYKDLNHQL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4PFRYKDLNHQLROFF","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4PFRYKDL","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:b4f750f63bd89d7fa313eab502c8b3b35d48ad63fc7c42ba846a56b7d5f44933","target":"graph","created_at":"2026-05-17T23:54:25Z","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":"We derive and analyse a new iterative algorithm for detecting network core--periphery structure. Using techniques in nonlinear Perron-Frobenius theory, we prove global convergence to the unique solution of a relaxed version of a natural discrete optimization problem. On sparse networks, the cost of each iteration scales linearly with the number of nodes, making the algorithm feasible for large-scale problems. We give an alternative interpretation of the algorithm from the perspective of maximum likelihood reordering of a new logistic core--periphery random graph model. This viewpoint also give","authors_text":"Desmond J. Higham, Francesco Tudisco","cross_cats":["math.NA","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-04-25T22:20:39Z","title":"A Nonlinear Spectral Method for Core--Periphery Detection in Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09820","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":"sha256:8c35cde197564f8ef3914699ad4dda781231859417e94a0ffc01192054620b93","target":"record","created_at":"2026-05-17T23:54:25Z","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":"a322b94e433a1af31b8e92a8265ec1979f618785060d142aced524c8032cf603","cross_cats_sorted":["math.NA","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-04-25T22:20:39Z","title_canon_sha256":"96bd9f2bc23e6cc05edb3d4ac3137013c52a36e95d543ae345fa832a9ef75d60"},"schema_version":"1.0","source":{"id":"1804.09820","kind":"arxiv","version":2}},"canonical_sha256":"e3cb1c286b69e0b8b8a530cf58ef51b3f899aea064869c7a3134e8e5ed93752a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3cb1c286b69e0b8b8a530cf58ef51b3f899aea064869c7a3134e8e5ed93752a","first_computed_at":"2026-05-17T23:54:25.125214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:25.125214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+d0uPD0y+hUl3Z5t1doWDxNNCtsIVntK9LOmnIz7Lo5Xv+I0S7FNmmyLBVG9UH+xk0YvV2Hb1U5IJvUfFRkKAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:25.125980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c35cde197564f8ef3914699ad4dda781231859417e94a0ffc01192054620b93","sha256:b4f750f63bd89d7fa313eab502c8b3b35d48ad63fc7c42ba846a56b7d5f44933"],"state_sha256":"da497f6d2b6e969b1da07a71a76da11a44d78e25b1dd287be65c613aee545432"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8SwW00SsGfezuJfExtk3alZjf59zs5CJzteazVfteJBVraH4bEFrOoJEm1GKwGUawjBuPvL6paivTy5aHbFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:05:39.484113Z","bundle_sha256":"cf6466ada5e18f59d6ea5c42c368ff0fa1573a464aa50e9613c4ba79ca516248"}}