{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:G5EAGY57PI3CSGZDT4HDALRK3V","short_pith_number":"pith:G5EAGY57","canonical_record":{"source":{"id":"0911.1821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-11-10T03:12:18Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"50ccad02444fac21a53f8ad00805ecdce87a9b52575d2a0404e38070ab6c8db5","abstract_canon_sha256":"f6f108b7ff368daafbcc758c083ab4e995197930e250a51154cbffa2b5d6692b"},"schema_version":"1.0"},"canonical_sha256":"37480363bf7a36291b239f0e302e2add4ec8952810199ecc8bd418b5efb44157","source":{"kind":"arxiv","id":"0911.1821","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1821","created_at":"2026-05-18T02:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1821v1","created_at":"2026-05-18T02:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1821","created_at":"2026-05-18T02:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"G5EAGY57PI3C","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G5EAGY57PI3CSGZD","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G5EAGY57","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:G5EAGY57PI3CSGZDT4HDALRK3V","target":"record","payload":{"canonical_record":{"source":{"id":"0911.1821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-11-10T03:12:18Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"50ccad02444fac21a53f8ad00805ecdce87a9b52575d2a0404e38070ab6c8db5","abstract_canon_sha256":"f6f108b7ff368daafbcc758c083ab4e995197930e250a51154cbffa2b5d6692b"},"schema_version":"1.0"},"canonical_sha256":"37480363bf7a36291b239f0e302e2add4ec8952810199ecc8bd418b5efb44157","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:49.285515Z","signature_b64":"+wwkyUf5+bYJdWxVPw9/r4rXgJrQkPGMgIVjrSMWJ6EZWy574nhL7S1jKCOBvPPaPQDkirGtsCMX0eHYnHxOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37480363bf7a36291b239f0e302e2add4ec8952810199ecc8bd418b5efb44157","last_reissued_at":"2026-05-18T02:10:49.284706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:49.284706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.1821","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":"2026-05-18T02:10:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3HgMAWPDW1e5YPd3uCgEzM3bb2DQXgSV6BuBnmAIlehCCdVnnbKTtVOxxy/La7BAP9szqx5V/2lqOCr1bA7xAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:08:22.803801Z"},"content_sha256":"3a746178997c37ff98761262443520430d257ac689126ee1dc726563258257e6","schema_version":"1.0","event_id":"sha256:3a746178997c37ff98761262443520430d257ac689126ee1dc726563258257e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:G5EAGY57PI3CSGZDT4HDALRK3V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal synchronization on strongly connected directed networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"nlin.PS","authors_text":"Markus Brede","submitted_at":"2009-11-10T03:12:18Z","abstract_excerpt":"In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with non-vanishing complex parts of the spectrum and (ii) a class of networks with real spectrum but slightly larger eigenratios than (i). We relate the superior PFSs to a strongly skewed out-degree distribution, the density of double links and a hierarchical periphery-core organization. Ensembles (i) and (ii) are found to differ in the density of double links and the pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1821","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":"2026-05-18T02:10:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ee39uaF1Rjwth9LIYNmzXXpRL6PKM23OjKQA1GFe8fC7ptNvNolox7vwFT6zg2isN/acofW3vvkn5dgK8FaCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:08:22.804481Z"},"content_sha256":"78bb1f74ada60ff8c017a19acb9b2991487b8ff4cd71dc1ee2b535d159c8b382","schema_version":"1.0","event_id":"sha256:78bb1f74ada60ff8c017a19acb9b2991487b8ff4cd71dc1ee2b535d159c8b382"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5EAGY57PI3CSGZDT4HDALRK3V/bundle.json","state_url":"https://pith.science/pith/G5EAGY57PI3CSGZDT4HDALRK3V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5EAGY57PI3CSGZDT4HDALRK3V/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":"2026-05-26T11:08:22Z","links":{"resolver":"https://pith.science/pith/G5EAGY57PI3CSGZDT4HDALRK3V","bundle":"https://pith.science/pith/G5EAGY57PI3CSGZDT4HDALRK3V/bundle.json","state":"https://pith.science/pith/G5EAGY57PI3CSGZDT4HDALRK3V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5EAGY57PI3CSGZDT4HDALRK3V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:G5EAGY57PI3CSGZDT4HDALRK3V","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":"f6f108b7ff368daafbcc758c083ab4e995197930e250a51154cbffa2b5d6692b","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-11-10T03:12:18Z","title_canon_sha256":"50ccad02444fac21a53f8ad00805ecdce87a9b52575d2a0404e38070ab6c8db5"},"schema_version":"1.0","source":{"id":"0911.1821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1821","created_at":"2026-05-18T02:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1821v1","created_at":"2026-05-18T02:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1821","created_at":"2026-05-18T02:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"G5EAGY57PI3C","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G5EAGY57PI3CSGZD","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G5EAGY57","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:78bb1f74ada60ff8c017a19acb9b2991487b8ff4cd71dc1ee2b535d159c8b382","target":"graph","created_at":"2026-05-18T02:10:49Z","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":"In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with non-vanishing complex parts of the spectrum and (ii) a class of networks with real spectrum but slightly larger eigenratios than (i). We relate the superior PFSs to a strongly skewed out-degree distribution, the density of double links and a hierarchical periphery-core organization. Ensembles (i) and (ii) are found to differ in the density of double links and the pa","authors_text":"Markus Brede","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-11-10T03:12:18Z","title":"Optimal synchronization on strongly connected directed networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1821","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":"sha256:3a746178997c37ff98761262443520430d257ac689126ee1dc726563258257e6","target":"record","created_at":"2026-05-18T02:10:49Z","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":"f6f108b7ff368daafbcc758c083ab4e995197930e250a51154cbffa2b5d6692b","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-11-10T03:12:18Z","title_canon_sha256":"50ccad02444fac21a53f8ad00805ecdce87a9b52575d2a0404e38070ab6c8db5"},"schema_version":"1.0","source":{"id":"0911.1821","kind":"arxiv","version":1}},"canonical_sha256":"37480363bf7a36291b239f0e302e2add4ec8952810199ecc8bd418b5efb44157","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37480363bf7a36291b239f0e302e2add4ec8952810199ecc8bd418b5efb44157","first_computed_at":"2026-05-18T02:10:49.284706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:49.284706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+wwkyUf5+bYJdWxVPw9/r4rXgJrQkPGMgIVjrSMWJ6EZWy574nhL7S1jKCOBvPPaPQDkirGtsCMX0eHYnHxOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:49.285515Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a746178997c37ff98761262443520430d257ac689126ee1dc726563258257e6","sha256:78bb1f74ada60ff8c017a19acb9b2991487b8ff4cd71dc1ee2b535d159c8b382"],"state_sha256":"38e5945c28b4ed3768c6d9b7791814e82abed8f2b2eb346bbe4058a58446ca21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BPFw3Rg3FnVFbL260z0n5KqfxTJp0NrR53RNNhgAkX5L6+0ImB8CPi/eIpW5K9OH17invWU3uXfgekNMtPZdDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:08:22.807880Z","bundle_sha256":"d683ff5511f428869c83aa45f99372b52c9194129700ad94c1361565cd3fad9d"}}