{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:HJLSHXEP6LYOH4H6HE47T3XVMJ","short_pith_number":"pith:HJLSHXEP","canonical_record":{"source":{"id":"0907.0511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-07-03T17:29:12Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"054912fc0540d5bce4b3f5e0f1404fc4adf713d4fc5ee9c1ad39f1c499477818","abstract_canon_sha256":"4cd7315b4be025baf3059c73837ca676388a891431b19b4bd7a3ddabc1a2c738"},"schema_version":"1.0"},"canonical_sha256":"3a5723dc8ff2f0e3f0fe3939f9eef56262d027175581fded0c5227477783d1d1","source":{"kind":"arxiv","id":"0907.0511","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0511","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0511v3","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0511","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"HJLSHXEP6LYO","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HJLSHXEP6LYOH4H6","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HJLSHXEP","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:HJLSHXEP6LYOH4H6HE47T3XVMJ","target":"record","payload":{"canonical_record":{"source":{"id":"0907.0511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-07-03T17:29:12Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"054912fc0540d5bce4b3f5e0f1404fc4adf713d4fc5ee9c1ad39f1c499477818","abstract_canon_sha256":"4cd7315b4be025baf3059c73837ca676388a891431b19b4bd7a3ddabc1a2c738"},"schema_version":"1.0"},"canonical_sha256":"3a5723dc8ff2f0e3f0fe3939f9eef56262d027175581fded0c5227477783d1d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:03.226357Z","signature_b64":"qguIwVN8YYwaHMBAogVZsO25YuctNHUKu8oo5atMYTLRpNoauIXvipuYiF+RpHbllwOtAQ423atl6f4fEIi3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a5723dc8ff2f0e3f0fe3939f9eef56262d027175581fded0c5227477783d1d1","last_reissued_at":"2026-05-18T04:25:03.225920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:03.225920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.0511","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2U6coOejHeZof7Ig7jJCvkJf6ey/h18pgHrXhaN8GYiw2QHR7PbfZmIM4t8n6j10bNte2m3MwVhYGtZTKDBRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:59:49.371025Z"},"content_sha256":"d4da71f894a3fff2c9472a29188498b55b011475e407bd4a3c580f1849e36453","schema_version":"1.0","event_id":"sha256:d4da71f894a3fff2c9472a29188498b55b011475e407bd4a3c580f1849e36453"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:HJLSHXEP6LYOH4H6HE47T3XVMJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality in the one-dimensional chain of phase-coupled oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"cond-mat.stat-mech","authors_text":"G. Refael, Jeffrey L. Rogers, M. C. Cross, Oleg Kogan, Tony E. Lee","submitted_at":"2009-07-03T17:29:12Z","abstract_excerpt":"We apply a recently developed renormalization group (RG) method to study synchronization in a one-dimensional chain of phase-coupled oscillators in the regime of weak randomness. The RG predicts how oscillators with randomly distributed frequencies and couplings form frequency-synchronized clusters. Although the RG was originally intended for strong randomness, i.e. for distributions with long tails, we find good agreement with numerical simulations even in the regime of weak randomness. We use the RG flow to derive how the correlation length scales with the width of the coupling distribution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0511","kind":"arxiv","version":3},"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":"2026-05-18T04:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1sbDeQMowh2rnujRW1CV6I7a4VP9CefEwO+oNsg1ppfM+w9JGMYOXe/5AqoPPCDyopgI5Vm3k4SLBEpZALwrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:59:49.371379Z"},"content_sha256":"bde774efef8999a27395a9088aa5dfdb063391b2d0ef70d5fc93ddb7901ea7f4","schema_version":"1.0","event_id":"sha256:bde774efef8999a27395a9088aa5dfdb063391b2d0ef70d5fc93ddb7901ea7f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJLSHXEP6LYOH4H6HE47T3XVMJ/bundle.json","state_url":"https://pith.science/pith/HJLSHXEP6LYOH4H6HE47T3XVMJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJLSHXEP6LYOH4H6HE47T3XVMJ/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":"2026-06-01T21:59:49Z","links":{"resolver":"https://pith.science/pith/HJLSHXEP6LYOH4H6HE47T3XVMJ","bundle":"https://pith.science/pith/HJLSHXEP6LYOH4H6HE47T3XVMJ/bundle.json","state":"https://pith.science/pith/HJLSHXEP6LYOH4H6HE47T3XVMJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJLSHXEP6LYOH4H6HE47T3XVMJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:HJLSHXEP6LYOH4H6HE47T3XVMJ","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":"4cd7315b4be025baf3059c73837ca676388a891431b19b4bd7a3ddabc1a2c738","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-07-03T17:29:12Z","title_canon_sha256":"054912fc0540d5bce4b3f5e0f1404fc4adf713d4fc5ee9c1ad39f1c499477818"},"schema_version":"1.0","source":{"id":"0907.0511","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0511","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0511v3","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0511","created_at":"2026-05-18T04:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"HJLSHXEP6LYO","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HJLSHXEP6LYOH4H6","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HJLSHXEP","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:bde774efef8999a27395a9088aa5dfdb063391b2d0ef70d5fc93ddb7901ea7f4","target":"graph","created_at":"2026-05-18T04:25:03Z","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 apply a recently developed renormalization group (RG) method to study synchronization in a one-dimensional chain of phase-coupled oscillators in the regime of weak randomness. The RG predicts how oscillators with randomly distributed frequencies and couplings form frequency-synchronized clusters. Although the RG was originally intended for strong randomness, i.e. for distributions with long tails, we find good agreement with numerical simulations even in the regime of weak randomness. We use the RG flow to derive how the correlation length scales with the width of the coupling distribution ","authors_text":"G. Refael, Jeffrey L. Rogers, M. C. Cross, Oleg Kogan, Tony E. Lee","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-07-03T17:29:12Z","title":"Universality in the one-dimensional chain of phase-coupled oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0511","kind":"arxiv","version":3},"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:d4da71f894a3fff2c9472a29188498b55b011475e407bd4a3c580f1849e36453","target":"record","created_at":"2026-05-18T04:25:03Z","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":"4cd7315b4be025baf3059c73837ca676388a891431b19b4bd7a3ddabc1a2c738","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-07-03T17:29:12Z","title_canon_sha256":"054912fc0540d5bce4b3f5e0f1404fc4adf713d4fc5ee9c1ad39f1c499477818"},"schema_version":"1.0","source":{"id":"0907.0511","kind":"arxiv","version":3}},"canonical_sha256":"3a5723dc8ff2f0e3f0fe3939f9eef56262d027175581fded0c5227477783d1d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a5723dc8ff2f0e3f0fe3939f9eef56262d027175581fded0c5227477783d1d1","first_computed_at":"2026-05-18T04:25:03.225920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:03.225920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qguIwVN8YYwaHMBAogVZsO25YuctNHUKu8oo5atMYTLRpNoauIXvipuYiF+RpHbllwOtAQ423atl6f4fEIi3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:03.226357Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0511","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4da71f894a3fff2c9472a29188498b55b011475e407bd4a3c580f1849e36453","sha256:bde774efef8999a27395a9088aa5dfdb063391b2d0ef70d5fc93ddb7901ea7f4"],"state_sha256":"54b29bba830239e32e96a7f383f51ad01367485defe4a270dc6d871858bc1f2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sy+cci5ppDRyE43qsqp50NIreFN3dqWOerwd9ROTNdfYj5Qls0N7luMi5j1y17YkYLTe7SecM6uqKq+Di04UCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:59:49.373188Z","bundle_sha256":"902a8b8adc8d57227b3ba8fdc47fc4ffe8ea3bd1175094f141a559f78e38a420"}}