{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5EBR5EY45LIQ7YHBENSJCXJDQU","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":"8d11c592c6ca1b989e7a66c248620d66465b0dd488a51e6abe74bc78426d7613","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2011-03-02T07:56:40Z","title_canon_sha256":"dae7411b5aec4056bc4a7d96ae9246ffcb8acec497f56447326fa816c4235f47"},"schema_version":"1.0","source":{"id":"1103.0363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0363","created_at":"2026-05-18T02:03:01Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0363v1","created_at":"2026-05-18T02:03:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0363","created_at":"2026-05-18T02:03:01Z"},{"alias_kind":"pith_short_12","alias_value":"5EBR5EY45LIQ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5EBR5EY45LIQ7YHB","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5EBR5EY4","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:fc1fae249361bcd84e50e42d12dbb2b695d96f933550d26da686b83b2c4f0260","target":"graph","created_at":"2026-05-18T02:03:01Z","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":"A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensional center manifold on a space of generalized functions. The dynamics on the manifold is derived for any coupling functions. When the coupling function is $\\sin \\theta $, a bifurcation diagram conjectured by Kuramoto is rigorously obtained. When it is not $\\sin \\theta $, a new type of bifurcation phenomenon is found due to the discontinuity of the projection operator to the center subspace.","authors_text":"Hayato Chiba, Isao Nishikawa","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2011-03-02T07:56:40Z","title":"Center manifold reduction for large populations of globally coupled phase oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0363","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":"sha256:3095c5e389efa2aab6a464a6389884e54ddcf02a9a0bf950382934fc056a394f","target":"record","created_at":"2026-05-18T02:03:01Z","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":"8d11c592c6ca1b989e7a66c248620d66465b0dd488a51e6abe74bc78426d7613","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2011-03-02T07:56:40Z","title_canon_sha256":"dae7411b5aec4056bc4a7d96ae9246ffcb8acec497f56447326fa816c4235f47"},"schema_version":"1.0","source":{"id":"1103.0363","kind":"arxiv","version":1}},"canonical_sha256":"e9031e931cead10fe0e12364915d238532c860e103b1139c42fc84e04ac390f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9031e931cead10fe0e12364915d238532c860e103b1139c42fc84e04ac390f3","first_computed_at":"2026-05-18T02:03:01.247799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:01.247799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W6Jvmbx1esb1hkn9Nvz23HFu7H1qN4fq+hykDy4M9L3LRtaXFz+tNHqjsol4nivdoW3t3irQy4AWTEcIOzZkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:01.248868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3095c5e389efa2aab6a464a6389884e54ddcf02a9a0bf950382934fc056a394f","sha256:fc1fae249361bcd84e50e42d12dbb2b695d96f933550d26da686b83b2c4f0260"],"state_sha256":"e81f341ccf6633544cf1e3494b14952297100f35983138d90e643cc0b34ed6b2"}