{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KNFSRNXCQKMFXIW22QZLTJ3FIO","short_pith_number":"pith:KNFSRNXC","canonical_record":{"source":{"id":"1707.00713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2017-07-03T18:08:54Z","cross_cats_sorted":["cond-mat.dis-nn","math.DS"],"title_canon_sha256":"fff5a9f3364146f0c70d3bd8692cecb408317cc3a1d900db1c46fd466dd8e6ae","abstract_canon_sha256":"d7606f564dfd1ad41317f06f9ec44cf76c40b10fe24e67fb0281dc057e39618f"},"schema_version":"1.0"},"canonical_sha256":"534b28b6e282985ba2dad432b9a76543acd8b00b8ff96c61fc152e3dde1c87a0","source":{"kind":"arxiv","id":"1707.00713","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00713","created_at":"2026-05-18T00:35:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00713v1","created_at":"2026-05-18T00:35:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00713","created_at":"2026-05-18T00:35:31Z"},{"alias_kind":"pith_short_12","alias_value":"KNFSRNXCQKMF","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KNFSRNXCQKMFXIW2","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KNFSRNXC","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KNFSRNXCQKMFXIW22QZLTJ3FIO","target":"record","payload":{"canonical_record":{"source":{"id":"1707.00713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2017-07-03T18:08:54Z","cross_cats_sorted":["cond-mat.dis-nn","math.DS"],"title_canon_sha256":"fff5a9f3364146f0c70d3bd8692cecb408317cc3a1d900db1c46fd466dd8e6ae","abstract_canon_sha256":"d7606f564dfd1ad41317f06f9ec44cf76c40b10fe24e67fb0281dc057e39618f"},"schema_version":"1.0"},"canonical_sha256":"534b28b6e282985ba2dad432b9a76543acd8b00b8ff96c61fc152e3dde1c87a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:31.044404Z","signature_b64":"UaM1VkJNSAUAfjdl9CPa8JZNHRDFrY4nYTLZAoYNNWjGynQHLSc96IEfchNYYDOt1AxOF6S+ysFkaFnnVRMfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"534b28b6e282985ba2dad432b9a76543acd8b00b8ff96c61fc152e3dde1c87a0","last_reissued_at":"2026-05-18T00:35:31.044005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:31.044005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.00713","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":"2026-05-18T00:35:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vo7aod6FW/fPXctA/tCiREq1u75yCtfAD8fZObN6RmUqTZy2JYYFd6+qP5p+eH6D1lIgnXvsCUZUwsLIA8X7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:32:26.190414Z"},"content_sha256":"a341dc7b9ff1483fb2f2b6c4cd9c0238f0d5d4f341274e244bf987ed884d3bf7","schema_version":"1.0","event_id":"sha256:a341dc7b9ff1483fb2f2b6c4cd9c0238f0d5d4f341274e244bf987ed884d3bf7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KNFSRNXCQKMFXIW22QZLTJ3FIO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolic Geometry of Kuramoto Oscillator Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.DS"],"primary_cat":"nlin.AO","authors_text":"Bolun Chen, Jan R. Engelbrecht, Renato Mirollo","submitted_at":"2017-07-03T18:08:54Z","abstract_excerpt":"Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the M\\\"obius group acting on the state space $T^N$ (the $N$-fold torus). This result has been used to explain the existence of the $N-3$ constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this M\\\"obius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk $\\Delta$ wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00713","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":"2026-05-18T00:35:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hbjDn3RidMWrCPmD32v1XEx1elEZ4SK3E5Fuy83zJfMz80mQGaOb6QKWfldm2tFO2zml0tUBiSm5tDKpTdD3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:32:26.190767Z"},"content_sha256":"9c982fff25a4ece84811735ba8630aec6d7f3968d015ad796aa6cfcc3e8eb4a8","schema_version":"1.0","event_id":"sha256:9c982fff25a4ece84811735ba8630aec6d7f3968d015ad796aa6cfcc3e8eb4a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNFSRNXCQKMFXIW22QZLTJ3FIO/bundle.json","state_url":"https://pith.science/pith/KNFSRNXCQKMFXIW22QZLTJ3FIO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNFSRNXCQKMFXIW22QZLTJ3FIO/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":"2026-06-26T04:32:26Z","links":{"resolver":"https://pith.science/pith/KNFSRNXCQKMFXIW22QZLTJ3FIO","bundle":"https://pith.science/pith/KNFSRNXCQKMFXIW22QZLTJ3FIO/bundle.json","state":"https://pith.science/pith/KNFSRNXCQKMFXIW22QZLTJ3FIO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNFSRNXCQKMFXIW22QZLTJ3FIO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KNFSRNXCQKMFXIW22QZLTJ3FIO","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":"d7606f564dfd1ad41317f06f9ec44cf76c40b10fe24e67fb0281dc057e39618f","cross_cats_sorted":["cond-mat.dis-nn","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2017-07-03T18:08:54Z","title_canon_sha256":"fff5a9f3364146f0c70d3bd8692cecb408317cc3a1d900db1c46fd466dd8e6ae"},"schema_version":"1.0","source":{"id":"1707.00713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00713","created_at":"2026-05-18T00:35:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00713v1","created_at":"2026-05-18T00:35:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00713","created_at":"2026-05-18T00:35:31Z"},{"alias_kind":"pith_short_12","alias_value":"KNFSRNXCQKMF","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KNFSRNXCQKMFXIW2","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KNFSRNXC","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:9c982fff25a4ece84811735ba8630aec6d7f3968d015ad796aa6cfcc3e8eb4a8","target":"graph","created_at":"2026-05-18T00:35:31Z","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":"Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the M\\\"obius group acting on the state space $T^N$ (the $N$-fold torus). This result has been used to explain the existence of the $N-3$ constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this M\\\"obius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk $\\Delta$ wit","authors_text":"Bolun Chen, Jan R. Engelbrecht, Renato Mirollo","cross_cats":["cond-mat.dis-nn","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2017-07-03T18:08:54Z","title":"Hyperbolic Geometry of Kuramoto Oscillator Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00713","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:a341dc7b9ff1483fb2f2b6c4cd9c0238f0d5d4f341274e244bf987ed884d3bf7","target":"record","created_at":"2026-05-18T00:35:31Z","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":"d7606f564dfd1ad41317f06f9ec44cf76c40b10fe24e67fb0281dc057e39618f","cross_cats_sorted":["cond-mat.dis-nn","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2017-07-03T18:08:54Z","title_canon_sha256":"fff5a9f3364146f0c70d3bd8692cecb408317cc3a1d900db1c46fd466dd8e6ae"},"schema_version":"1.0","source":{"id":"1707.00713","kind":"arxiv","version":1}},"canonical_sha256":"534b28b6e282985ba2dad432b9a76543acd8b00b8ff96c61fc152e3dde1c87a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"534b28b6e282985ba2dad432b9a76543acd8b00b8ff96c61fc152e3dde1c87a0","first_computed_at":"2026-05-18T00:35:31.044005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:31.044005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UaM1VkJNSAUAfjdl9CPa8JZNHRDFrY4nYTLZAoYNNWjGynQHLSc96IEfchNYYDOt1AxOF6S+ysFkaFnnVRMfCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:31.044404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a341dc7b9ff1483fb2f2b6c4cd9c0238f0d5d4f341274e244bf987ed884d3bf7","sha256:9c982fff25a4ece84811735ba8630aec6d7f3968d015ad796aa6cfcc3e8eb4a8"],"state_sha256":"2d56bf8436c8b05db8a3e21971637cc6253af03b5cacfac64f0e536ab57b0772"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wTrI71cgp+XLUS6Q+PI7oHLFprsCA7C7NtOSG2Tc+lIoW+Y6c+TEWiEmgGLSchl/3BjsAOUZy3il2MxLsOCLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T04:32:26.192823Z","bundle_sha256":"d5dd96381d640ec0ce165779976fc1cdaecd641b807c5e1a1560f02b25057c03"}}