{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7QDOFHN3ZCKUSERITNCJ5KVDWL","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":"39628c83b934c7db13e224c1043015a69091b4f9a49432e4d044b7474d08d8f2","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-08T07:55:23Z","title_canon_sha256":"8762f266e7ba928d4e0396b537d2f0254ed4fe8f5f192d1e379f29ba3cf24b1d"},"schema_version":"1.0","source":{"id":"1603.02406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02406","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02406v1","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02406","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"7QDOFHN3ZCKU","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7QDOFHN3ZCKUSERI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7QDOFHN3","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:e01107de95fe28f124db15e8037fceaa3182ca0b07759430f46bc412d2d8fc55","target":"graph","created_at":"2026-05-18T01:19:23Z","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 extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through cholinergic activation. Our method extends and simplifies the recent work of Kurebayashi (Physical Revi","authors_text":"Bard Ermentrout, Youngmin Park","cross_cats":["q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-08T07:55:23Z","title":"Weakly Coupled Oscillators in a Slowly Varying World"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02406","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":"sha256:1838c48c051459a7c2904e466060be000e8d28378d1aedcda81eb4b5b02c5aa6","target":"record","created_at":"2026-05-18T01:19:23Z","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":"39628c83b934c7db13e224c1043015a69091b4f9a49432e4d044b7474d08d8f2","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-08T07:55:23Z","title_canon_sha256":"8762f266e7ba928d4e0396b537d2f0254ed4fe8f5f192d1e379f29ba3cf24b1d"},"schema_version":"1.0","source":{"id":"1603.02406","kind":"arxiv","version":1}},"canonical_sha256":"fc06e29dbbc8954912289b449eaaa3b2d4cdc36a5e4b719fcdf8d440f532d584","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc06e29dbbc8954912289b449eaaa3b2d4cdc36a5e4b719fcdf8d440f532d584","first_computed_at":"2026-05-18T01:19:23.434851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:23.434851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OtrPMqBO35yIpw9frgOPmzGPBJdegrXsO8ENpj/gM1fR8al7Z6ushtRhPiFSJsrSSfImfhxOEcrro4gVBMSdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:23.435724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1838c48c051459a7c2904e466060be000e8d28378d1aedcda81eb4b5b02c5aa6","sha256:e01107de95fe28f124db15e8037fceaa3182ca0b07759430f46bc412d2d8fc55"],"state_sha256":"9835111ffaae82d22aca7db7bc4a5facc3177931b0c081eea3f3a19c24ded479"}