{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PJBW3K7TQBWCESSNFI2H54AGWU","short_pith_number":"pith:PJBW3K7T","canonical_record":{"source":{"id":"1401.1863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-08T23:57:18Z","cross_cats_sorted":["math.OC","q-bio.NC"],"title_canon_sha256":"3da41bfa4b1d60e405f2dc262aad6583b6cd6f86e2ae28d2ebd31b7155127b52","abstract_canon_sha256":"db742bff3810996e552e2dcdb6865045a5f8a269cd332af7ff2652ca1a8e0efa"},"schema_version":"1.0"},"canonical_sha256":"7a436dabf3806c224a4d2a347ef006b51a7d475b4056c80a2f5a0fe71cbae36c","source":{"kind":"arxiv","id":"1401.1863","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1863","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1863v1","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1863","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"PJBW3K7TQBWC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PJBW3K7TQBWCESSN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PJBW3K7T","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PJBW3K7TQBWCESSNFI2H54AGWU","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-08T23:57:18Z","cross_cats_sorted":["math.OC","q-bio.NC"],"title_canon_sha256":"3da41bfa4b1d60e405f2dc262aad6583b6cd6f86e2ae28d2ebd31b7155127b52","abstract_canon_sha256":"db742bff3810996e552e2dcdb6865045a5f8a269cd332af7ff2652ca1a8e0efa"},"schema_version":"1.0"},"canonical_sha256":"7a436dabf3806c224a4d2a347ef006b51a7d475b4056c80a2f5a0fe71cbae36c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:56.488956Z","signature_b64":"/3UvklqoQNeJT+w9/7cZ3hp5erFLaZu0xO8ZlJR4nbl77o0Jwb0IHGkZAQd+334g/HESBASh6xFrZLbG9ZdDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a436dabf3806c224a4d2a347ef006b51a7d475b4056c80a2f5a0fe71cbae36c","last_reissued_at":"2026-05-18T03:02:56.488345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:56.488345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1863","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":"2026-05-18T03:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDinj4nW9/qvL93D/qz72vL4CFDyfkGeu5w9x+HcYH0G1QI/4Avzm/g/JuDdr1OgsMUhnFj6KWly1KCWh+jHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:37:33.029501Z"},"content_sha256":"f336e19741136cbfcd342a5ed351b583f6ba416e0c8cdd4236999313bcd2f250","schema_version":"1.0","event_id":"sha256:f336e19741136cbfcd342a5ed351b583f6ba416e0c8cdd4236999313bcd2f250"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PJBW3K7TQBWCESSNFI2H54AGWU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Subharmonic Entrainment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-bio.NC"],"primary_cat":"math.DS","authors_text":"Anatoly Zlotnik, Jr-Shin Li","submitted_at":"2014-01-08T23:57:18Z","abstract_excerpt":"For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the actuated process. Such subharmonic synchrony, which is dynamically established when N control cycles occur for every M cycles of a forced oscillator, is referred to as N:M entrainment. In many applications, entrainment must be established in an optimal manner, for example by minimizing control energy or the transient time to phase locking. We present a theory for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1863","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":"2026-05-18T03:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7BppwsJ/G1o3TRrz+pJqPBEyXf4HNjTjkbMiKRRk3NrqSel8TsAY7bzjbWcCIlR0+Hl6xjofNMM+bxcREVRJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:37:33.029852Z"},"content_sha256":"c9650202c103c4de921018e0bafa806466e8a1e19fac82f86eee19da6e91c295","schema_version":"1.0","event_id":"sha256:c9650202c103c4de921018e0bafa806466e8a1e19fac82f86eee19da6e91c295"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJBW3K7TQBWCESSNFI2H54AGWU/bundle.json","state_url":"https://pith.science/pith/PJBW3K7TQBWCESSNFI2H54AGWU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJBW3K7TQBWCESSNFI2H54AGWU/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":"2026-06-01T23:37:33Z","links":{"resolver":"https://pith.science/pith/PJBW3K7TQBWCESSNFI2H54AGWU","bundle":"https://pith.science/pith/PJBW3K7TQBWCESSNFI2H54AGWU/bundle.json","state":"https://pith.science/pith/PJBW3K7TQBWCESSNFI2H54AGWU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJBW3K7TQBWCESSNFI2H54AGWU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PJBW3K7TQBWCESSNFI2H54AGWU","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":"db742bff3810996e552e2dcdb6865045a5f8a269cd332af7ff2652ca1a8e0efa","cross_cats_sorted":["math.OC","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-08T23:57:18Z","title_canon_sha256":"3da41bfa4b1d60e405f2dc262aad6583b6cd6f86e2ae28d2ebd31b7155127b52"},"schema_version":"1.0","source":{"id":"1401.1863","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1863","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1863v1","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1863","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"PJBW3K7TQBWC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PJBW3K7TQBWCESSN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PJBW3K7T","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:c9650202c103c4de921018e0bafa806466e8a1e19fac82f86eee19da6e91c295","target":"graph","created_at":"2026-05-18T03:02:56Z","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":"For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the actuated process. Such subharmonic synchrony, which is dynamically established when N control cycles occur for every M cycles of a forced oscillator, is referred to as N:M entrainment. In many applications, entrainment must be established in an optimal manner, for example by minimizing control energy or the transient time to phase locking. We present a theory for","authors_text":"Anatoly Zlotnik, Jr-Shin Li","cross_cats":["math.OC","q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-08T23:57:18Z","title":"Optimal Subharmonic Entrainment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1863","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:f336e19741136cbfcd342a5ed351b583f6ba416e0c8cdd4236999313bcd2f250","target":"record","created_at":"2026-05-18T03:02:56Z","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":"db742bff3810996e552e2dcdb6865045a5f8a269cd332af7ff2652ca1a8e0efa","cross_cats_sorted":["math.OC","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-08T23:57:18Z","title_canon_sha256":"3da41bfa4b1d60e405f2dc262aad6583b6cd6f86e2ae28d2ebd31b7155127b52"},"schema_version":"1.0","source":{"id":"1401.1863","kind":"arxiv","version":1}},"canonical_sha256":"7a436dabf3806c224a4d2a347ef006b51a7d475b4056c80a2f5a0fe71cbae36c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a436dabf3806c224a4d2a347ef006b51a7d475b4056c80a2f5a0fe71cbae36c","first_computed_at":"2026-05-18T03:02:56.488345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:56.488345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/3UvklqoQNeJT+w9/7cZ3hp5erFLaZu0xO8ZlJR4nbl77o0Jwb0IHGkZAQd+334g/HESBASh6xFrZLbG9ZdDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:56.488956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1863","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f336e19741136cbfcd342a5ed351b583f6ba416e0c8cdd4236999313bcd2f250","sha256:c9650202c103c4de921018e0bafa806466e8a1e19fac82f86eee19da6e91c295"],"state_sha256":"1f7f954a990917ecea5ee32dab7e5424f026465c99133d378f99c7a1fb817ca3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DJly+e59s1d//eMw+nPVOTj2BbO6AqSNoFEDDJmZIoHuIwFg+txnYmQRrrt12jRlb7OMX7MrvHdx49vAaahVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:37:33.031790Z","bundle_sha256":"93d4643bad31c3992bfb231f85c2209c93770276a7d38facf46b82179b494237"}}