{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DLPF44E5ZMLO5MA7N5DCAQYSKD","short_pith_number":"pith:DLPF44E5","canonical_record":{"source":{"id":"1411.4818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T12:00:13Z","cross_cats_sorted":[],"title_canon_sha256":"03102f9ac6e831c31e2919477612c214c6f805a346a3c186d492aec9053ad71d","abstract_canon_sha256":"280572eb228633de9b64aa85711b0e6d07927bf9024bdd265ecf7a10341bf7b5"},"schema_version":"1.0"},"canonical_sha256":"1ade5e709dcb16eeb01f6f4620431250c556a10b61f9264bb9e3cd87358d7d5d","source":{"kind":"arxiv","id":"1411.4818","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4818","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4818v1","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4818","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"DLPF44E5ZMLO","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DLPF44E5ZMLO5MA7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DLPF44E5","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DLPF44E5ZMLO5MA7N5DCAQYSKD","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T12:00:13Z","cross_cats_sorted":[],"title_canon_sha256":"03102f9ac6e831c31e2919477612c214c6f805a346a3c186d492aec9053ad71d","abstract_canon_sha256":"280572eb228633de9b64aa85711b0e6d07927bf9024bdd265ecf7a10341bf7b5"},"schema_version":"1.0"},"canonical_sha256":"1ade5e709dcb16eeb01f6f4620431250c556a10b61f9264bb9e3cd87358d7d5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:51.176043Z","signature_b64":"DSuCh6pdhtSlTeAOQN3NC/9F5B9UUGNacVAnbVf/Vslw4WirviocYhTR+WXUIhyEJXf7xN46GJbTKF1B0W0CDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ade5e709dcb16eeb01f6f4620431250c556a10b61f9264bb9e3cd87358d7d5d","last_reissued_at":"2026-05-18T02:34:51.175684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:51.175684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4818","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":"2026-05-18T02:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cgoqAoda0wj8MUlLbo1rdmAuVZ6q5LsRqfExEqy0g0NE9cX9Tj3ytZWxUbLmV+V23lRJ1EWaxHo3/jP4wa/NCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:27:08.005844Z"},"content_sha256":"57ef294e6814449c70025fcb629c3abcacb6c61e930af6e8226a1575fdf2e051","schema_version":"1.0","event_id":"sha256:57ef294e6814449c70025fcb629c3abcacb6c61e930af6e8226a1575fdf2e051"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DLPF44E5ZMLO5MA7N5DCAQYSKD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic perturbations with delay of coupled differential equations on manifolds with application to a sunflower-like equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Luca Bisconti, Marco Spadini","submitted_at":"2014-11-18T12:00:13Z","abstract_excerpt":"We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of branches of $T$-periodic solutions to the considered equations. As main application of our methods, we study a generalized version of the sunflower equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4818","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":"2026-05-18T02:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sW2ANDugTNQrQJQnRN/IKrLHH9VeAABkLLGbY/ukeVYBFyytG3k/nO6Z8juJ2B1S+njSAgKumRFhfxpMWarNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:27:08.006217Z"},"content_sha256":"a112c39d61db4df91a221c6ac2bfd988c328b25993e91f5f8059709bab290865","schema_version":"1.0","event_id":"sha256:a112c39d61db4df91a221c6ac2bfd988c328b25993e91f5f8059709bab290865"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DLPF44E5ZMLO5MA7N5DCAQYSKD/bundle.json","state_url":"https://pith.science/pith/DLPF44E5ZMLO5MA7N5DCAQYSKD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DLPF44E5ZMLO5MA7N5DCAQYSKD/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":"2026-06-05T09:27:08Z","links":{"resolver":"https://pith.science/pith/DLPF44E5ZMLO5MA7N5DCAQYSKD","bundle":"https://pith.science/pith/DLPF44E5ZMLO5MA7N5DCAQYSKD/bundle.json","state":"https://pith.science/pith/DLPF44E5ZMLO5MA7N5DCAQYSKD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DLPF44E5ZMLO5MA7N5DCAQYSKD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DLPF44E5ZMLO5MA7N5DCAQYSKD","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":"280572eb228633de9b64aa85711b0e6d07927bf9024bdd265ecf7a10341bf7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T12:00:13Z","title_canon_sha256":"03102f9ac6e831c31e2919477612c214c6f805a346a3c186d492aec9053ad71d"},"schema_version":"1.0","source":{"id":"1411.4818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4818","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4818v1","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4818","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"DLPF44E5ZMLO","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DLPF44E5ZMLO5MA7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DLPF44E5","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:a112c39d61db4df91a221c6ac2bfd988c328b25993e91f5f8059709bab290865","target":"graph","created_at":"2026-05-18T02:34:51Z","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 investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of branches of $T$-periodic solutions to the considered equations. As main application of our methods, we study a generalized version of the sunflower equation.","authors_text":"Luca Bisconti, Marco Spadini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T12:00:13Z","title":"Periodic perturbations with delay of coupled differential equations on manifolds with application to a sunflower-like equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4818","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":"sha256:57ef294e6814449c70025fcb629c3abcacb6c61e930af6e8226a1575fdf2e051","target":"record","created_at":"2026-05-18T02:34:51Z","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":"280572eb228633de9b64aa85711b0e6d07927bf9024bdd265ecf7a10341bf7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T12:00:13Z","title_canon_sha256":"03102f9ac6e831c31e2919477612c214c6f805a346a3c186d492aec9053ad71d"},"schema_version":"1.0","source":{"id":"1411.4818","kind":"arxiv","version":1}},"canonical_sha256":"1ade5e709dcb16eeb01f6f4620431250c556a10b61f9264bb9e3cd87358d7d5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ade5e709dcb16eeb01f6f4620431250c556a10b61f9264bb9e3cd87358d7d5d","first_computed_at":"2026-05-18T02:34:51.175684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:51.175684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DSuCh6pdhtSlTeAOQN3NC/9F5B9UUGNacVAnbVf/Vslw4WirviocYhTR+WXUIhyEJXf7xN46GJbTKF1B0W0CDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:51.176043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57ef294e6814449c70025fcb629c3abcacb6c61e930af6e8226a1575fdf2e051","sha256:a112c39d61db4df91a221c6ac2bfd988c328b25993e91f5f8059709bab290865"],"state_sha256":"64b12a61e97321923f447fbc943bcf9b44136a90653fb1179787be95648c62d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSFzvOlB4pC++eswahzwQCcC2o5m59+BN+Wrc5GWGJQBX7w57YkmakxPoqVLCdP/abooEYKM20mTcPPtbFX7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:27:08.008235Z","bundle_sha256":"9e2dcdb4bbbb3b0b3609dab0b0735518b6f55259a0db12e5e7ab7c01803d7ef0"}}