{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FZRA7XJIYIGYCAC3VYBWLPAKHZ","short_pith_number":"pith:FZRA7XJI","canonical_record":{"source":{"id":"1606.07307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-23T13:26:39Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"5cb6c3057132de28a605afaf208b690d57222c397774511b5a69d3b23ef30dcd","abstract_canon_sha256":"9c90f9d8271c88f9c713982245af79aaedc63e02855290d641787c2fc034422b"},"schema_version":"1.0"},"canonical_sha256":"2e620fdd28c20d81005bae0365bc0a3e75eadcfed176c59b964743dcd69c27ab","source":{"kind":"arxiv","id":"1606.07307","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07307","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07307v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07307","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"FZRA7XJIYIGY","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FZRA7XJIYIGYCAC3","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FZRA7XJI","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FZRA7XJIYIGYCAC3VYBWLPAKHZ","target":"record","payload":{"canonical_record":{"source":{"id":"1606.07307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-23T13:26:39Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"5cb6c3057132de28a605afaf208b690d57222c397774511b5a69d3b23ef30dcd","abstract_canon_sha256":"9c90f9d8271c88f9c713982245af79aaedc63e02855290d641787c2fc034422b"},"schema_version":"1.0"},"canonical_sha256":"2e620fdd28c20d81005bae0365bc0a3e75eadcfed176c59b964743dcd69c27ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:27.399887Z","signature_b64":"DiZytWlSaSJhVonzFLZud0NUUT23CCUllcKjuq+aibXKtjVosCyrSthrH6FcgoCiPtRyIzubRTCQoxH4b3rkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e620fdd28c20d81005bae0365bc0a3e75eadcfed176c59b964743dcd69c27ab","last_reissued_at":"2026-05-18T01:04:27.399324Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:27.399324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.07307","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yppzWmKoQmyUfqGzcMr1aCUQZqBAJJepcmLRxmtto/vF5tA3/vnCb+5Riu3UeU90Lepx6DEqrTfvbLGEQZJwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:39:32.953906Z"},"content_sha256":"64da8b76d7a437e27862c391d38fc2eefb5565d0e4516e65eef434f0e0acdc07","schema_version":"1.0","event_id":"sha256:64da8b76d7a437e27862c391d38fc2eefb5565d0e4516e65eef434f0e0acdc07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FZRA7XJIYIGYCAC3VYBWLPAKHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcation and Stability Analysis of Bistable Neuromodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"math.DS","authors_text":"Jon Borresen, Stephen Lynch","submitted_at":"2016-06-23T13:26:39Z","abstract_excerpt":"This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and periodic bifurcations). For the first time, bifurcation diagrams are plotted using a feedback mechanism. It is shown that the stability curves and bifurcation diagrams must be dealt with simultaneously in order to fully understand the dynamics of the systems involved. Synaptic weights, biases and gradients of transfer functions are varied and the system is sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07307","kind":"arxiv","version":2},"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":"2026-05-18T01:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u8qEmpFthHAMnGNuzOSgtxKYNQmktpwbbisrpLYCotI59ARiTEh9gtbGvdEWdTy/bxO1FbvHMDjQm55KjLj/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:39:32.954252Z"},"content_sha256":"6aec92900762145dc9da77409ff1a0805dffec612b01726188b64b7d68675d67","schema_version":"1.0","event_id":"sha256:6aec92900762145dc9da77409ff1a0805dffec612b01726188b64b7d68675d67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZRA7XJIYIGYCAC3VYBWLPAKHZ/bundle.json","state_url":"https://pith.science/pith/FZRA7XJIYIGYCAC3VYBWLPAKHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZRA7XJIYIGYCAC3VYBWLPAKHZ/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":"2026-06-05T14:39:32Z","links":{"resolver":"https://pith.science/pith/FZRA7XJIYIGYCAC3VYBWLPAKHZ","bundle":"https://pith.science/pith/FZRA7XJIYIGYCAC3VYBWLPAKHZ/bundle.json","state":"https://pith.science/pith/FZRA7XJIYIGYCAC3VYBWLPAKHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZRA7XJIYIGYCAC3VYBWLPAKHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FZRA7XJIYIGYCAC3VYBWLPAKHZ","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":"9c90f9d8271c88f9c713982245af79aaedc63e02855290d641787c2fc034422b","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-23T13:26:39Z","title_canon_sha256":"5cb6c3057132de28a605afaf208b690d57222c397774511b5a69d3b23ef30dcd"},"schema_version":"1.0","source":{"id":"1606.07307","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07307","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07307v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07307","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"FZRA7XJIYIGY","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FZRA7XJIYIGYCAC3","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FZRA7XJI","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:6aec92900762145dc9da77409ff1a0805dffec612b01726188b64b7d68675d67","target":"graph","created_at":"2026-05-18T01:04:27Z","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":"This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and periodic bifurcations). For the first time, bifurcation diagrams are plotted using a feedback mechanism. It is shown that the stability curves and bifurcation diagrams must be dealt with simultaneously in order to fully understand the dynamics of the systems involved. Synaptic weights, biases and gradients of transfer functions are varied and the system is sho","authors_text":"Jon Borresen, Stephen Lynch","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-23T13:26:39Z","title":"Bifurcation and Stability Analysis of Bistable Neuromodules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07307","kind":"arxiv","version":2},"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":"sha256:64da8b76d7a437e27862c391d38fc2eefb5565d0e4516e65eef434f0e0acdc07","target":"record","created_at":"2026-05-18T01:04:27Z","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":"9c90f9d8271c88f9c713982245af79aaedc63e02855290d641787c2fc034422b","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-23T13:26:39Z","title_canon_sha256":"5cb6c3057132de28a605afaf208b690d57222c397774511b5a69d3b23ef30dcd"},"schema_version":"1.0","source":{"id":"1606.07307","kind":"arxiv","version":2}},"canonical_sha256":"2e620fdd28c20d81005bae0365bc0a3e75eadcfed176c59b964743dcd69c27ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e620fdd28c20d81005bae0365bc0a3e75eadcfed176c59b964743dcd69c27ab","first_computed_at":"2026-05-18T01:04:27.399324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:27.399324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DiZytWlSaSJhVonzFLZud0NUUT23CCUllcKjuq+aibXKtjVosCyrSthrH6FcgoCiPtRyIzubRTCQoxH4b3rkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:27.399887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07307","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64da8b76d7a437e27862c391d38fc2eefb5565d0e4516e65eef434f0e0acdc07","sha256:6aec92900762145dc9da77409ff1a0805dffec612b01726188b64b7d68675d67"],"state_sha256":"a0ad9f77adabf03d4b120a213882f61d26c541e0001cbac375dfcd0c83f9288d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z2TasmDccsBOeD/tSXo3xK8jq9caBY3xE6B1Vd8DMDE/C7p2ukeu17wGL46ORBLA7yrokXF2fKqeAc/TqoriBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:39:32.956180Z","bundle_sha256":"a9e0c6e4389f70f07b6355c2f169617cce07dff50a7f898f0079e7b5364edcd9"}}