{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:G3FHOS2LYB3CUGM2WW462TP6BN","short_pith_number":"pith:G3FHOS2L","canonical_record":{"source":{"id":"1908.06324","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-17T17:39:51Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"3a652fa9e56bf1008472ff36d3424fd3c4f6b4bc3886d728728eb93a49241355","abstract_canon_sha256":"4823b410981c54769496c08041fa4c4705066203bc9efefb1542f75adc73c42f"},"schema_version":"1.0"},"canonical_sha256":"36ca774b4bc0762a199ab5b9ed4dfe0b4aa84a1d06102ecdba0ef094fb49169b","source":{"kind":"arxiv","id":"1908.06324","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06324","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06324v5","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06324","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"G3FHOS2LYB3C","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_16","alias_value":"G3FHOS2LYB3CUGM2","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_8","alias_value":"G3FHOS2L","created_at":"2026-07-05T08:00:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:G3FHOS2LYB3CUGM2WW462TP6BN","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06324","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-17T17:39:51Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"3a652fa9e56bf1008472ff36d3424fd3c4f6b4bc3886d728728eb93a49241355","abstract_canon_sha256":"4823b410981c54769496c08041fa4c4705066203bc9efefb1542f75adc73c42f"},"schema_version":"1.0"},"canonical_sha256":"36ca774b4bc0762a199ab5b9ed4dfe0b4aa84a1d06102ecdba0ef094fb49169b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:28.670744Z","signature_b64":"QR6zCFq+jnFG3+5aIZxdPjeBPFu/Ne3HPW2D2HzziZ3vmPXRx6dLGwme5THfQL7djeTIyHLvFGkDhcjUQIPAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36ca774b4bc0762a199ab5b9ed4dfe0b4aa84a1d06102ecdba0ef094fb49169b","last_reissued_at":"2026-07-05T08:00:28.670276Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:28.670276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06324","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:00:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q3hygJTWn0oGTK7kztjvmK8atF0gDlECyApbN2IcPTh7IEctCUUhRL6WKCqExHH2X5RMJbv4vL/npZslm7ASDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:37:15.296916Z"},"content_sha256":"006d888499c9e1cf6a6e829caf8afed7303cd8e995e26ef6ed1ef036f21a2cdc","schema_version":"1.0","event_id":"sha256:006d888499c9e1cf6a6e829caf8afed7303cd8e995e26ef6ed1ef036f21a2cdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:G3FHOS2LYB3CUGM2WW462TP6BN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of neural fields with exponential temporal kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"math.DS","authors_text":"Elham Shamsara, Fatihcan M. Atay, J\\\"urgen Jost, Marius E. Yamakou","submitted_at":"2019-08-17T17:39:51Z","abstract_excerpt":"We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not. Through a dynamic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06324","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06324/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:00:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qew2fHYrD2sNhQ0IhuMFNEsVp1l4xAuLJUHfDXTL05xugT/v91mBzCUkwoK+/FECMsZqw8sOLC8MPC6A08J5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:37:15.297821Z"},"content_sha256":"6c87b43e7fa4f522b03e7e9b9384426c9615a6c039b4465a8f2a57f5883ae448","schema_version":"1.0","event_id":"sha256:6c87b43e7fa4f522b03e7e9b9384426c9615a6c039b4465a8f2a57f5883ae448"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3FHOS2LYB3CUGM2WW462TP6BN/bundle.json","state_url":"https://pith.science/pith/G3FHOS2LYB3CUGM2WW462TP6BN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3FHOS2LYB3CUGM2WW462TP6BN/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":"2026-08-16T22:37:15Z","links":{"resolver":"https://pith.science/pith/G3FHOS2LYB3CUGM2WW462TP6BN","bundle":"https://pith.science/pith/G3FHOS2LYB3CUGM2WW462TP6BN/bundle.json","state":"https://pith.science/pith/G3FHOS2LYB3CUGM2WW462TP6BN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3FHOS2LYB3CUGM2WW462TP6BN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:G3FHOS2LYB3CUGM2WW462TP6BN","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":"4823b410981c54769496c08041fa4c4705066203bc9efefb1542f75adc73c42f","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-17T17:39:51Z","title_canon_sha256":"3a652fa9e56bf1008472ff36d3424fd3c4f6b4bc3886d728728eb93a49241355"},"schema_version":"1.0","source":{"id":"1908.06324","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06324","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06324v5","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06324","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"G3FHOS2LYB3C","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_16","alias_value":"G3FHOS2LYB3CUGM2","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_8","alias_value":"G3FHOS2L","created_at":"2026-07-05T08:00:28Z"}],"graph_snapshots":[{"event_id":"sha256:6c87b43e7fa4f522b03e7e9b9384426c9615a6c039b4465a8f2a57f5883ae448","target":"graph","created_at":"2026-07-05T08:00:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.06324/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not. Through a dynamic","authors_text":"Elham Shamsara, Fatihcan M. Atay, J\\\"urgen Jost, Marius E. Yamakou","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-17T17:39:51Z","title":"Dynamics of neural fields with exponential temporal kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06324","kind":"arxiv","version":5},"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":"sha256:006d888499c9e1cf6a6e829caf8afed7303cd8e995e26ef6ed1ef036f21a2cdc","target":"record","created_at":"2026-07-05T08:00:28Z","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":"4823b410981c54769496c08041fa4c4705066203bc9efefb1542f75adc73c42f","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-17T17:39:51Z","title_canon_sha256":"3a652fa9e56bf1008472ff36d3424fd3c4f6b4bc3886d728728eb93a49241355"},"schema_version":"1.0","source":{"id":"1908.06324","kind":"arxiv","version":5}},"canonical_sha256":"36ca774b4bc0762a199ab5b9ed4dfe0b4aa84a1d06102ecdba0ef094fb49169b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36ca774b4bc0762a199ab5b9ed4dfe0b4aa84a1d06102ecdba0ef094fb49169b","first_computed_at":"2026-07-05T08:00:28.670276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:00:28.670276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QR6zCFq+jnFG3+5aIZxdPjeBPFu/Ne3HPW2D2HzziZ3vmPXRx6dLGwme5THfQL7djeTIyHLvFGkDhcjUQIPAAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:00:28.670744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06324","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:006d888499c9e1cf6a6e829caf8afed7303cd8e995e26ef6ed1ef036f21a2cdc","sha256:6c87b43e7fa4f522b03e7e9b9384426c9615a6c039b4465a8f2a57f5883ae448"],"state_sha256":"c0063e90b6f85ed6165110fd449ff9665c3c9ea9975c00590b20dc8906ead94b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"guS/4u/6gbWACYVo8+6o0nnPHMcWg9aENPhU+hsIzfz7wwN3jy2XvZh7oQierrSBc24YAnCuDXqn43dCrmIxDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T22:37:15.303317Z","bundle_sha256":"10e16f75f7e8949e8c1347d3f908213960220a049ca5e4f6030c8411befa4515"}}