{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TNY5B4J5YVRAQACYH7ZX6EJF67","short_pith_number":"pith:TNY5B4J5","canonical_record":{"source":{"id":"1209.2849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-13T10:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"19ec11d23fab01250747960cea39b7d85b55281789617bbb79b072345e4608d6","abstract_canon_sha256":"e54fec717a3dc68f4996e559bbc80388e65a4d8f2a53fb2642e8bc097b7f100a"},"schema_version":"1.0"},"canonical_sha256":"9b71d0f13dc5620800583ff37f1125f7f91dccb432932299000c19bb6454071d","source":{"kind":"arxiv","id":"1209.2849","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2849","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2849v2","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2849","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"pith_short_12","alias_value":"TNY5B4J5YVRA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TNY5B4J5YVRAQACY","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TNY5B4J5","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TNY5B4J5YVRAQACYH7ZX6EJF67","target":"record","payload":{"canonical_record":{"source":{"id":"1209.2849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-13T10:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"19ec11d23fab01250747960cea39b7d85b55281789617bbb79b072345e4608d6","abstract_canon_sha256":"e54fec717a3dc68f4996e559bbc80388e65a4d8f2a53fb2642e8bc097b7f100a"},"schema_version":"1.0"},"canonical_sha256":"9b71d0f13dc5620800583ff37f1125f7f91dccb432932299000c19bb6454071d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:32.848847Z","signature_b64":"E6Uf1JQ33lKtCWQ0UhRf8jkjT+G+sYileEyzEMYD0Ijn9NqbEAw9BmW5gVlAOa7b05MJR5EovQYYtMHIT8ugDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b71d0f13dc5620800583ff37f1125f7f91dccb432932299000c19bb6454071d","last_reissued_at":"2026-05-18T00:28:32.848140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:32.848140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.2849","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":"2026-05-18T00:28:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rc1hCHBSzknOO6OBJi0gUxXfWEBALqG1oIm4rXm+NieQY0kr9iQYQmdicYOzZwlYryLJCPQUhxR9lycih7dtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:58:02.425366Z"},"content_sha256":"b7ef97120a8d73fc6c2526784d15817bd123f3e8fe2788c10a83bed5b5046eb2","schema_version":"1.0","event_id":"sha256:b7ef97120a8d73fc6c2526784d15817bd123f3e8fe2788c10a83bed5b5046eb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TNY5B4J5YVRAQACYH7ZX6EJF67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Local Bifurcations in Neural Field Models with Transmission Delays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sebastiaan G. Janssens, Sid Visser, Stephan A. van Gils, Yuri A. Kuznetsov","submitted_at":"2012-09-13T10:43:32Z","abstract_excerpt":"Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2849","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":"2026-05-18T00:28:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8/tHIYRWr9DYlhgymYJHcGOdbqzYjrvAjUQMyFmXp+PGUbi8VU6blhBs0ijivRPXnwY9I5fbpNAWwM2hnAc0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:58:02.426037Z"},"content_sha256":"be5b5f1f4ba71ec030ceb81b584a494c5564be1afdbac3ad629bb7f7e027660b","schema_version":"1.0","event_id":"sha256:be5b5f1f4ba71ec030ceb81b584a494c5564be1afdbac3ad629bb7f7e027660b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNY5B4J5YVRAQACYH7ZX6EJF67/bundle.json","state_url":"https://pith.science/pith/TNY5B4J5YVRAQACYH7ZX6EJF67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNY5B4J5YVRAQACYH7ZX6EJF67/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":"2026-05-25T22:58:02Z","links":{"resolver":"https://pith.science/pith/TNY5B4J5YVRAQACYH7ZX6EJF67","bundle":"https://pith.science/pith/TNY5B4J5YVRAQACYH7ZX6EJF67/bundle.json","state":"https://pith.science/pith/TNY5B4J5YVRAQACYH7ZX6EJF67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNY5B4J5YVRAQACYH7ZX6EJF67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TNY5B4J5YVRAQACYH7ZX6EJF67","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":"e54fec717a3dc68f4996e559bbc80388e65a4d8f2a53fb2642e8bc097b7f100a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-13T10:43:32Z","title_canon_sha256":"19ec11d23fab01250747960cea39b7d85b55281789617bbb79b072345e4608d6"},"schema_version":"1.0","source":{"id":"1209.2849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2849","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2849v2","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2849","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"pith_short_12","alias_value":"TNY5B4J5YVRA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TNY5B4J5YVRAQACY","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TNY5B4J5","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:be5b5f1f4ba71ec030ceb81b584a494c5564be1afdbac3ad629bb7f7e027660b","target":"graph","created_at":"2026-05-18T00:28:32Z","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":"Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions","authors_text":"Sebastiaan G. Janssens, Sid Visser, Stephan A. van Gils, Yuri A. Kuznetsov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-13T10:43:32Z","title":"On Local Bifurcations in Neural Field Models with Transmission Delays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2849","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:b7ef97120a8d73fc6c2526784d15817bd123f3e8fe2788c10a83bed5b5046eb2","target":"record","created_at":"2026-05-18T00:28:32Z","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":"e54fec717a3dc68f4996e559bbc80388e65a4d8f2a53fb2642e8bc097b7f100a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-13T10:43:32Z","title_canon_sha256":"19ec11d23fab01250747960cea39b7d85b55281789617bbb79b072345e4608d6"},"schema_version":"1.0","source":{"id":"1209.2849","kind":"arxiv","version":2}},"canonical_sha256":"9b71d0f13dc5620800583ff37f1125f7f91dccb432932299000c19bb6454071d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b71d0f13dc5620800583ff37f1125f7f91dccb432932299000c19bb6454071d","first_computed_at":"2026-05-18T00:28:32.848140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:32.848140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E6Uf1JQ33lKtCWQ0UhRf8jkjT+G+sYileEyzEMYD0Ijn9NqbEAw9BmW5gVlAOa7b05MJR5EovQYYtMHIT8ugDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:32.848847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7ef97120a8d73fc6c2526784d15817bd123f3e8fe2788c10a83bed5b5046eb2","sha256:be5b5f1f4ba71ec030ceb81b584a494c5564be1afdbac3ad629bb7f7e027660b"],"state_sha256":"5c430c6678ce3174269fc2d60e92899270d4c997cc8d4b88f0d9337a02bdc9ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HC1Ne4ozzw61/LIKPguedDr7AlkMKZEOo4/vyxeVw3YpOY185n2DXnV18uFFS8oNt/C9CTlE/RTBSSUXiEYEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:58:02.429525Z","bundle_sha256":"66ab6b311fab1340988109293c095e81b6e5432fe01f90c561a793e72c62085f"}}