{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DDT6NWKH6GEB3RWCDWX3OZKOIQ","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":"ffd58f5b009e5fb1e782ea5fde6b4c50892a97352a99a8d7525476232791ebc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-02T20:27:52Z","title_canon_sha256":"5ee0335a454e84afa0f6143c2893991e130bcb2c1733b0af3095c48497047805"},"schema_version":"1.0","source":{"id":"1210.0919","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0919","created_at":"2026-05-18T01:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0919v1","created_at":"2026-05-18T01:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0919","created_at":"2026-05-18T01:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"DDT6NWKH6GEB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"DDT6NWKH6GEB3RWC","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"DDT6NWKH","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:1efbb79025681a9407bef452b3b7b5742f4cdf11684587058fd13da9b4f30cef","target":"graph","created_at":"2026-05-18T01:54:11Z","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 develop the theory of compound functional differential equations, which are tensor and exterior products of linear functional differential equations. Of particular interest is the equation $\\dot x(t)=-\\alpha(t)x(t)-\\beta(t)x(t-1)$ with a single delay, where the delay coefficient is of one sign, say $\\delta\\beta(t)\\ge 0$ with $\\delta\\in{-1,1}$. Positivity properties are studied, with the result that if $(-1)^k=\\delta$ then the $k$-fold exterior product of the above system generates a linear process which is positive with respect to a certain cone in the phase space. Additionally, if the coef","authors_text":"John Mallet-Paret, Roger D. Nussbaum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-02T20:27:52Z","title":"Tensor Products, Positive Linear Operators, and Delay-Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0919","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":"sha256:4407dc284805b1d677b05225f3a98feb73d8bf176c1d02b7997b0c00a8a119a1","target":"record","created_at":"2026-05-18T01:54:11Z","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":"ffd58f5b009e5fb1e782ea5fde6b4c50892a97352a99a8d7525476232791ebc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-02T20:27:52Z","title_canon_sha256":"5ee0335a454e84afa0f6143c2893991e130bcb2c1733b0af3095c48497047805"},"schema_version":"1.0","source":{"id":"1210.0919","kind":"arxiv","version":1}},"canonical_sha256":"18e7e6d947f1881dc6c21dafb7654e441bfa7e5782262953871622ce2f86c76c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18e7e6d947f1881dc6c21dafb7654e441bfa7e5782262953871622ce2f86c76c","first_computed_at":"2026-05-18T01:54:11.357486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:11.357486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8HgU7/mSKKgKdvOWfEovq1W5BFiHX4pjPm36HwjwCGd9zT6x37kiNMASeUdYgLi48AfUgJeL7fdBSsAMZAWMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:11.358111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0919","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4407dc284805b1d677b05225f3a98feb73d8bf176c1d02b7997b0c00a8a119a1","sha256:1efbb79025681a9407bef452b3b7b5742f4cdf11684587058fd13da9b4f30cef"],"state_sha256":"ce553d032c97761740d3ee808f75cd590fc58e1543c45ad30c51ff8f54061c1e"}