{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DTTPWEXMCSCNY6BOBLOS23PJ6C","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":"fb1d7cd584e92ef5cd085de3c2a58685b95fc61427a41b03411c54433fdbe08b","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-11T16:40:54Z","title_canon_sha256":"c417374b3ec8ae1219d836e2b94b05be05e5b63912a9ca35e78f82040ec411f8"},"schema_version":"1.0","source":{"id":"1611.03772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03772","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03772v2","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03772","created_at":"2026-05-18T00:36:24Z"},{"alias_kind":"pith_short_12","alias_value":"DTTPWEXMCSCN","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTTPWEXMCSCNY6BO","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTTPWEXM","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:71af676abf12e1637d339dae2738a33db8ff89268f14e4c0ec70d7ba785d5a29","target":"graph","created_at":"2026-05-18T00:36:24Z","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 study Helson matrices (also known as multiplicative Hankel matrices), i.e. infinite matrices of the form $M(\\alpha) = \\{\\alpha(nm)\\}_{n,m=1}^\\infty$, where $\\alpha$ is a sequence of complex numbers. Helson matrices are considered as linear operators on $\\ell^2(\\mathbb{N})$. By interpreting Helson matrices as Hankel matrices in countably many variables we use the theory of multivariate moment problems to show that $M(\\alpha)$ is non-negative if and only if $\\alpha$ is the moment sequence of a measure $\\mu$ on $\\mathbb{R}^\\infty$, assuming that $\\alpha$ does not grow too fast. We then charact","authors_text":"Alexander Pushnitski, Karl-Mikael Perfekt","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-11T16:40:54Z","title":"On Helson matrices: moment problems, non-negativity, boundedness, and finite rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03772","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":"sha256:1679d8cb6c8455e9b0c8f1abf4b8e1aac05183978c1dffc1a4dba0c9a55233dd","target":"record","created_at":"2026-05-18T00:36:24Z","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":"fb1d7cd584e92ef5cd085de3c2a58685b95fc61427a41b03411c54433fdbe08b","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-11T16:40:54Z","title_canon_sha256":"c417374b3ec8ae1219d836e2b94b05be05e5b63912a9ca35e78f82040ec411f8"},"schema_version":"1.0","source":{"id":"1611.03772","kind":"arxiv","version":2}},"canonical_sha256":"1ce6fb12ec1484dc782e0add2d6de9f080f04beb3e79c5bb37c45c3b5c694923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ce6fb12ec1484dc782e0add2d6de9f080f04beb3e79c5bb37c45c3b5c694923","first_computed_at":"2026-05-18T00:36:24.509042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:24.509042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EEhyzwD40h5Aa09u862QGcEp8jQbh0hv4BZuSqyP0E0eiKr8G2H/nwQs59xDL7uBZucrAKRBj0CTfGSO/qj6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:24.509824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1679d8cb6c8455e9b0c8f1abf4b8e1aac05183978c1dffc1a4dba0c9a55233dd","sha256:71af676abf12e1637d339dae2738a33db8ff89268f14e4c0ec70d7ba785d5a29"],"state_sha256":"66c02984990a30a8e03cc1f96315efa86f7f67726e998b5e7bc6a78fdaa01f6f"}