{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YFZQV6GCQHSPJWA7DOTH4K3MLU","short_pith_number":"pith:YFZQV6GC","canonical_record":{"source":{"id":"1411.1539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-06T09:23:19Z","cross_cats_sorted":[],"title_canon_sha256":"2fb716a731699bbf651b883aebe73d43059f5e8c9cef2c190e37486ed03834d8","abstract_canon_sha256":"cc6da49cd6e241bee5417cd332482b678ef18df646c2c570f439ea11c8029573"},"schema_version":"1.0"},"canonical_sha256":"c1730af8c281e4f4d81f1ba67e2b6c5d024133af232f487444606d77fdef1438","source":{"kind":"arxiv","id":"1411.1539","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1539","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1539v1","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1539","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"pith_short_12","alias_value":"YFZQV6GCQHSP","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YFZQV6GCQHSPJWA7","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YFZQV6GC","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YFZQV6GCQHSPJWA7DOTH4K3MLU","target":"record","payload":{"canonical_record":{"source":{"id":"1411.1539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-06T09:23:19Z","cross_cats_sorted":[],"title_canon_sha256":"2fb716a731699bbf651b883aebe73d43059f5e8c9cef2c190e37486ed03834d8","abstract_canon_sha256":"cc6da49cd6e241bee5417cd332482b678ef18df646c2c570f439ea11c8029573"},"schema_version":"1.0"},"canonical_sha256":"c1730af8c281e4f4d81f1ba67e2b6c5d024133af232f487444606d77fdef1438","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:27.652590Z","signature_b64":"kUYey1FsjzXJUWJzildvRFReArz71YcrkUW9bva/hfuijE98L98fR6YgOuxYXh3ICjbApYBYY85yL1W6jHi5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1730af8c281e4f4d81f1ba67e2b6c5d024133af232f487444606d77fdef1438","last_reissued_at":"2026-05-18T02:38:27.651961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:27.651961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.1539","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J1MKUdxRriaisGq97PWonnUV67RdKCr5eab4UaWfRm14gZntaSL5MOyA6cesxf1nUp0w+7gOWOpjQQx5WBDCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:40:18.784617Z"},"content_sha256":"f61b6551cd2521b1f3cbde27808d4aace4f3a3626901881d5955448fb002504b","schema_version":"1.0","event_id":"sha256:f61b6551cd2521b1f3cbde27808d4aace4f3a3626901881d5955448fb002504b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YFZQV6GCQHSPJWA7DOTH4K3MLU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeros of the Zak transform of totally positive functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Tobias Kloos","submitted_at":"2014-11-06T09:23:19Z","abstract_excerpt":"We study the Zak transform of totally positive (TP) functions. We use the convergence of the Zak transform of TP functions of finite type to prove that the Zak transforms of all TP functions without Gaussian factor in the Fourier transform have only one zero in their fundamental domain of quasi-periodicity. Our proof is based on complex analysis, especially the Theorem of Hurwitz and some real analytic arguments, where we use the connection of TP functions of finite type and exponential B-splines."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1539","kind":"arxiv","version":1},"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":"2026-05-18T02:38:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53NeaIdbpy+0bGFDAQ1mONRhcVAdyhSrQDRynLI4ST7wGArNyHF+ccI2BViy8s6yW/7OgC1K0iR7iIHH4sPmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:40:18.784957Z"},"content_sha256":"99b0de667ebb0429efb48994ba9a0ff7f6dafd3c59d3cfa13fb20c05d6bd2e3e","schema_version":"1.0","event_id":"sha256:99b0de667ebb0429efb48994ba9a0ff7f6dafd3c59d3cfa13fb20c05d6bd2e3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFZQV6GCQHSPJWA7DOTH4K3MLU/bundle.json","state_url":"https://pith.science/pith/YFZQV6GCQHSPJWA7DOTH4K3MLU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFZQV6GCQHSPJWA7DOTH4K3MLU/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":"2026-06-27T01:40:18Z","links":{"resolver":"https://pith.science/pith/YFZQV6GCQHSPJWA7DOTH4K3MLU","bundle":"https://pith.science/pith/YFZQV6GCQHSPJWA7DOTH4K3MLU/bundle.json","state":"https://pith.science/pith/YFZQV6GCQHSPJWA7DOTH4K3MLU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFZQV6GCQHSPJWA7DOTH4K3MLU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YFZQV6GCQHSPJWA7DOTH4K3MLU","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":"cc6da49cd6e241bee5417cd332482b678ef18df646c2c570f439ea11c8029573","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-06T09:23:19Z","title_canon_sha256":"2fb716a731699bbf651b883aebe73d43059f5e8c9cef2c190e37486ed03834d8"},"schema_version":"1.0","source":{"id":"1411.1539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1539","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1539v1","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1539","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"pith_short_12","alias_value":"YFZQV6GCQHSP","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YFZQV6GCQHSPJWA7","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YFZQV6GC","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:99b0de667ebb0429efb48994ba9a0ff7f6dafd3c59d3cfa13fb20c05d6bd2e3e","target":"graph","created_at":"2026-05-18T02:38:27Z","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":"We study the Zak transform of totally positive (TP) functions. We use the convergence of the Zak transform of TP functions of finite type to prove that the Zak transforms of all TP functions without Gaussian factor in the Fourier transform have only one zero in their fundamental domain of quasi-periodicity. Our proof is based on complex analysis, especially the Theorem of Hurwitz and some real analytic arguments, where we use the connection of TP functions of finite type and exponential B-splines.","authors_text":"Tobias Kloos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-06T09:23:19Z","title":"Zeros of the Zak transform of totally positive functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1539","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:f61b6551cd2521b1f3cbde27808d4aace4f3a3626901881d5955448fb002504b","target":"record","created_at":"2026-05-18T02:38:27Z","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":"cc6da49cd6e241bee5417cd332482b678ef18df646c2c570f439ea11c8029573","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-06T09:23:19Z","title_canon_sha256":"2fb716a731699bbf651b883aebe73d43059f5e8c9cef2c190e37486ed03834d8"},"schema_version":"1.0","source":{"id":"1411.1539","kind":"arxiv","version":1}},"canonical_sha256":"c1730af8c281e4f4d81f1ba67e2b6c5d024133af232f487444606d77fdef1438","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1730af8c281e4f4d81f1ba67e2b6c5d024133af232f487444606d77fdef1438","first_computed_at":"2026-05-18T02:38:27.651961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:27.651961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kUYey1FsjzXJUWJzildvRFReArz71YcrkUW9bva/hfuijE98L98fR6YgOuxYXh3ICjbApYBYY85yL1W6jHi5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:27.652590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f61b6551cd2521b1f3cbde27808d4aace4f3a3626901881d5955448fb002504b","sha256:99b0de667ebb0429efb48994ba9a0ff7f6dafd3c59d3cfa13fb20c05d6bd2e3e"],"state_sha256":"afd28d014f887a64ea49a24fe85561fe41936d19b1b2638726d11473979533c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ziGQK6a2h+LN9uSJaO3HrM85tK7a1RXWGiLUxdj9rz6NoLxHEINJZDDKc83nZq5qVi2inW87DY+00MxC6bwAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:40:18.787151Z","bundle_sha256":"28de452e18361593832514190f188cb205d6563068843ae5641750ea648ef57c"}}