{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YWKKZIZU6BUQMHY7ZRFUSHEFRV","short_pith_number":"pith:YWKKZIZU","canonical_record":{"source":{"id":"1512.05583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-17T14:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"106cf10aa576362bf5b05d051c463272489b02c8d7f80780615fd03260d3dc4e","abstract_canon_sha256":"4425fba1c544271720d26f89e32caa472cd8033429460ee1754a1a5cf74f434d"},"schema_version":"1.0"},"canonical_sha256":"c594aca334f069061f1fcc4b491c858d7b3fbeeb360182e62ed81b7ffae5a05b","source":{"kind":"arxiv","id":"1512.05583","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05583","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05583v1","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05583","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"YWKKZIZU6BUQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YWKKZIZU6BUQMHY7","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YWKKZIZU","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YWKKZIZU6BUQMHY7ZRFUSHEFRV","target":"record","payload":{"canonical_record":{"source":{"id":"1512.05583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-17T14:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"106cf10aa576362bf5b05d051c463272489b02c8d7f80780615fd03260d3dc4e","abstract_canon_sha256":"4425fba1c544271720d26f89e32caa472cd8033429460ee1754a1a5cf74f434d"},"schema_version":"1.0"},"canonical_sha256":"c594aca334f069061f1fcc4b491c858d7b3fbeeb360182e62ed81b7ffae5a05b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:09.740827Z","signature_b64":"IdoLZ3mtP64dDphQIFlw+8qpTmcEuF90HWpHQXI1nobpHpMDRUSE/R7RtRiYILwEFhYuBEGmwIYRDtip18g3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c594aca334f069061f1fcc4b491c858d7b3fbeeb360182e62ed81b7ffae5a05b","last_reissued_at":"2026-05-18T01:24:09.740154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:09.740154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.05583","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":"2026-05-18T01:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SvetO7KeiLwoSVMkf76P7oi6UPxTnsWAHZuH5W4tzY2bT8TaFGORqcP4jP+SU1ZUFHZ5+nzvxYL6RlBEiDLPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T05:51:51.120185Z"},"content_sha256":"300d69a1f4ceb091584ed7229e68d1042392df2f3a169c81a9f78ef789a32f81","schema_version":"1.0","event_id":"sha256:300d69a1f4ceb091584ed7229e68d1042392df2f3a169c81a9f78ef789a32f81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YWKKZIZU6BUQMHY7ZRFUSHEFRV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local universality of the number of zeros of random trigonometric polynomials with continuous coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Federico Dalmao, Guillaume Poly, Ivan Nourdin, Jean-Marc Aza\\\"is, Jos\\'e Le\\'on","submitted_at":"2015-12-17T14:01:21Z","abstract_excerpt":"Let $X_N$ be a random trigonometric polynomial of degree $N$ with iid coefficients and let $Z_N(I)$ denote the (random) number of its zeros lying in the compact interval $I\\subset\\mathbb{R}$. Recently, a number of important advances were made in the understanding of the asymptotic behaviour of $Z_N(I)$ as $N\\to\\infty$, in the case of standard Gaussian coefficients. The main theorem of the present paper is a universality result, that states that the limit of $Z_N(I)$ does not really depend on the exact distribution of the coefficients of $X_N$. More precisely, assuming that these latter are iid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05583","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":"2026-05-18T01:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZP5LnJhO+ldn+dzsLzhJfX5qTkZdwJJOXkWwdI36D1p5FZQmtmnNsqUI6yEo7cdlc1whMg8cOn3e9UcHzOOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T05:51:51.120869Z"},"content_sha256":"a281f09f8a81c4e06a333a09ed7069199bb55e1105d7dbf23e1539316f3453c1","schema_version":"1.0","event_id":"sha256:a281f09f8a81c4e06a333a09ed7069199bb55e1105d7dbf23e1539316f3453c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWKKZIZU6BUQMHY7ZRFUSHEFRV/bundle.json","state_url":"https://pith.science/pith/YWKKZIZU6BUQMHY7ZRFUSHEFRV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWKKZIZU6BUQMHY7ZRFUSHEFRV/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":"2026-05-25T05:51:51Z","links":{"resolver":"https://pith.science/pith/YWKKZIZU6BUQMHY7ZRFUSHEFRV","bundle":"https://pith.science/pith/YWKKZIZU6BUQMHY7ZRFUSHEFRV/bundle.json","state":"https://pith.science/pith/YWKKZIZU6BUQMHY7ZRFUSHEFRV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWKKZIZU6BUQMHY7ZRFUSHEFRV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YWKKZIZU6BUQMHY7ZRFUSHEFRV","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":"4425fba1c544271720d26f89e32caa472cd8033429460ee1754a1a5cf74f434d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-17T14:01:21Z","title_canon_sha256":"106cf10aa576362bf5b05d051c463272489b02c8d7f80780615fd03260d3dc4e"},"schema_version":"1.0","source":{"id":"1512.05583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05583","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05583v1","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05583","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"YWKKZIZU6BUQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YWKKZIZU6BUQMHY7","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YWKKZIZU","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:a281f09f8a81c4e06a333a09ed7069199bb55e1105d7dbf23e1539316f3453c1","target":"graph","created_at":"2026-05-18T01:24:09Z","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":"Let $X_N$ be a random trigonometric polynomial of degree $N$ with iid coefficients and let $Z_N(I)$ denote the (random) number of its zeros lying in the compact interval $I\\subset\\mathbb{R}$. Recently, a number of important advances were made in the understanding of the asymptotic behaviour of $Z_N(I)$ as $N\\to\\infty$, in the case of standard Gaussian coefficients. The main theorem of the present paper is a universality result, that states that the limit of $Z_N(I)$ does not really depend on the exact distribution of the coefficients of $X_N$. More precisely, assuming that these latter are iid","authors_text":"Federico Dalmao, Guillaume Poly, Ivan Nourdin, Jean-Marc Aza\\\"is, Jos\\'e Le\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-17T14:01:21Z","title":"Local universality of the number of zeros of random trigonometric polynomials with continuous coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05583","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":"sha256:300d69a1f4ceb091584ed7229e68d1042392df2f3a169c81a9f78ef789a32f81","target":"record","created_at":"2026-05-18T01:24:09Z","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":"4425fba1c544271720d26f89e32caa472cd8033429460ee1754a1a5cf74f434d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-17T14:01:21Z","title_canon_sha256":"106cf10aa576362bf5b05d051c463272489b02c8d7f80780615fd03260d3dc4e"},"schema_version":"1.0","source":{"id":"1512.05583","kind":"arxiv","version":1}},"canonical_sha256":"c594aca334f069061f1fcc4b491c858d7b3fbeeb360182e62ed81b7ffae5a05b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c594aca334f069061f1fcc4b491c858d7b3fbeeb360182e62ed81b7ffae5a05b","first_computed_at":"2026-05-18T01:24:09.740154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:09.740154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IdoLZ3mtP64dDphQIFlw+8qpTmcEuF90HWpHQXI1nobpHpMDRUSE/R7RtRiYILwEFhYuBEGmwIYRDtip18g3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:09.740827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:300d69a1f4ceb091584ed7229e68d1042392df2f3a169c81a9f78ef789a32f81","sha256:a281f09f8a81c4e06a333a09ed7069199bb55e1105d7dbf23e1539316f3453c1"],"state_sha256":"55d92813ea4b245195fd86dba73f3409afe52326bdf4c858d1caadb6cbb5fea4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/A2n4x9ZsUA/YE3jerlTya0D0u6n8irPvNGwtIIdhj3EIJAbmELY26ylqtrzWCnpoNnQIPfLEL7b8+cFvlWyBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T05:51:51.124236Z","bundle_sha256":"66d8a702804123d3e7d32f13f7fb06f6e12e3aa9ceac13cda918bf3fbaf31194"}}