{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:SZIBK4HBVGN5NDVSCKXU6UE74Z","short_pith_number":"pith:SZIBK4HB","canonical_record":{"source":{"id":"2109.10844","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-09-22T17:14:42Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"578841504184a38558b55d9e83f704da5cfb572f3e1729fac3b8953937c22eaf","abstract_canon_sha256":"0e140ed27fe16f78efb0dac806f521b4989d33f39e1f180d48ae9e3100402dce"},"schema_version":"1.0"},"canonical_sha256":"96501570e1a99bd68eb212af4f509fe666d30473aacb181f334c2d16eb7f37f9","source":{"kind":"arxiv","id":"2109.10844","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10844","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10844v3","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10844","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"SZIBK4HBVGN5","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"SZIBK4HBVGN5NDVS","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"SZIBK4HB","created_at":"2026-07-05T05:06:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:SZIBK4HBVGN5NDVSCKXU6UE74Z","target":"record","payload":{"canonical_record":{"source":{"id":"2109.10844","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-09-22T17:14:42Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"578841504184a38558b55d9e83f704da5cfb572f3e1729fac3b8953937c22eaf","abstract_canon_sha256":"0e140ed27fe16f78efb0dac806f521b4989d33f39e1f180d48ae9e3100402dce"},"schema_version":"1.0"},"canonical_sha256":"96501570e1a99bd68eb212af4f509fe666d30473aacb181f334c2d16eb7f37f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:28.385775Z","signature_b64":"zGI110NxtmN9b64q/qN/6aqwhSO7xjKHeZ37Px5PVaULMdTrqKX9QYcERKCiok+aVfU1Ovaqptpn65JAqZLQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96501570e1a99bd68eb212af4f509fe666d30473aacb181f334c2d16eb7f37f9","last_reissued_at":"2026-07-05T05:06:28.385342Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:28.385342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.10844","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Aa7A4gudXMUabb9XgnD6gSCCf5Tj3mf05AqESweSaDb+HlcRkPT5AOlM3O2Rf88wTj2wqk1zt5ZUOsq3hghBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:11:15.700853Z"},"content_sha256":"fa6a2adadc159e662276c0e92587127a1f7f365452a4361df53caa8bb2dd6df5","schema_version":"1.0","event_id":"sha256:fa6a2adadc159e662276c0e92587127a1f7f365452a4361df53caa8bb2dd6df5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:SZIBK4HBVGN5NDVSCKXU6UE74Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilbert spaces and low-lying zeros of L-functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Andr\\'es Chirre, Emanuel Carneiro, Micah B. Milinovich","submitted_at":"2021-09-22T17:14:42Z","abstract_excerpt":"Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of $L$-functions in a family at a low-lying height on the critical line (measured by the analytic conductor). To solve the Fourier optimization problems that arise, we provide a unified framework based on the theory of reproducing kernel Hilbert spaces of entire functions (there is one such space associated to each symmetry type). Explicit expressions for the reproducing kernels are given. We also revisit the problem of estimating the hei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10844","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.10844/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33gKved36vN/2KhlYJIR6vAPmSRLopq90LImOtgNE006n3af2+YHY5ecnyQTcDgYfAzGhs7TE3lNnAyAz2QIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:11:15.701227Z"},"content_sha256":"d692290099d58d995297160ee8cd84c1f1cdc08ba946da1232fc6f22c235e977","schema_version":"1.0","event_id":"sha256:d692290099d58d995297160ee8cd84c1f1cdc08ba946da1232fc6f22c235e977"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SZIBK4HBVGN5NDVSCKXU6UE74Z/bundle.json","state_url":"https://pith.science/pith/SZIBK4HBVGN5NDVSCKXU6UE74Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SZIBK4HBVGN5NDVSCKXU6UE74Z/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":"2026-07-09T03:11:15Z","links":{"resolver":"https://pith.science/pith/SZIBK4HBVGN5NDVSCKXU6UE74Z","bundle":"https://pith.science/pith/SZIBK4HBVGN5NDVSCKXU6UE74Z/bundle.json","state":"https://pith.science/pith/SZIBK4HBVGN5NDVSCKXU6UE74Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SZIBK4HBVGN5NDVSCKXU6UE74Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SZIBK4HBVGN5NDVSCKXU6UE74Z","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":"0e140ed27fe16f78efb0dac806f521b4989d33f39e1f180d48ae9e3100402dce","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-09-22T17:14:42Z","title_canon_sha256":"578841504184a38558b55d9e83f704da5cfb572f3e1729fac3b8953937c22eaf"},"schema_version":"1.0","source":{"id":"2109.10844","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10844","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10844v3","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10844","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"SZIBK4HBVGN5","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"SZIBK4HBVGN5NDVS","created_at":"2026-07-05T05:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"SZIBK4HB","created_at":"2026-07-05T05:06:28Z"}],"graph_snapshots":[{"event_id":"sha256:d692290099d58d995297160ee8cd84c1f1cdc08ba946da1232fc6f22c235e977","target":"graph","created_at":"2026-07-05T05:06:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.10844/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of $L$-functions in a family at a low-lying height on the critical line (measured by the analytic conductor). To solve the Fourier optimization problems that arise, we provide a unified framework based on the theory of reproducing kernel Hilbert spaces of entire functions (there is one such space associated to each symmetry type). Explicit expressions for the reproducing kernels are given. We also revisit the problem of estimating the hei","authors_text":"Andr\\'es Chirre, Emanuel Carneiro, Micah B. Milinovich","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-09-22T17:14:42Z","title":"Hilbert spaces and low-lying zeros of L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10844","kind":"arxiv","version":3},"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:fa6a2adadc159e662276c0e92587127a1f7f365452a4361df53caa8bb2dd6df5","target":"record","created_at":"2026-07-05T05:06:28Z","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":"0e140ed27fe16f78efb0dac806f521b4989d33f39e1f180d48ae9e3100402dce","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-09-22T17:14:42Z","title_canon_sha256":"578841504184a38558b55d9e83f704da5cfb572f3e1729fac3b8953937c22eaf"},"schema_version":"1.0","source":{"id":"2109.10844","kind":"arxiv","version":3}},"canonical_sha256":"96501570e1a99bd68eb212af4f509fe666d30473aacb181f334c2d16eb7f37f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96501570e1a99bd68eb212af4f509fe666d30473aacb181f334c2d16eb7f37f9","first_computed_at":"2026-07-05T05:06:28.385342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:28.385342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zGI110NxtmN9b64q/qN/6aqwhSO7xjKHeZ37Px5PVaULMdTrqKX9QYcERKCiok+aVfU1Ovaqptpn65JAqZLQBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:28.385775Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.10844","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa6a2adadc159e662276c0e92587127a1f7f365452a4361df53caa8bb2dd6df5","sha256:d692290099d58d995297160ee8cd84c1f1cdc08ba946da1232fc6f22c235e977"],"state_sha256":"9c0f7a0264d8e26df0bb5e46d2e0179965cffca69c1bf6536edfffdfb96a27b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOJvXgqgL6J/D1WKAPQffdIEiZjML4Fe36nVj14IAhsxYtycYgy+IjfBza9unqu3hRXSiewawOlFbQBe9v6mDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T03:11:15.703496Z","bundle_sha256":"2952d4fb85b021039fb699190d90356c1db64eda70813527717fac440c157f68"}}