{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:44BGG5TW3TSFJEQXQGET3BU63O","short_pith_number":"pith:44BGG5TW","canonical_record":{"source":{"id":"1101.1199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-06T12:19:06Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1d022dca1d4237ab70b62052f8a07b10a2a466a69adc3510ff8f8c2d9f4a60b0","abstract_canon_sha256":"2b249175519db60d51f6bea14d1411f46b53b54fde81e427b38065c174cf6c93"},"schema_version":"1.0"},"canonical_sha256":"e702637676dce454921781893d869edb90b7038d4573899bfbb4018eabf2ca4b","source":{"kind":"arxiv","id":"1101.1199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1199","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1199v1","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1199","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"pith_short_12","alias_value":"44BGG5TW3TSF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"44BGG5TW3TSFJEQX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"44BGG5TW","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:44BGG5TW3TSFJEQXQGET3BU63O","target":"record","payload":{"canonical_record":{"source":{"id":"1101.1199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-06T12:19:06Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1d022dca1d4237ab70b62052f8a07b10a2a466a69adc3510ff8f8c2d9f4a60b0","abstract_canon_sha256":"2b249175519db60d51f6bea14d1411f46b53b54fde81e427b38065c174cf6c93"},"schema_version":"1.0"},"canonical_sha256":"e702637676dce454921781893d869edb90b7038d4573899bfbb4018eabf2ca4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:06.824996Z","signature_b64":"X+jCJP+MCdW+Wia5Cz2AB6MmVAujlSgeZa1jdGnzOMXWjMFrLoT6yJQHmJ+rRKxN6BU9WEHnon57piZwEuc6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e702637676dce454921781893d869edb90b7038d4573899bfbb4018eabf2ca4b","last_reissued_at":"2026-05-18T02:59:06.824328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:06.824328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.1199","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":"2026-05-18T02:59:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6gsmsLjPxur/uEuHFFYKmA4f2Tfbiaf0G8+3hHUODkUOPodaN0xir3gsE/s6w5oYy/jYPvUKgMTQJ06umy66BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:04:55.966882Z"},"content_sha256":"22d9bde071b96296936dcb283a4527aa46a97d8a3a52909257c8fda7fe163643","schema_version":"1.0","event_id":"sha256:22d9bde071b96296936dcb283a4527aa46a97d8a3a52909257c8fda7fe163643"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:44BGG5TW3TSFJEQXQGET3BU63O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero free regions for Dirichlet series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Christophe Delaunay (ICJ), Elie Mosaki (ICJ), Emmanuel Fricain (ICJ), Olivier Robert","submitted_at":"2011-01-06T12:19:06Z","abstract_excerpt":"In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for $L$-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a Beurling-Nyman type criterion for the Siegel zero problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1199","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":"2026-05-18T02:59:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXg9wGgPpjQGmsj0oM1sSGod33Hi7tKWnZaG1lDaI7knZ3zVa1Z/Jmj81SK+bOMEju3Nudw5quDE4G6iwBaSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:04:55.967215Z"},"content_sha256":"c919b2d25bdcd8908a9e23c0f09716a19ca6e6339fb5930b1275bd88ecfaa535","schema_version":"1.0","event_id":"sha256:c919b2d25bdcd8908a9e23c0f09716a19ca6e6339fb5930b1275bd88ecfaa535"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/44BGG5TW3TSFJEQXQGET3BU63O/bundle.json","state_url":"https://pith.science/pith/44BGG5TW3TSFJEQXQGET3BU63O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/44BGG5TW3TSFJEQXQGET3BU63O/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":"2026-06-22T03:04:55Z","links":{"resolver":"https://pith.science/pith/44BGG5TW3TSFJEQXQGET3BU63O","bundle":"https://pith.science/pith/44BGG5TW3TSFJEQXQGET3BU63O/bundle.json","state":"https://pith.science/pith/44BGG5TW3TSFJEQXQGET3BU63O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/44BGG5TW3TSFJEQXQGET3BU63O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:44BGG5TW3TSFJEQXQGET3BU63O","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":"2b249175519db60d51f6bea14d1411f46b53b54fde81e427b38065c174cf6c93","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-06T12:19:06Z","title_canon_sha256":"1d022dca1d4237ab70b62052f8a07b10a2a466a69adc3510ff8f8c2d9f4a60b0"},"schema_version":"1.0","source":{"id":"1101.1199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1199","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1199v1","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1199","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"pith_short_12","alias_value":"44BGG5TW3TSF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"44BGG5TW3TSFJEQX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"44BGG5TW","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:c919b2d25bdcd8908a9e23c0f09716a19ca6e6339fb5930b1275bd88ecfaa535","target":"graph","created_at":"2026-05-18T02:59:06Z","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":"In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for $L$-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a Beurling-Nyman type criterion for the Siegel zero problem.","authors_text":"Christophe Delaunay (ICJ), Elie Mosaki (ICJ), Emmanuel Fricain (ICJ), Olivier Robert","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-06T12:19:06Z","title":"Zero free regions for Dirichlet series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1199","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":"sha256:22d9bde071b96296936dcb283a4527aa46a97d8a3a52909257c8fda7fe163643","target":"record","created_at":"2026-05-18T02:59:06Z","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":"2b249175519db60d51f6bea14d1411f46b53b54fde81e427b38065c174cf6c93","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-06T12:19:06Z","title_canon_sha256":"1d022dca1d4237ab70b62052f8a07b10a2a466a69adc3510ff8f8c2d9f4a60b0"},"schema_version":"1.0","source":{"id":"1101.1199","kind":"arxiv","version":1}},"canonical_sha256":"e702637676dce454921781893d869edb90b7038d4573899bfbb4018eabf2ca4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e702637676dce454921781893d869edb90b7038d4573899bfbb4018eabf2ca4b","first_computed_at":"2026-05-18T02:59:06.824328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:06.824328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X+jCJP+MCdW+Wia5Cz2AB6MmVAujlSgeZa1jdGnzOMXWjMFrLoT6yJQHmJ+rRKxN6BU9WEHnon57piZwEuc6CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:06.824996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22d9bde071b96296936dcb283a4527aa46a97d8a3a52909257c8fda7fe163643","sha256:c919b2d25bdcd8908a9e23c0f09716a19ca6e6339fb5930b1275bd88ecfaa535"],"state_sha256":"73bcac2376b4b1f7fa7d12c56d352d91d5626006041a08cc34a3baac44898b49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/LNYyhFtUEPWeC+/6H41OUTbt43UBABBy8p+lSv/Pbm/AYzq7qTpAmRsxEK8PcLVJtDYqAyOEXdZsyXBwRjZDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T03:04:55.969253Z","bundle_sha256":"a278e0ebf45f150e252d71fc8e7f39c4426e2dde0d5937252ea3133283dbd627"}}