{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MUUZCFFIFP2LCCCXOMN6GRMBWL","short_pith_number":"pith:MUUZCFFI","canonical_record":{"source":{"id":"2506.07892","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T16:07:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"aa7618671152ab99136f16302f1f839a2ea543384746ee1b30742338f6e215f6","abstract_canon_sha256":"4cc8b78b5802838aca6666c366e63fd17985b34a73807de75abb32caae5a1c82"},"schema_version":"1.0"},"canonical_sha256":"65299114a82bf4b10857731be34581b2f80530742dd4220225cc05f79da75add","source":{"kind":"arxiv","id":"2506.07892","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07892","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07892v1","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07892","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"MUUZCFFIFP2L","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"pith_short_16","alias_value":"MUUZCFFIFP2LCCCX","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"pith_short_8","alias_value":"MUUZCFFI","created_at":"2026-07-05T11:18:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MUUZCFFIFP2LCCCXOMN6GRMBWL","target":"record","payload":{"canonical_record":{"source":{"id":"2506.07892","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T16:07:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"aa7618671152ab99136f16302f1f839a2ea543384746ee1b30742338f6e215f6","abstract_canon_sha256":"4cc8b78b5802838aca6666c366e63fd17985b34a73807de75abb32caae5a1c82"},"schema_version":"1.0"},"canonical_sha256":"65299114a82bf4b10857731be34581b2f80530742dd4220225cc05f79da75add","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:34.982872Z","signature_b64":"XBdbhdkRW7BHEOuhDDHyZpM7y8tkN9CL+enTz0B4s53AW2ad9+EJVlROH4l5RE1g9tfW2SKrpLyS0zePiEYbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65299114a82bf4b10857731be34581b2f80530742dd4220225cc05f79da75add","last_reissued_at":"2026-07-05T11:18:34.982429Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:34.982429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.07892","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":"2026-07-05T11:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AoVhp5BDAQZrXsGPtr6pI6QyWewN8nio382EjHmZGiu8Ha0Xk5dMH/EIfj8161L0t8uW8bm5RGP3Pc1nW6KdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T02:26:11.355437Z"},"content_sha256":"5f7317f23610fa157dab0a74d0c8b0085034a7bd5fbb4cc768fec434176e7c07","schema_version":"1.0","event_id":"sha256:5f7317f23610fa157dab0a74d0c8b0085034a7bd5fbb4cc768fec434176e7c07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MUUZCFFIFP2LCCCXOMN6GRMBWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analyticity of Exponential Dirichlet Series and Applications to the Approximate Controllability of Parabolic Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Mohamed Ouzahra","submitted_at":"2025-06-09T16:07:19Z","abstract_excerpt":"In this paper, we investigate the analyticity of a class of exponential Dirichlet series. We then explicitly determine the coefficients of their power series decomposition and provide an estimate for the remainder. As an application, we study the approximate controllability property of linear parabolic equations with locally distributed or lumped controls by employing the moment method, which relies on the exponential Dirichlet series associated with the spectrum of the system's operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07892","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.07892/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":"2026-07-05T11:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Ad+SfFaVnRPZS1mhgEduW3YEBpVx68UiFGR42gLkDDTDSgQll0e7qyCJ8JYt9wNE6l5EkLAMe0yBhqDcZd0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T02:26:11.355933Z"},"content_sha256":"a7da2439ffb1fd77d4e4c7e2dde48d7722d30cc447069fcb0d9d7a36ada858ab","schema_version":"1.0","event_id":"sha256:a7da2439ffb1fd77d4e4c7e2dde48d7722d30cc447069fcb0d9d7a36ada858ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUUZCFFIFP2LCCCXOMN6GRMBWL/bundle.json","state_url":"https://pith.science/pith/MUUZCFFIFP2LCCCXOMN6GRMBWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUUZCFFIFP2LCCCXOMN6GRMBWL/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":"2026-08-08T02:26:11Z","links":{"resolver":"https://pith.science/pith/MUUZCFFIFP2LCCCXOMN6GRMBWL","bundle":"https://pith.science/pith/MUUZCFFIFP2LCCCXOMN6GRMBWL/bundle.json","state":"https://pith.science/pith/MUUZCFFIFP2LCCCXOMN6GRMBWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUUZCFFIFP2LCCCXOMN6GRMBWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MUUZCFFIFP2LCCCXOMN6GRMBWL","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":"4cc8b78b5802838aca6666c366e63fd17985b34a73807de75abb32caae5a1c82","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T16:07:19Z","title_canon_sha256":"aa7618671152ab99136f16302f1f839a2ea543384746ee1b30742338f6e215f6"},"schema_version":"1.0","source":{"id":"2506.07892","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07892","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07892v1","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07892","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"MUUZCFFIFP2L","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"pith_short_16","alias_value":"MUUZCFFIFP2LCCCX","created_at":"2026-07-05T11:18:34Z"},{"alias_kind":"pith_short_8","alias_value":"MUUZCFFI","created_at":"2026-07-05T11:18:34Z"}],"graph_snapshots":[{"event_id":"sha256:a7da2439ffb1fd77d4e4c7e2dde48d7722d30cc447069fcb0d9d7a36ada858ab","target":"graph","created_at":"2026-07-05T11:18:34Z","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/2506.07892/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the analyticity of a class of exponential Dirichlet series. We then explicitly determine the coefficients of their power series decomposition and provide an estimate for the remainder. As an application, we study the approximate controllability property of linear parabolic equations with locally distributed or lumped controls by employing the moment method, which relies on the exponential Dirichlet series associated with the spectrum of the system's operator.","authors_text":"Mohamed Ouzahra","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T16:07:19Z","title":"Analyticity of Exponential Dirichlet Series and Applications to the Approximate Controllability of Parabolic Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07892","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":"sha256:5f7317f23610fa157dab0a74d0c8b0085034a7bd5fbb4cc768fec434176e7c07","target":"record","created_at":"2026-07-05T11:18:34Z","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":"4cc8b78b5802838aca6666c366e63fd17985b34a73807de75abb32caae5a1c82","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T16:07:19Z","title_canon_sha256":"aa7618671152ab99136f16302f1f839a2ea543384746ee1b30742338f6e215f6"},"schema_version":"1.0","source":{"id":"2506.07892","kind":"arxiv","version":1}},"canonical_sha256":"65299114a82bf4b10857731be34581b2f80530742dd4220225cc05f79da75add","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65299114a82bf4b10857731be34581b2f80530742dd4220225cc05f79da75add","first_computed_at":"2026-07-05T11:18:34.982429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:34.982429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XBdbhdkRW7BHEOuhDDHyZpM7y8tkN9CL+enTz0B4s53AW2ad9+EJVlROH4l5RE1g9tfW2SKrpLyS0zePiEYbCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:34.982872Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07892","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f7317f23610fa157dab0a74d0c8b0085034a7bd5fbb4cc768fec434176e7c07","sha256:a7da2439ffb1fd77d4e4c7e2dde48d7722d30cc447069fcb0d9d7a36ada858ab"],"state_sha256":"c84b584d8669bdfd98325220c87eae1bf3f691d513bb88e2cb6408b8d0a07f93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ty0c1uA8AJT8qVjYhPcsf6E97ujhOjnhCx3R8d8Q6eA+fQQrW+maWEZj88NZvhq2GZgE1FLEpMpunoQMlrhEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T02:26:11.359514Z","bundle_sha256":"60b7c86f41415edff064790d74cf8d93f313221ea0eb33c21e6a3b65f9f199ac"}}