{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:M7GHND3KSUENRDXC64OLK45OPM","short_pith_number":"pith:M7GHND3K","canonical_record":{"source":{"id":"2502.04859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-07T11:50:04Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"9d8284c0e3a786fd3a2750e4712e93b1114713383974a8cedc77ea78863f783c","abstract_canon_sha256":"0a2e08ba5c8d12ea3e29022ed9714c50b4cd3941c1cc2c32225c50e4ec3b69d4"},"schema_version":"1.0"},"canonical_sha256":"67cc768f6a9508d88ee2f71cb573ae7b166aba917dcace2692e6e7bb7b874014","source":{"kind":"arxiv","id":"2502.04859","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.04859","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"arxiv_version","alias_value":"2502.04859v1","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04859","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"pith_short_12","alias_value":"M7GHND3KSUEN","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"pith_short_16","alias_value":"M7GHND3KSUENRDXC","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"pith_short_8","alias_value":"M7GHND3K","created_at":"2026-07-05T10:10:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:M7GHND3KSUENRDXC64OLK45OPM","target":"record","payload":{"canonical_record":{"source":{"id":"2502.04859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-07T11:50:04Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"9d8284c0e3a786fd3a2750e4712e93b1114713383974a8cedc77ea78863f783c","abstract_canon_sha256":"0a2e08ba5c8d12ea3e29022ed9714c50b4cd3941c1cc2c32225c50e4ec3b69d4"},"schema_version":"1.0"},"canonical_sha256":"67cc768f6a9508d88ee2f71cb573ae7b166aba917dcace2692e6e7bb7b874014","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:58.656209Z","signature_b64":"6PEWiZdje3TgtqYt99bC4FaHdnfYiqVUi0+1fNd9fMt/ynG3MeLBeKzOiiSRYycnJXIphtGduhRqCymcwhvvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67cc768f6a9508d88ee2f71cb573ae7b166aba917dcace2692e6e7bb7b874014","last_reissued_at":"2026-07-05T10:10:58.655631Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:58.655631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.04859","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":"2026-07-05T10:10:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9OL3w+P5DncbwoaiIN3jPR6b3wpVjjVN43XU8j1i6usqwd6CSlEO8uZ3mmHlugwO457mK8Ds9WFGh0zxsE6hDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T21:08:35.766670Z"},"content_sha256":"cd550f0caa4a2d986da9b27ef459ab77d2f8c0fd810c8c469c083c339b718838","schema_version":"1.0","event_id":"sha256:cd550f0caa4a2d986da9b27ef459ab77d2f8c0fd810c8c469c083c339b718838"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:M7GHND3KSUENRDXC64OLK45OPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective multipliers for weights whose log are H\\\"older continuous. Application to the cost of fast boundary controls for the 1D Schr{\\\"o}dinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CA","authors_text":"Pierre Lissy (CERMICS)","submitted_at":"2025-02-07T11:50:04Z","abstract_excerpt":"We give a simple proof of the Beurling-Malliavin multiplier theorem (BM1) in the particular case of weights that verify the usual finite logarithmic integral condition and such that their log are H{\\\"o}lder continuous with exponent less than 1. Our proof has the advantage to give an explicit version of BM1, in the sense that one can give precise estimates from below and above for the multiplier, in terms of the exponential type we want to reach, and the constants appearing in the H{\\\"o}lder condition of our weights. The same ideas can be applied to a particular weight, that will lead to an imp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04859","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/2502.04859/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":"2026-07-05T10:10:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdRW/GNawWyYFBAhH4tRrU49k5Vzd5NJNduoYEgJByCLFCI9EPgRXJKxS6qB/HAhrxdAtZEsy/AqLq3588HkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T21:08:35.767175Z"},"content_sha256":"851acd779d4f7630a6e1b072a14a854080c06cd4c77f48f918420d59a28b88dd","schema_version":"1.0","event_id":"sha256:851acd779d4f7630a6e1b072a14a854080c06cd4c77f48f918420d59a28b88dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7GHND3KSUENRDXC64OLK45OPM/bundle.json","state_url":"https://pith.science/pith/M7GHND3KSUENRDXC64OLK45OPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7GHND3KSUENRDXC64OLK45OPM/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":"2026-08-12T21:08:35Z","links":{"resolver":"https://pith.science/pith/M7GHND3KSUENRDXC64OLK45OPM","bundle":"https://pith.science/pith/M7GHND3KSUENRDXC64OLK45OPM/bundle.json","state":"https://pith.science/pith/M7GHND3KSUENRDXC64OLK45OPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7GHND3KSUENRDXC64OLK45OPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:M7GHND3KSUENRDXC64OLK45OPM","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":"0a2e08ba5c8d12ea3e29022ed9714c50b4cd3941c1cc2c32225c50e4ec3b69d4","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-07T11:50:04Z","title_canon_sha256":"9d8284c0e3a786fd3a2750e4712e93b1114713383974a8cedc77ea78863f783c"},"schema_version":"1.0","source":{"id":"2502.04859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.04859","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"arxiv_version","alias_value":"2502.04859v1","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04859","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"pith_short_12","alias_value":"M7GHND3KSUEN","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"pith_short_16","alias_value":"M7GHND3KSUENRDXC","created_at":"2026-07-05T10:10:58Z"},{"alias_kind":"pith_short_8","alias_value":"M7GHND3K","created_at":"2026-07-05T10:10:58Z"}],"graph_snapshots":[{"event_id":"sha256:851acd779d4f7630a6e1b072a14a854080c06cd4c77f48f918420d59a28b88dd","target":"graph","created_at":"2026-07-05T10:10:58Z","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/2502.04859/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a simple proof of the Beurling-Malliavin multiplier theorem (BM1) in the particular case of weights that verify the usual finite logarithmic integral condition and such that their log are H{\\\"o}lder continuous with exponent less than 1. Our proof has the advantage to give an explicit version of BM1, in the sense that one can give precise estimates from below and above for the multiplier, in terms of the exponential type we want to reach, and the constants appearing in the H{\\\"o}lder condition of our weights. The same ideas can be applied to a particular weight, that will lead to an imp","authors_text":"Pierre Lissy (CERMICS)","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-07T11:50:04Z","title":"Effective multipliers for weights whose log are H\\\"older continuous. Application to the cost of fast boundary controls for the 1D Schr{\\\"o}dinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04859","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:cd550f0caa4a2d986da9b27ef459ab77d2f8c0fd810c8c469c083c339b718838","target":"record","created_at":"2026-07-05T10:10:58Z","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":"0a2e08ba5c8d12ea3e29022ed9714c50b4cd3941c1cc2c32225c50e4ec3b69d4","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-07T11:50:04Z","title_canon_sha256":"9d8284c0e3a786fd3a2750e4712e93b1114713383974a8cedc77ea78863f783c"},"schema_version":"1.0","source":{"id":"2502.04859","kind":"arxiv","version":1}},"canonical_sha256":"67cc768f6a9508d88ee2f71cb573ae7b166aba917dcace2692e6e7bb7b874014","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67cc768f6a9508d88ee2f71cb573ae7b166aba917dcace2692e6e7bb7b874014","first_computed_at":"2026-07-05T10:10:58.655631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:10:58.655631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6PEWiZdje3TgtqYt99bC4FaHdnfYiqVUi0+1fNd9fMt/ynG3MeLBeKzOiiSRYycnJXIphtGduhRqCymcwhvvDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:10:58.656209Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.04859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd550f0caa4a2d986da9b27ef459ab77d2f8c0fd810c8c469c083c339b718838","sha256:851acd779d4f7630a6e1b072a14a854080c06cd4c77f48f918420d59a28b88dd"],"state_sha256":"0aa55b485aeb8f0a9391cdd41089d9c599bac56696f901ee8e32af7650ecf2a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQlV0Pl1OUDSNRWHM0XtoqD2s7etF/O1zDjXA05qxHWz60nkRzksmZIv/3pzGlagYywdC8apgfvWlt+GF3rLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T21:08:35.771598Z","bundle_sha256":"f75d4eb6ba9392cd56e0e1962a52afde23dc199691a6501f09a7e25e5abd2637"}}