{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JGBPRCASBJLVAAQ3OAUTRRRUKW","short_pith_number":"pith:JGBPRCAS","canonical_record":{"source":{"id":"1506.03015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-09T17:37:41Z","cross_cats_sorted":[],"title_canon_sha256":"d9424948d289759a637a40676d570e0193b994cb87dad26871179a6438b791e7","abstract_canon_sha256":"e8e7500eb6d9ca0870ef23caa1c5c66d79a8d4835a58666b2d565563e81b9611"},"schema_version":"1.0"},"canonical_sha256":"4982f888120a5750021b702938c634558ffbfd0fc14412dc94744ebbfe79a6d2","source":{"kind":"arxiv","id":"1506.03015","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03015","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03015v2","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03015","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"JGBPRCASBJLV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JGBPRCASBJLVAAQ3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JGBPRCAS","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JGBPRCASBJLVAAQ3OAUTRRRUKW","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-09T17:37:41Z","cross_cats_sorted":[],"title_canon_sha256":"d9424948d289759a637a40676d570e0193b994cb87dad26871179a6438b791e7","abstract_canon_sha256":"e8e7500eb6d9ca0870ef23caa1c5c66d79a8d4835a58666b2d565563e81b9611"},"schema_version":"1.0"},"canonical_sha256":"4982f888120a5750021b702938c634558ffbfd0fc14412dc94744ebbfe79a6d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:28.352144Z","signature_b64":"KW0+jkJNQxYQ2z6rgetoDn30U0oD3FuAzzQ6vFkTDFO6zR5M99+Q4r6bchDX+6GoqIGsA8uwZAOr3BLkeSSxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4982f888120a5750021b702938c634558ffbfd0fc14412dc94744ebbfe79a6d2","last_reissued_at":"2026-05-18T00:44:28.351532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:28.351532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03015","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wo8VBWXmGnUucbBN1QDL95w1a5xHvokUiFbBMevkSS1cqCy2c5Mp1QD0TOHoK3NH7wyZ1MDGk8QYjyoAydg0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:15:41.811824Z"},"content_sha256":"b0d44628256e0e87eae0b2a64d8b9195b2d1f45c76e921f631ea5024b9296d2b","schema_version":"1.0","event_id":"sha256:b0d44628256e0e87eae0b2a64d8b9195b2d1f45c76e921f631ea5024b9296d2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JGBPRCASBJLVAAQ3OAUTRRRUKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectrally reasonable measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Micha{\\l} Wojciechowski, Przemys{\\l}aw Ohrysko","submitted_at":"2015-06-09T17:37:41Z","abstract_excerpt":"In this paper we investigate the problems related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier-Stieltjes transform). Since it is known that the set of all such measures does not have a Banach algebra structure we consider the set of all suitable perturbations called spectrally reasonable measures. In particular, we exhibit a broad class of spectrally reasonable measures which contains absolutely continuous ones. On the other hand, we show that except trivial cases all discrete (purely atomic) measures do not posses this property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03015","kind":"arxiv","version":2},"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":"2026-05-18T00:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SXswrT1O4GJCbevBTgOIGfumfb/gJVosh0nln20biIcXEqdkWPwkHy2jrN7l/mfbJjKtZ0GiTmjrA1AwnPQVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:15:41.812169Z"},"content_sha256":"34dbcea7879e484f0ecb20a2434295f82dd7268a773559e78df00ae28c77fabc","schema_version":"1.0","event_id":"sha256:34dbcea7879e484f0ecb20a2434295f82dd7268a773559e78df00ae28c77fabc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JGBPRCASBJLVAAQ3OAUTRRRUKW/bundle.json","state_url":"https://pith.science/pith/JGBPRCASBJLVAAQ3OAUTRRRUKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JGBPRCASBJLVAAQ3OAUTRRRUKW/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":"2026-06-26T23:15:41Z","links":{"resolver":"https://pith.science/pith/JGBPRCASBJLVAAQ3OAUTRRRUKW","bundle":"https://pith.science/pith/JGBPRCASBJLVAAQ3OAUTRRRUKW/bundle.json","state":"https://pith.science/pith/JGBPRCASBJLVAAQ3OAUTRRRUKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JGBPRCASBJLVAAQ3OAUTRRRUKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JGBPRCASBJLVAAQ3OAUTRRRUKW","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":"e8e7500eb6d9ca0870ef23caa1c5c66d79a8d4835a58666b2d565563e81b9611","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-09T17:37:41Z","title_canon_sha256":"d9424948d289759a637a40676d570e0193b994cb87dad26871179a6438b791e7"},"schema_version":"1.0","source":{"id":"1506.03015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03015","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03015v2","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03015","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"JGBPRCASBJLV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JGBPRCASBJLVAAQ3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JGBPRCAS","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:34dbcea7879e484f0ecb20a2434295f82dd7268a773559e78df00ae28c77fabc","target":"graph","created_at":"2026-05-18T00:44:28Z","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"},"paper":{"abstract_excerpt":"In this paper we investigate the problems related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier-Stieltjes transform). Since it is known that the set of all such measures does not have a Banach algebra structure we consider the set of all suitable perturbations called spectrally reasonable measures. In particular, we exhibit a broad class of spectrally reasonable measures which contains absolutely continuous ones. On the other hand, we show that except trivial cases all discrete (purely atomic) measures do not posses this property.","authors_text":"Micha{\\l} Wojciechowski, Przemys{\\l}aw Ohrysko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-09T17:37:41Z","title":"Spectrally reasonable measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03015","kind":"arxiv","version":2},"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:b0d44628256e0e87eae0b2a64d8b9195b2d1f45c76e921f631ea5024b9296d2b","target":"record","created_at":"2026-05-18T00:44:28Z","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":"e8e7500eb6d9ca0870ef23caa1c5c66d79a8d4835a58666b2d565563e81b9611","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-09T17:37:41Z","title_canon_sha256":"d9424948d289759a637a40676d570e0193b994cb87dad26871179a6438b791e7"},"schema_version":"1.0","source":{"id":"1506.03015","kind":"arxiv","version":2}},"canonical_sha256":"4982f888120a5750021b702938c634558ffbfd0fc14412dc94744ebbfe79a6d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4982f888120a5750021b702938c634558ffbfd0fc14412dc94744ebbfe79a6d2","first_computed_at":"2026-05-18T00:44:28.351532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:28.351532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KW0+jkJNQxYQ2z6rgetoDn30U0oD3FuAzzQ6vFkTDFO6zR5M99+Q4r6bchDX+6GoqIGsA8uwZAOr3BLkeSSxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:28.352144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0d44628256e0e87eae0b2a64d8b9195b2d1f45c76e921f631ea5024b9296d2b","sha256:34dbcea7879e484f0ecb20a2434295f82dd7268a773559e78df00ae28c77fabc"],"state_sha256":"e53de76031906c68816ab56cca7ae5e0c5fe1d0a9d0d7ce997720288713a55fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43y4LHjtPVTOC51cARMzfjlFYTNNxFljMiK+H7w/7WoZa9SR5QDVaY1G1fyfaPj14rdjAP8ME/BzavjHvhm7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:15:41.814034Z","bundle_sha256":"c6ed0cfc5369d0c780b6902b147b8ca8bd45f61b3f457a0a5c06ee5e4a2b2e19"}}