{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:A3KH52KMLBXR6QCC242OEF7UQT","short_pith_number":"pith:A3KH52KM","canonical_record":{"source":{"id":"1811.11560","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-28T13:51:35Z","cross_cats_sorted":[],"title_canon_sha256":"3877689c93b3e7e5ed0575bb59a5025dc04bcd9ecf5f30168c15c6f82f879a3e","abstract_canon_sha256":"debdaf2bd5cb31d837086359aa3858af867db3ce60bb52de46f900b2a647e8e4"},"schema_version":"1.0"},"canonical_sha256":"06d47ee94c586f1f4042d734e217f484c65199e7b4d859d92a1bdb18eb58a442","source":{"kind":"arxiv","id":"1811.11560","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11560","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11560v3","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11560","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"A3KH52KMLBXR","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A3KH52KMLBXR6QCC","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A3KH52KM","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:A3KH52KMLBXR6QCC242OEF7UQT","target":"record","payload":{"canonical_record":{"source":{"id":"1811.11560","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-28T13:51:35Z","cross_cats_sorted":[],"title_canon_sha256":"3877689c93b3e7e5ed0575bb59a5025dc04bcd9ecf5f30168c15c6f82f879a3e","abstract_canon_sha256":"debdaf2bd5cb31d837086359aa3858af867db3ce60bb52de46f900b2a647e8e4"},"schema_version":"1.0"},"canonical_sha256":"06d47ee94c586f1f4042d734e217f484c65199e7b4d859d92a1bdb18eb58a442","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:22.196850Z","signature_b64":"clOMu00RsX+X2cxBkQaWGu7vfSGIqcTnYe1eFjIg34K5PTRjw4TnGlx3J5SGcQ4IL271zQKiQbPRt22OvhxFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06d47ee94c586f1f4042d734e217f484c65199e7b4d859d92a1bdb18eb58a442","last_reissued_at":"2026-05-17T23:48:22.196196Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:22.196196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.11560","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":"2026-05-17T23:48:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPf3jw6xwYi1TtrkQoLKqBbnN4g1GtpoM7GnWAwDcMHX9GtP0Rcdab67s3xXMU4Wkq+T55tndHWr7L2NK0liAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:33:36.588720Z"},"content_sha256":"21e0262817c920c367e5251d41daedcfebc805fd06dcaccbb7f2f57835fcd53b","schema_version":"1.0","event_id":"sha256:21e0262817c920c367e5251d41daedcfebc805fd06dcaccbb7f2f57835fcd53b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:A3KH52KMLBXR6QCC242OEF7UQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spectral radius formula for Fourier-Stieltjes algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Maria Roginskaya, Przemys{\\l}aw Ohrysko","submitted_at":"2018-11-28T13:51:35Z","abstract_excerpt":"In this short note we first extend the validity of the spectral radius formula obtained in \\cite{ag} to Fourier--Stieltjes algebras. The second part is devoted to showing that for the measure algebra on any locally compact non-discrete Abelian group there are no non-trivial constraints between three quantities: the norm, the spectral radius and the supremum of the Fourier--Stieltjes transform even if we restrict our attention to measures with all convolution powers singular with respect to Haar measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11560","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":""},"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":"2026-05-17T23:48:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gr+5UgGnWxBZ48EsNZzDXVWXCZCZcSuebXekE2uSz0XEo+QhjZ1E+eeoRa/deoLYNCWp9lKfV8yQuWkZuZQHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:33:36.589612Z"},"content_sha256":"5b0e4695d848e59d9d839624167543807399992c220fa6e8956262e3e247d3ed","schema_version":"1.0","event_id":"sha256:5b0e4695d848e59d9d839624167543807399992c220fa6e8956262e3e247d3ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3KH52KMLBXR6QCC242OEF7UQT/bundle.json","state_url":"https://pith.science/pith/A3KH52KMLBXR6QCC242OEF7UQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3KH52KMLBXR6QCC242OEF7UQT/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":"2026-05-31T21:33:36Z","links":{"resolver":"https://pith.science/pith/A3KH52KMLBXR6QCC242OEF7UQT","bundle":"https://pith.science/pith/A3KH52KMLBXR6QCC242OEF7UQT/bundle.json","state":"https://pith.science/pith/A3KH52KMLBXR6QCC242OEF7UQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3KH52KMLBXR6QCC242OEF7UQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A3KH52KMLBXR6QCC242OEF7UQT","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":"debdaf2bd5cb31d837086359aa3858af867db3ce60bb52de46f900b2a647e8e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-28T13:51:35Z","title_canon_sha256":"3877689c93b3e7e5ed0575bb59a5025dc04bcd9ecf5f30168c15c6f82f879a3e"},"schema_version":"1.0","source":{"id":"1811.11560","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11560","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11560v3","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11560","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"A3KH52KMLBXR","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A3KH52KMLBXR6QCC","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A3KH52KM","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:5b0e4695d848e59d9d839624167543807399992c220fa6e8956262e3e247d3ed","target":"graph","created_at":"2026-05-17T23:48:22Z","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 short note we first extend the validity of the spectral radius formula obtained in \\cite{ag} to Fourier--Stieltjes algebras. The second part is devoted to showing that for the measure algebra on any locally compact non-discrete Abelian group there are no non-trivial constraints between three quantities: the norm, the spectral radius and the supremum of the Fourier--Stieltjes transform even if we restrict our attention to measures with all convolution powers singular with respect to Haar measure.","authors_text":"Maria Roginskaya, Przemys{\\l}aw Ohrysko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-28T13:51:35Z","title":"The spectral radius formula for Fourier-Stieltjes algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11560","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":"sha256:21e0262817c920c367e5251d41daedcfebc805fd06dcaccbb7f2f57835fcd53b","target":"record","created_at":"2026-05-17T23:48:22Z","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":"debdaf2bd5cb31d837086359aa3858af867db3ce60bb52de46f900b2a647e8e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-28T13:51:35Z","title_canon_sha256":"3877689c93b3e7e5ed0575bb59a5025dc04bcd9ecf5f30168c15c6f82f879a3e"},"schema_version":"1.0","source":{"id":"1811.11560","kind":"arxiv","version":3}},"canonical_sha256":"06d47ee94c586f1f4042d734e217f484c65199e7b4d859d92a1bdb18eb58a442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06d47ee94c586f1f4042d734e217f484c65199e7b4d859d92a1bdb18eb58a442","first_computed_at":"2026-05-17T23:48:22.196196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:22.196196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"clOMu00RsX+X2cxBkQaWGu7vfSGIqcTnYe1eFjIg34K5PTRjw4TnGlx3J5SGcQ4IL271zQKiQbPRt22OvhxFAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:22.196850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.11560","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21e0262817c920c367e5251d41daedcfebc805fd06dcaccbb7f2f57835fcd53b","sha256:5b0e4695d848e59d9d839624167543807399992c220fa6e8956262e3e247d3ed"],"state_sha256":"2dfe067925ec09444adf39028074ceb2fd9d8ab1b7defb9992e5542426c0706b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vul7cRsas+dghJiHzlb+cZaOxX998Hp51thhn+bITlVrvjMTOKlMQVqG/KVpwoSJ/8kCKL2W7G74haeXHDjpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:33:36.593699Z","bundle_sha256":"a824535aec71d2f57803994f796f5b0ae7705e21b459a84859eaea19d3170f59"}}