{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BVWBOYON7C5KKDWIP6PWOLSQ54","short_pith_number":"pith:BVWBOYON","canonical_record":{"source":{"id":"1411.2336","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-10T06:18:02Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"e85ae9f3d3460bf43af65932c08a4dab924fba59c4b6bc61c26e021d0f7348ae","abstract_canon_sha256":"77ecf987ababb854e682a63399a02850f248873b6bbe57ee7d9ce45d2d25c4e9"},"schema_version":"1.0"},"canonical_sha256":"0d6c1761cdf8baa50ec87f9f672e50ef1620ea3b4775a9f74d06b3d43f1228a8","source":{"kind":"arxiv","id":"1411.2336","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2336","created_at":"2026-05-18T02:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2336v2","created_at":"2026-05-18T02:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2336","created_at":"2026-05-18T02:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"BVWBOYON7C5K","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BVWBOYON7C5KKDWI","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BVWBOYON","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BVWBOYON7C5KKDWIP6PWOLSQ54","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2336","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-10T06:18:02Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"e85ae9f3d3460bf43af65932c08a4dab924fba59c4b6bc61c26e021d0f7348ae","abstract_canon_sha256":"77ecf987ababb854e682a63399a02850f248873b6bbe57ee7d9ce45d2d25c4e9"},"schema_version":"1.0"},"canonical_sha256":"0d6c1761cdf8baa50ec87f9f672e50ef1620ea3b4775a9f74d06b3d43f1228a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:58.690757Z","signature_b64":"olljEXfVRo3rJwPK5xNssKfDyhGaj0PEpGjUSmoQXmSROXUaBy7IDq1E/VE4cB5wMILkgeZSv2HeZR6LAfF4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d6c1761cdf8baa50ec87f9f672e50ef1620ea3b4775a9f74d06b3d43f1228a8","last_reissued_at":"2026-05-18T02:26:58.690392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:58.690392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2336","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":"2026-05-18T02:26:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+vIUCuLMq+Gx9vbUpfJPvsHt6t1LYYXi6IkTO7pkMgAmeaBf4jKOe3ehAQJot7spHsk3LhcqHfhzsFLLFugVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:19:26.494805Z"},"content_sha256":"5b3f4e3d10261cdcc84dce4562a3cf212982ba7d6c2813bfb48b3f09f4d01bcf","schema_version":"1.0","event_id":"sha256:5b3f4e3d10261cdcc84dce4562a3cf212982ba7d6c2813bfb48b3f09f4d01bcf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BVWBOYON7C5KKDWIP6PWOLSQ54","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-Fourier algebras on compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Ebrahim Samei, Hun Hee Lee, Nico Spronk","submitted_at":"2014-11-10T06:18:02Z","abstract_excerpt":"Let $G$ be a compact group. For $1\\leq p\\leq\\infty$ we introduce a class of Banach function algebras $\\mathrm{A}^p(G)$ on $G$ which are the Fourier algebras in the case $p=1$, and for $p=2$ are certain algebras discovered in \\cite{forrestss1}. In the case $p\\not=2$ we find that $\\mathrm{A}^p(G)\\cong \\mathrm{A}^p(H)$ if and only if $G$ and $H$ are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call $p$-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and represen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2336","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":"2026-05-18T02:26:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NbAXn34Kk5pW8etDfdMy/oNck44Urg0oDh3IpeGu8YTd4bnrrF6OZyNsLBxmsAQj8PkFPQEaHQ2DopUbySNzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:19:26.495503Z"},"content_sha256":"9901a434c4fcaace54921c05a83668cae0a94bcc812dabf3d1a6306429cf00e9","schema_version":"1.0","event_id":"sha256:9901a434c4fcaace54921c05a83668cae0a94bcc812dabf3d1a6306429cf00e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVWBOYON7C5KKDWIP6PWOLSQ54/bundle.json","state_url":"https://pith.science/pith/BVWBOYON7C5KKDWIP6PWOLSQ54/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVWBOYON7C5KKDWIP6PWOLSQ54/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":"2026-05-27T11:19:26Z","links":{"resolver":"https://pith.science/pith/BVWBOYON7C5KKDWIP6PWOLSQ54","bundle":"https://pith.science/pith/BVWBOYON7C5KKDWIP6PWOLSQ54/bundle.json","state":"https://pith.science/pith/BVWBOYON7C5KKDWIP6PWOLSQ54/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVWBOYON7C5KKDWIP6PWOLSQ54/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BVWBOYON7C5KKDWIP6PWOLSQ54","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":"77ecf987ababb854e682a63399a02850f248873b6bbe57ee7d9ce45d2d25c4e9","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-10T06:18:02Z","title_canon_sha256":"e85ae9f3d3460bf43af65932c08a4dab924fba59c4b6bc61c26e021d0f7348ae"},"schema_version":"1.0","source":{"id":"1411.2336","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2336","created_at":"2026-05-18T02:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2336v2","created_at":"2026-05-18T02:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2336","created_at":"2026-05-18T02:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"BVWBOYON7C5K","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BVWBOYON7C5KKDWI","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BVWBOYON","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:9901a434c4fcaace54921c05a83668cae0a94bcc812dabf3d1a6306429cf00e9","target":"graph","created_at":"2026-05-18T02:26:58Z","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"},"paper":{"abstract_excerpt":"Let $G$ be a compact group. For $1\\leq p\\leq\\infty$ we introduce a class of Banach function algebras $\\mathrm{A}^p(G)$ on $G$ which are the Fourier algebras in the case $p=1$, and for $p=2$ are certain algebras discovered in \\cite{forrestss1}. In the case $p\\not=2$ we find that $\\mathrm{A}^p(G)\\cong \\mathrm{A}^p(H)$ if and only if $G$ and $H$ are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call $p$-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and represen","authors_text":"Ebrahim Samei, Hun Hee Lee, Nico Spronk","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-10T06:18:02Z","title":"$p$-Fourier algebras on compact groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2336","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":"sha256:5b3f4e3d10261cdcc84dce4562a3cf212982ba7d6c2813bfb48b3f09f4d01bcf","target":"record","created_at":"2026-05-18T02:26:58Z","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":"77ecf987ababb854e682a63399a02850f248873b6bbe57ee7d9ce45d2d25c4e9","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-10T06:18:02Z","title_canon_sha256":"e85ae9f3d3460bf43af65932c08a4dab924fba59c4b6bc61c26e021d0f7348ae"},"schema_version":"1.0","source":{"id":"1411.2336","kind":"arxiv","version":2}},"canonical_sha256":"0d6c1761cdf8baa50ec87f9f672e50ef1620ea3b4775a9f74d06b3d43f1228a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d6c1761cdf8baa50ec87f9f672e50ef1620ea3b4775a9f74d06b3d43f1228a8","first_computed_at":"2026-05-18T02:26:58.690392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:58.690392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"olljEXfVRo3rJwPK5xNssKfDyhGaj0PEpGjUSmoQXmSROXUaBy7IDq1E/VE4cB5wMILkgeZSv2HeZR6LAfF4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:58.690757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2336","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b3f4e3d10261cdcc84dce4562a3cf212982ba7d6c2813bfb48b3f09f4d01bcf","sha256:9901a434c4fcaace54921c05a83668cae0a94bcc812dabf3d1a6306429cf00e9"],"state_sha256":"e4a7bc7a3e45ea25c90d9cf75049a9935cbf930dc08ef8e6123730845f1d32d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2xMkEuV8pPUu9c1/nxX/3OkAEc6HXQWcGvV6cGKqFCC4epUTOIIx1VeFN8HCVzVxLCK2xJuuWQ6cP7j/4BL5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:19:26.499232Z","bundle_sha256":"57dd24088cdab95622d5fb9ace5967f5f290de6887ef2b14a52bbabfe92f9db8"}}