{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UQ7337IXM64VKE77LUMYRGKEQ3","short_pith_number":"pith:UQ7337IX","canonical_record":{"source":{"id":"1606.05964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-20T03:06:25Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"16f491125f6ff8235c589d4ffab6b0b340954ea31b2dd48122316ebf39d408b4","abstract_canon_sha256":"2054cbc7813d832e6428987fe7b678cf4d2473003a29bde4d5540967b811efb0"},"schema_version":"1.0"},"canonical_sha256":"a43fbdfd1767b95513ff5d1988994486f860fd500ee2d3438b8ec402ae02142d","source":{"kind":"arxiv","id":"1606.05964","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05964","created_at":"2026-05-18T01:12:15Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05964v1","created_at":"2026-05-18T01:12:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05964","created_at":"2026-05-18T01:12:15Z"},{"alias_kind":"pith_short_12","alias_value":"UQ7337IXM64V","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UQ7337IXM64VKE77","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UQ7337IX","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UQ7337IXM64VKE77LUMYRGKEQ3","target":"record","payload":{"canonical_record":{"source":{"id":"1606.05964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-20T03:06:25Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"16f491125f6ff8235c589d4ffab6b0b340954ea31b2dd48122316ebf39d408b4","abstract_canon_sha256":"2054cbc7813d832e6428987fe7b678cf4d2473003a29bde4d5540967b811efb0"},"schema_version":"1.0"},"canonical_sha256":"a43fbdfd1767b95513ff5d1988994486f860fd500ee2d3438b8ec402ae02142d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:15.680133Z","signature_b64":"LxPgvTJjMX1iPn6GaRpQtQrLGz8byJ+orOkEbLySDrrpcJ1EoMlq8UiMLkOvY8JwsnA4B9wqA2bl2NI2uioTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a43fbdfd1767b95513ff5d1988994486f860fd500ee2d3438b8ec402ae02142d","last_reissued_at":"2026-05-18T01:12:15.679772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:15.679772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.05964","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":"2026-05-18T01:12:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnXNtqsp1retjDCa43GJlp12RiYTS/xWWsXiBVJOcMokkMdD9c9KQfNWaK4oN6aPnsQ5hB0lDb0btMYDEC4MCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:26:01.035024Z"},"content_sha256":"bef01a0ffc4ba1479adf46032ee3c43332783a28aca95f05f0b4a868450fe66a","schema_version":"1.0","event_id":"sha256:bef01a0ffc4ba1479adf46032ee3c43332783a28aca95f05f0b4a868450fe66a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UQ7337IXM64VKE77LUMYRGKEQ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier algebras of hypergroups and central algebras on compact (quantum) groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Jason Crann, Mahmood Alaghmandan","submitted_at":"2016-06-20T03:06:25Z","abstract_excerpt":"This paper concerns the study of regular Fourier hypergroups through multipliers of their associated Fourier algebras. We establish hypergroup analogues of well-known characterizations of group amenability, introduce a notion of weak amenability for hypergroups, and show that every discrete commutative hypergroup is weakly amenable with constant 1. Using similar techniques, we provide a sufficient condition for amenability of hypergroup Fourier algebras, which, as an immediate application, answers one direction of a conjecture of Azimifard--Samei--Spronk [J. Funct. Anal. 256(5) 1544-1564, 2009"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05964","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":""},"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":"2026-05-18T01:12:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SEOXdQXhKQyqD43zoMKJ6fzLUAsiRwiM95Fbje0Vmrpesu4DtaIvtWSQzs0NeZHKbekSCeDVQM/IeE6MT0BEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:26:01.035387Z"},"content_sha256":"dc94183c0f569da4e6b75b85e6d837d64583d6eba98d590965876645fdf1dc2a","schema_version":"1.0","event_id":"sha256:dc94183c0f569da4e6b75b85e6d837d64583d6eba98d590965876645fdf1dc2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQ7337IXM64VKE77LUMYRGKEQ3/bundle.json","state_url":"https://pith.science/pith/UQ7337IXM64VKE77LUMYRGKEQ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQ7337IXM64VKE77LUMYRGKEQ3/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":"2026-06-23T15:26:01Z","links":{"resolver":"https://pith.science/pith/UQ7337IXM64VKE77LUMYRGKEQ3","bundle":"https://pith.science/pith/UQ7337IXM64VKE77LUMYRGKEQ3/bundle.json","state":"https://pith.science/pith/UQ7337IXM64VKE77LUMYRGKEQ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQ7337IXM64VKE77LUMYRGKEQ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UQ7337IXM64VKE77LUMYRGKEQ3","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":"2054cbc7813d832e6428987fe7b678cf4d2473003a29bde4d5540967b811efb0","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-20T03:06:25Z","title_canon_sha256":"16f491125f6ff8235c589d4ffab6b0b340954ea31b2dd48122316ebf39d408b4"},"schema_version":"1.0","source":{"id":"1606.05964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05964","created_at":"2026-05-18T01:12:15Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05964v1","created_at":"2026-05-18T01:12:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05964","created_at":"2026-05-18T01:12:15Z"},{"alias_kind":"pith_short_12","alias_value":"UQ7337IXM64V","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UQ7337IXM64VKE77","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UQ7337IX","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:dc94183c0f569da4e6b75b85e6d837d64583d6eba98d590965876645fdf1dc2a","target":"graph","created_at":"2026-05-18T01:12:15Z","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":"This paper concerns the study of regular Fourier hypergroups through multipliers of their associated Fourier algebras. We establish hypergroup analogues of well-known characterizations of group amenability, introduce a notion of weak amenability for hypergroups, and show that every discrete commutative hypergroup is weakly amenable with constant 1. Using similar techniques, we provide a sufficient condition for amenability of hypergroup Fourier algebras, which, as an immediate application, answers one direction of a conjecture of Azimifard--Samei--Spronk [J. Funct. Anal. 256(5) 1544-1564, 2009","authors_text":"Jason Crann, Mahmood Alaghmandan","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-20T03:06:25Z","title":"Fourier algebras of hypergroups and central algebras on compact (quantum) groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05964","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:bef01a0ffc4ba1479adf46032ee3c43332783a28aca95f05f0b4a868450fe66a","target":"record","created_at":"2026-05-18T01:12:15Z","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":"2054cbc7813d832e6428987fe7b678cf4d2473003a29bde4d5540967b811efb0","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-20T03:06:25Z","title_canon_sha256":"16f491125f6ff8235c589d4ffab6b0b340954ea31b2dd48122316ebf39d408b4"},"schema_version":"1.0","source":{"id":"1606.05964","kind":"arxiv","version":1}},"canonical_sha256":"a43fbdfd1767b95513ff5d1988994486f860fd500ee2d3438b8ec402ae02142d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a43fbdfd1767b95513ff5d1988994486f860fd500ee2d3438b8ec402ae02142d","first_computed_at":"2026-05-18T01:12:15.679772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:15.679772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LxPgvTJjMX1iPn6GaRpQtQrLGz8byJ+orOkEbLySDrrpcJ1EoMlq8UiMLkOvY8JwsnA4B9wqA2bl2NI2uioTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:15.680133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bef01a0ffc4ba1479adf46032ee3c43332783a28aca95f05f0b4a868450fe66a","sha256:dc94183c0f569da4e6b75b85e6d837d64583d6eba98d590965876645fdf1dc2a"],"state_sha256":"78477aa1ea0be0961776532712c8904ece9f5f9a5ee824b14126e25ce860826b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQau/Mv9Qao00X28nYg0B7GN+8gmw2B8P/4t6lm3SxYYO2T0kJ42cg1v3m7T9FpsLRc5dVVQ0Mj0MLh4V32wBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:26:01.037359Z","bundle_sha256":"8957563669d2ef0b47aac6dded277eb96d5a933e93effe96c5b6aab076cc54d8"}}