{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:F5Y7E3SBMVANHCD7PAXGH3VTC6","short_pith_number":"pith:F5Y7E3SB","canonical_record":{"source":{"id":"1808.03805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-11T13:54:57Z","cross_cats_sorted":[],"title_canon_sha256":"98d260d0bc8c9f906092010bcb241f1b8ab4114da55c7091e7b305a1a98cb771","abstract_canon_sha256":"700e87fd2f1c537df17925d5d2e9a2638da28914b9be580253b4a52c2e16b6be"},"schema_version":"1.0"},"canonical_sha256":"2f71f26e416540d3887f782e63eeb3178242e2ae7cfd4a01239f4b174abf0bd9","source":{"kind":"arxiv","id":"1808.03805","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03805","created_at":"2026-05-18T00:08:19Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03805v1","created_at":"2026-05-18T00:08:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03805","created_at":"2026-05-18T00:08:19Z"},{"alias_kind":"pith_short_12","alias_value":"F5Y7E3SBMVAN","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F5Y7E3SBMVANHCD7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F5Y7E3SB","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:F5Y7E3SBMVANHCD7PAXGH3VTC6","target":"record","payload":{"canonical_record":{"source":{"id":"1808.03805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-11T13:54:57Z","cross_cats_sorted":[],"title_canon_sha256":"98d260d0bc8c9f906092010bcb241f1b8ab4114da55c7091e7b305a1a98cb771","abstract_canon_sha256":"700e87fd2f1c537df17925d5d2e9a2638da28914b9be580253b4a52c2e16b6be"},"schema_version":"1.0"},"canonical_sha256":"2f71f26e416540d3887f782e63eeb3178242e2ae7cfd4a01239f4b174abf0bd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:19.655006Z","signature_b64":"Ri5Dn7e63PS0I1d6+zB0fo7nzSwU4b9VwD0iwEEfBw6kzJoThleqN0NTAHHB2O/GaBF9T+Nl6wjOGs2AV0++DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f71f26e416540d3887f782e63eeb3178242e2ae7cfd4a01239f4b174abf0bd9","last_reissued_at":"2026-05-18T00:08:19.654382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:19.654382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.03805","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":"2026-05-18T00:08:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rzXcwHtg4HpgYW3HpM62/jWwtV7rfxgnJt49y9Hh6rf3JSmBSpcG676IZhCV1w8ezR6YkFDfQQLG4EUzxfqFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:24:52.630061Z"},"content_sha256":"67aa0aa190f8251fcaf9b449522220e19b5e7a5e5a3285bf588c61f35d04a96b","schema_version":"1.0","event_id":"sha256:67aa0aa190f8251fcaf9b449522220e19b5e7a5e5a3285bf588c61f35d04a96b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:F5Y7E3SBMVANHCD7PAXGH3VTC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on weak amenability of hypergroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mahmood Alaghmandan","submitted_at":"2018-08-11T13:54:57Z","abstract_excerpt":"We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the Cowling-Haagerup constant 1. As a corollary, we answer an open question of Eymard on Jacobi hypergroups. We also characterize the existence of bounded approximate identities for the hypergroup Fourier algebras of ultraspherical hypergroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03805","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":"2026-05-18T00:08:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PffJ/9pLKBL/LLGR2vHBdQeYGVCRF0jqSU/LNQ89OLAOw/adeUHh+EAmlj2V2JKqWdgpU4Mfhm0jlw088B0DAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:24:52.630757Z"},"content_sha256":"8a17d0f22da5c2c6443babdab152856cf38dca8213cbba8a696159bce3bffe33","schema_version":"1.0","event_id":"sha256:8a17d0f22da5c2c6443babdab152856cf38dca8213cbba8a696159bce3bffe33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5Y7E3SBMVANHCD7PAXGH3VTC6/bundle.json","state_url":"https://pith.science/pith/F5Y7E3SBMVANHCD7PAXGH3VTC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5Y7E3SBMVANHCD7PAXGH3VTC6/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":"2026-05-29T18:24:52Z","links":{"resolver":"https://pith.science/pith/F5Y7E3SBMVANHCD7PAXGH3VTC6","bundle":"https://pith.science/pith/F5Y7E3SBMVANHCD7PAXGH3VTC6/bundle.json","state":"https://pith.science/pith/F5Y7E3SBMVANHCD7PAXGH3VTC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5Y7E3SBMVANHCD7PAXGH3VTC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F5Y7E3SBMVANHCD7PAXGH3VTC6","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":"700e87fd2f1c537df17925d5d2e9a2638da28914b9be580253b4a52c2e16b6be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-11T13:54:57Z","title_canon_sha256":"98d260d0bc8c9f906092010bcb241f1b8ab4114da55c7091e7b305a1a98cb771"},"schema_version":"1.0","source":{"id":"1808.03805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03805","created_at":"2026-05-18T00:08:19Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03805v1","created_at":"2026-05-18T00:08:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03805","created_at":"2026-05-18T00:08:19Z"},{"alias_kind":"pith_short_12","alias_value":"F5Y7E3SBMVAN","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F5Y7E3SBMVANHCD7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F5Y7E3SB","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:8a17d0f22da5c2c6443babdab152856cf38dca8213cbba8a696159bce3bffe33","target":"graph","created_at":"2026-05-18T00:08:19Z","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":"We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the Cowling-Haagerup constant 1. As a corollary, we answer an open question of Eymard on Jacobi hypergroups. We also characterize the existence of bounded approximate identities for the hypergroup Fourier algebras of ultraspherical hypergroups.","authors_text":"Mahmood Alaghmandan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-11T13:54:57Z","title":"Remarks on weak amenability of hypergroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03805","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":"sha256:67aa0aa190f8251fcaf9b449522220e19b5e7a5e5a3285bf588c61f35d04a96b","target":"record","created_at":"2026-05-18T00:08:19Z","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":"700e87fd2f1c537df17925d5d2e9a2638da28914b9be580253b4a52c2e16b6be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-11T13:54:57Z","title_canon_sha256":"98d260d0bc8c9f906092010bcb241f1b8ab4114da55c7091e7b305a1a98cb771"},"schema_version":"1.0","source":{"id":"1808.03805","kind":"arxiv","version":1}},"canonical_sha256":"2f71f26e416540d3887f782e63eeb3178242e2ae7cfd4a01239f4b174abf0bd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f71f26e416540d3887f782e63eeb3178242e2ae7cfd4a01239f4b174abf0bd9","first_computed_at":"2026-05-18T00:08:19.654382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:19.654382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ri5Dn7e63PS0I1d6+zB0fo7nzSwU4b9VwD0iwEEfBw6kzJoThleqN0NTAHHB2O/GaBF9T+Nl6wjOGs2AV0++DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:19.655006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67aa0aa190f8251fcaf9b449522220e19b5e7a5e5a3285bf588c61f35d04a96b","sha256:8a17d0f22da5c2c6443babdab152856cf38dca8213cbba8a696159bce3bffe33"],"state_sha256":"ce8d878ad7d56eb8648f52502613c57de51aaa4da513a31da00f9c7c1aa7fb62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zoEwcq0ZD1ZYMT97N0gYVcPFABXgifC1oqLpJe9JPSJ0wwaRx3WU5ZT711yR9Kw5JPxHRAx2V+dt8WWkm5GaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:24:52.634770Z","bundle_sha256":"99d393628381b465a268b89e11d0b7adb132b77a3b17ec3788bbfe477f86ee3e"}}