{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:7NDXWYAGVRF4K3VVNX3KHFBMCL","short_pith_number":"pith:7NDXWYAG","canonical_record":{"source":{"id":"math/0611833","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2006-11-27T17:40:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"af9564d07eeb2ea6a54a5d84c8f6393ec5ea6854b1144db6deefdc21fb30112e","abstract_canon_sha256":"7d305e3254834a551b4f532940f8aae42b3a373994bb0910088a9ec68d6a6123"},"schema_version":"1.0"},"canonical_sha256":"fb477b6006ac4bc56eb56df6a3942c12d02d24bba5212090a485f6c0fa54f393","source":{"kind":"arxiv","id":"math/0611833","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611833","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611833v3","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611833","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"7NDXWYAGVRF4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7NDXWYAGVRF4K3VV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7NDXWYAG","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:7NDXWYAGVRF4K3VVNX3KHFBMCL","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611833","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2006-11-27T17:40:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"af9564d07eeb2ea6a54a5d84c8f6393ec5ea6854b1144db6deefdc21fb30112e","abstract_canon_sha256":"7d305e3254834a551b4f532940f8aae42b3a373994bb0910088a9ec68d6a6123"},"schema_version":"1.0"},"canonical_sha256":"fb477b6006ac4bc56eb56df6a3942c12d02d24bba5212090a485f6c0fa54f393","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:41.708499Z","signature_b64":"j8FKN9tkVo5/ExClN3pZUvSZeseVVLQpPqVdbDJS3PHFwBT78RQ+T39+AdCiuo7UdiJzab3jCX+BBnB7Jr9lCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb477b6006ac4bc56eb56df6a3942c12d02d24bba5212090a485f6c0fa54f393","last_reissued_at":"2026-05-18T04:31:41.707879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:41.707879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611833","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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qjuKt8QOr5MR9IBHdKYY9+16Lo0AxWuupKuskhHOVEXEe15WJgJPm3CAJL5qlV3Wpg+xf/nzP31ij+IGx7tOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:21:15.412608Z"},"content_sha256":"615238bb036832aaba56e96c7d5bca9507952543c2d057519dc793c95d8b5894","schema_version":"1.0","event_id":"sha256:615238bb036832aaba56e96c7d5bca9507952543c2d057519dc793c95d8b5894"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:7NDXWYAGVRF4K3VVNX3KHFBMCL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-Operator Spaces and Fig\\'a-Talamanca-Herz Algebras","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Matthew Daws","submitted_at":"2006-11-27T17:40:20Z","abstract_excerpt":"We study a generalisation of operator spaces modelled on $L_p$ spaces, instead of Hilbert spaces, using the notion of $p$-complete boundedness, as studied by Pisier and Le Merdy. We show that the Fig\\'a-Talamanca-Herz Algebras $A_p(G)$ becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact group $G$. We thus argue that we have presented a generalised of the use of operator spaces in studying the Fourier algebra $A(G)$, in the spirit of Ruan. Finally, we show that various notions o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611833","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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/RYAdjtRD1qYuvjn627aAtXDAwAvafHGAUTDlfpN8bNbyhTzmj0ZFQyWcY1TwcuotBcsxB43t8WbKMWHJplBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:21:15.412978Z"},"content_sha256":"063383e8e95094d8d5bb5a6016a01fee60674a6ea2c16c645849a3fc7f8bb85d","schema_version":"1.0","event_id":"sha256:063383e8e95094d8d5bb5a6016a01fee60674a6ea2c16c645849a3fc7f8bb85d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7NDXWYAGVRF4K3VVNX3KHFBMCL/bundle.json","state_url":"https://pith.science/pith/7NDXWYAGVRF4K3VVNX3KHFBMCL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7NDXWYAGVRF4K3VVNX3KHFBMCL/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":"2026-06-22T22:21:15Z","links":{"resolver":"https://pith.science/pith/7NDXWYAGVRF4K3VVNX3KHFBMCL","bundle":"https://pith.science/pith/7NDXWYAGVRF4K3VVNX3KHFBMCL/bundle.json","state":"https://pith.science/pith/7NDXWYAGVRF4K3VVNX3KHFBMCL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7NDXWYAGVRF4K3VVNX3KHFBMCL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:7NDXWYAGVRF4K3VVNX3KHFBMCL","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":"7d305e3254834a551b4f532940f8aae42b3a373994bb0910088a9ec68d6a6123","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.OA","submitted_at":"2006-11-27T17:40:20Z","title_canon_sha256":"af9564d07eeb2ea6a54a5d84c8f6393ec5ea6854b1144db6deefdc21fb30112e"},"schema_version":"1.0","source":{"id":"math/0611833","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611833","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611833v3","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611833","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"7NDXWYAGVRF4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7NDXWYAGVRF4K3VV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7NDXWYAG","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:063383e8e95094d8d5bb5a6016a01fee60674a6ea2c16c645849a3fc7f8bb85d","target":"graph","created_at":"2026-05-18T04:31:41Z","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 a generalisation of operator spaces modelled on $L_p$ spaces, instead of Hilbert spaces, using the notion of $p$-complete boundedness, as studied by Pisier and Le Merdy. We show that the Fig\\'a-Talamanca-Herz Algebras $A_p(G)$ becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact group $G$. We thus argue that we have presented a generalised of the use of operator spaces in studying the Fourier algebra $A(G)$, in the spirit of Ruan. Finally, we show that various notions o","authors_text":"Matthew Daws","cross_cats":["math.GR"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2006-11-27T17:40:20Z","title":"$p$-Operator Spaces and Fig\\'a-Talamanca-Herz Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611833","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":"sha256:615238bb036832aaba56e96c7d5bca9507952543c2d057519dc793c95d8b5894","target":"record","created_at":"2026-05-18T04:31:41Z","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":"7d305e3254834a551b4f532940f8aae42b3a373994bb0910088a9ec68d6a6123","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.OA","submitted_at":"2006-11-27T17:40:20Z","title_canon_sha256":"af9564d07eeb2ea6a54a5d84c8f6393ec5ea6854b1144db6deefdc21fb30112e"},"schema_version":"1.0","source":{"id":"math/0611833","kind":"arxiv","version":3}},"canonical_sha256":"fb477b6006ac4bc56eb56df6a3942c12d02d24bba5212090a485f6c0fa54f393","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb477b6006ac4bc56eb56df6a3942c12d02d24bba5212090a485f6c0fa54f393","first_computed_at":"2026-05-18T04:31:41.707879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:41.707879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j8FKN9tkVo5/ExClN3pZUvSZeseVVLQpPqVdbDJS3PHFwBT78RQ+T39+AdCiuo7UdiJzab3jCX+BBnB7Jr9lCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:41.708499Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611833","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:615238bb036832aaba56e96c7d5bca9507952543c2d057519dc793c95d8b5894","sha256:063383e8e95094d8d5bb5a6016a01fee60674a6ea2c16c645849a3fc7f8bb85d"],"state_sha256":"72c9cd9e9a9dcab7c3de1bf170a0f36047289f2f6ad768586f760055b52a90f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4JY5KVnmnCyD0TfC0wRmsea2yFT54eYMwA9HGwrSDixzWjVAV4fh52gRm6UkI71L7TxtmFneiTuBWeWGmKpvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:21:15.414968Z","bundle_sha256":"a655c50503f19749e9b5d09ce39ddc23fa883028c3d22a5564b427ec8fbdeda1"}}