{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:LJ4YRKH5PWMQ6YQFOZEB4RZRP4","short_pith_number":"pith:LJ4YRKH5","canonical_record":{"source":{"id":"1004.0215","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-01T19:32:12Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b808a9b4aa2e73c44d1f868d0c1f178d3891f8f6bba797599168990b7b4f6fdb","abstract_canon_sha256":"eb08920434026fb153263a4ff6f4d489d95f35f0ec5868dee92aa094e9eb9a2b"},"schema_version":"1.0"},"canonical_sha256":"5a7988a8fd7d990f620576481e47317f3731234b52e5f4bf307bbf0c79efe3d8","source":{"kind":"arxiv","id":"1004.0215","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0215","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0215v3","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0215","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"LJ4YRKH5PWMQ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LJ4YRKH5PWMQ6YQF","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LJ4YRKH5","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:LJ4YRKH5PWMQ6YQFOZEB4RZRP4","target":"record","payload":{"canonical_record":{"source":{"id":"1004.0215","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-01T19:32:12Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b808a9b4aa2e73c44d1f868d0c1f178d3891f8f6bba797599168990b7b4f6fdb","abstract_canon_sha256":"eb08920434026fb153263a4ff6f4d489d95f35f0ec5868dee92aa094e9eb9a2b"},"schema_version":"1.0"},"canonical_sha256":"5a7988a8fd7d990f620576481e47317f3731234b52e5f4bf307bbf0c79efe3d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:02.294460Z","signature_b64":"imJWQW6YASMx3rfR8BFKwwB724PhJgnHxC9OnCTlAbjDHRS8LjR820uXpg+pqGkMMCqVWiVt7aXIKBKKCQSvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a7988a8fd7d990f620576481e47317f3731234b52e5f4bf307bbf0c79efe3d8","last_reissued_at":"2026-05-18T02:58:02.293910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:02.293910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.0215","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":"2026-05-18T02:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EwL2gQOk9kDHpF5/lo4u0rTKZz1baNykyyvNJpTP3pJdf3VmREuYfI/cBuaX+er27bUp89BrpUWn43oMfrDgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:47:41.164342Z"},"content_sha256":"d250d9278724ff4bc44121c0c9b50c628cce9f02c666962505e5652b553642fb","schema_version":"1.0","event_id":"sha256:d250d9278724ff4bc44121c0c9b50c628cce9f02c666962505e5652b553642fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:LJ4YRKH5PWMQ6YQFOZEB4RZRP4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multipliers of locally compact quantum groups via Hilbert C$^*$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Matthew Daws","submitted_at":"2010-04-01T19:32:12Z","abstract_excerpt":"A result of Gilbert shows that every completely bounded multiplier $f$ of the Fourier algebra $A(G)$ arises from a pair of bounded continuous maps $\\alpha,\\beta:G \\rightarrow K$, where $K$ is a Hilbert space, and $f(s^{-1}t) = (\\beta(t)|\\alpha(s))$ for all $s,t\\in G$. We recast this in terms of adjointable operators acting between certain Hilbert C$^*$-modules, and show that an analogous construction works for completely bounded left multipliers of a locally compact quantum group. We find various ways to deal with right multipliers: one of these involves looking at the opposite quantum group, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0215","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":"2026-05-18T02:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1X1bqcTdMGlpWM65P9DKVkVWHZC1Zn9r3dbUc0zZaWOjOVShSqxI0ABBuU3k5mBwjgIwWxrBmofGU0MCZ1jzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:47:41.164699Z"},"content_sha256":"ec9bd77fb2659a92449f7d3cdd491c76de6d8376e90c174b0c5e4684696771c8","schema_version":"1.0","event_id":"sha256:ec9bd77fb2659a92449f7d3cdd491c76de6d8376e90c174b0c5e4684696771c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJ4YRKH5PWMQ6YQFOZEB4RZRP4/bundle.json","state_url":"https://pith.science/pith/LJ4YRKH5PWMQ6YQFOZEB4RZRP4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJ4YRKH5PWMQ6YQFOZEB4RZRP4/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":"2026-06-22T12:47:41Z","links":{"resolver":"https://pith.science/pith/LJ4YRKH5PWMQ6YQFOZEB4RZRP4","bundle":"https://pith.science/pith/LJ4YRKH5PWMQ6YQFOZEB4RZRP4/bundle.json","state":"https://pith.science/pith/LJ4YRKH5PWMQ6YQFOZEB4RZRP4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJ4YRKH5PWMQ6YQFOZEB4RZRP4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LJ4YRKH5PWMQ6YQFOZEB4RZRP4","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":"eb08920434026fb153263a4ff6f4d489d95f35f0ec5868dee92aa094e9eb9a2b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-01T19:32:12Z","title_canon_sha256":"b808a9b4aa2e73c44d1f868d0c1f178d3891f8f6bba797599168990b7b4f6fdb"},"schema_version":"1.0","source":{"id":"1004.0215","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0215","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0215v3","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0215","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"LJ4YRKH5PWMQ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LJ4YRKH5PWMQ6YQF","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LJ4YRKH5","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:ec9bd77fb2659a92449f7d3cdd491c76de6d8376e90c174b0c5e4684696771c8","target":"graph","created_at":"2026-05-18T02:58:02Z","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":"A result of Gilbert shows that every completely bounded multiplier $f$ of the Fourier algebra $A(G)$ arises from a pair of bounded continuous maps $\\alpha,\\beta:G \\rightarrow K$, where $K$ is a Hilbert space, and $f(s^{-1}t) = (\\beta(t)|\\alpha(s))$ for all $s,t\\in G$. We recast this in terms of adjointable operators acting between certain Hilbert C$^*$-modules, and show that an analogous construction works for completely bounded left multipliers of a locally compact quantum group. We find various ways to deal with right multipliers: one of these involves looking at the opposite quantum group, ","authors_text":"Matthew Daws","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-01T19:32:12Z","title":"Multipliers of locally compact quantum groups via Hilbert C$^*$-modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0215","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:d250d9278724ff4bc44121c0c9b50c628cce9f02c666962505e5652b553642fb","target":"record","created_at":"2026-05-18T02:58:02Z","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":"eb08920434026fb153263a4ff6f4d489d95f35f0ec5868dee92aa094e9eb9a2b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-01T19:32:12Z","title_canon_sha256":"b808a9b4aa2e73c44d1f868d0c1f178d3891f8f6bba797599168990b7b4f6fdb"},"schema_version":"1.0","source":{"id":"1004.0215","kind":"arxiv","version":3}},"canonical_sha256":"5a7988a8fd7d990f620576481e47317f3731234b52e5f4bf307bbf0c79efe3d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a7988a8fd7d990f620576481e47317f3731234b52e5f4bf307bbf0c79efe3d8","first_computed_at":"2026-05-18T02:58:02.293910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:02.293910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"imJWQW6YASMx3rfR8BFKwwB724PhJgnHxC9OnCTlAbjDHRS8LjR820uXpg+pqGkMMCqVWiVt7aXIKBKKCQSvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:02.294460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0215","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d250d9278724ff4bc44121c0c9b50c628cce9f02c666962505e5652b553642fb","sha256:ec9bd77fb2659a92449f7d3cdd491c76de6d8376e90c174b0c5e4684696771c8"],"state_sha256":"b9822f7449fb552941dcd24e32d4e0cfb826ec058379d07238ce2f6f281aec24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CR9fjm2URPhFv/KUvO5KFfth9fxVnYpWr1VPTAAaNo8f6+ujsjTNTqG3qdcjutVelGgzIWE7vE6gqq0ot8DzAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:47:41.166749Z","bundle_sha256":"c6b058a857194e42eaf7fb712ffce105a5f788bb5a0316b91d84e2b2cff1a30b"}}