{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JDZK7UDPWYZHPATGJGJQOE3MY4","short_pith_number":"pith:JDZK7UDP","canonical_record":{"source":{"id":"1809.09385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T09:51:53Z","cross_cats_sorted":["math.RT","math.SP"],"title_canon_sha256":"d42b77bdbf1e5f13608691e650df41c176b184866a724b31fdecc791fe7797f1","abstract_canon_sha256":"bc6bf72933d696ea4374f4709c8a2f2b243cdd6a2e436c7f286d20b71ba5a728"},"schema_version":"1.0"},"canonical_sha256":"48f2afd06fb632778266499307136cc73de5405effec48bafcdad27eb6d278d3","source":{"kind":"arxiv","id":"1809.09385","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09385","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09385v1","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09385","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"JDZK7UDPWYZH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JDZK7UDPWYZHPATG","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JDZK7UDP","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JDZK7UDPWYZHPATGJGJQOE3MY4","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T09:51:53Z","cross_cats_sorted":["math.RT","math.SP"],"title_canon_sha256":"d42b77bdbf1e5f13608691e650df41c176b184866a724b31fdecc791fe7797f1","abstract_canon_sha256":"bc6bf72933d696ea4374f4709c8a2f2b243cdd6a2e436c7f286d20b71ba5a728"},"schema_version":"1.0"},"canonical_sha256":"48f2afd06fb632778266499307136cc73de5405effec48bafcdad27eb6d278d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:53.520522Z","signature_b64":"q4qViAA/otD+avGFGKrU9MLMxwlrOajdNHdhx5Vvo0ch35O0DGTjVKhgtKeUWXzxUcMWoDlcrlcNxNbHkQORDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48f2afd06fb632778266499307136cc73de5405effec48bafcdad27eb6d278d3","last_reissued_at":"2026-05-18T00:04:53.519807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:53.519807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09385","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":"2026-05-18T00:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bEnXYca6Q8h1KlCu2hMlocSnZ/pfM20NWR/yIcbB+5tTC7HlcFrpLKuOxJq3ghnhyM6NB0MT0DNkpDagm4mqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:15:56.915253Z"},"content_sha256":"c0579635d222b722f2fec979dd550fed85f4e0b762d4f837e730afc5f93761ae","schema_version":"1.0","event_id":"sha256:c0579635d222b722f2fec979dd550fed85f4e0b762d4f837e730afc5f93761ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JDZK7UDPWYZHPATGJGJQOE3MY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral multipliers for functions of fixed $K$-type on $L^p(SL(2,\\mathbb{R}))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SP"],"primary_cat":"math.FA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Fulvio Ricci","submitted_at":"2018-09-25T09:51:53Z","abstract_excerpt":"We prove an $L^p$ spectral multiplier theorem for functions of the $K$-invariant sublaplacian $L$ acting on the space of functions of fixed $K$-type on the group $SL(2,\\mathbb{R}).$ As an application we compute the joint $L^p(SL(2,\\mathbb{R}))$ spectrum of $L$ and the derivative along $K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09385","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":"2026-05-18T00:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrgk3C+ZC6JA7sL1AnPwvRsZCCoZE7Ss++k9QA4n/4Agu6FhrmHpcPPUnytNY40bAJ/f2N5ghSWGYpRSbCWCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:15:56.915627Z"},"content_sha256":"62312fcc34df49b90ff490913aee87f217d1b84ec44f940b70256104f6023c9d","schema_version":"1.0","event_id":"sha256:62312fcc34df49b90ff490913aee87f217d1b84ec44f940b70256104f6023c9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDZK7UDPWYZHPATGJGJQOE3MY4/bundle.json","state_url":"https://pith.science/pith/JDZK7UDPWYZHPATGJGJQOE3MY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDZK7UDPWYZHPATGJGJQOE3MY4/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":"2026-06-03T15:15:56Z","links":{"resolver":"https://pith.science/pith/JDZK7UDPWYZHPATGJGJQOE3MY4","bundle":"https://pith.science/pith/JDZK7UDPWYZHPATGJGJQOE3MY4/bundle.json","state":"https://pith.science/pith/JDZK7UDPWYZHPATGJGJQOE3MY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDZK7UDPWYZHPATGJGJQOE3MY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JDZK7UDPWYZHPATGJGJQOE3MY4","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":"bc6bf72933d696ea4374f4709c8a2f2b243cdd6a2e436c7f286d20b71ba5a728","cross_cats_sorted":["math.RT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T09:51:53Z","title_canon_sha256":"d42b77bdbf1e5f13608691e650df41c176b184866a724b31fdecc791fe7797f1"},"schema_version":"1.0","source":{"id":"1809.09385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09385","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09385v1","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09385","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"JDZK7UDPWYZH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JDZK7UDPWYZHPATG","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JDZK7UDP","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:62312fcc34df49b90ff490913aee87f217d1b84ec44f940b70256104f6023c9d","target":"graph","created_at":"2026-05-18T00:04:53Z","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 prove an $L^p$ spectral multiplier theorem for functions of the $K$-invariant sublaplacian $L$ acting on the space of functions of fixed $K$-type on the group $SL(2,\\mathbb{R}).$ As an application we compute the joint $L^p(SL(2,\\mathbb{R}))$ spectrum of $L$ and the derivative along $K$.","authors_text":"B{\\l}a\\.zej Wr\\'obel, Fulvio Ricci","cross_cats":["math.RT","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T09:51:53Z","title":"Spectral multipliers for functions of fixed $K$-type on $L^p(SL(2,\\mathbb{R}))$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09385","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:c0579635d222b722f2fec979dd550fed85f4e0b762d4f837e730afc5f93761ae","target":"record","created_at":"2026-05-18T00:04:53Z","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":"bc6bf72933d696ea4374f4709c8a2f2b243cdd6a2e436c7f286d20b71ba5a728","cross_cats_sorted":["math.RT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T09:51:53Z","title_canon_sha256":"d42b77bdbf1e5f13608691e650df41c176b184866a724b31fdecc791fe7797f1"},"schema_version":"1.0","source":{"id":"1809.09385","kind":"arxiv","version":1}},"canonical_sha256":"48f2afd06fb632778266499307136cc73de5405effec48bafcdad27eb6d278d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48f2afd06fb632778266499307136cc73de5405effec48bafcdad27eb6d278d3","first_computed_at":"2026-05-18T00:04:53.519807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:53.519807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q4qViAA/otD+avGFGKrU9MLMxwlrOajdNHdhx5Vvo0ch35O0DGTjVKhgtKeUWXzxUcMWoDlcrlcNxNbHkQORDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:53.520522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0579635d222b722f2fec979dd550fed85f4e0b762d4f837e730afc5f93761ae","sha256:62312fcc34df49b90ff490913aee87f217d1b84ec44f940b70256104f6023c9d"],"state_sha256":"bff6d493c4585b0d2f2092de80884cd79eac4736af17d048129beb858adec12d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3qnCpGv/JXX/s0/Ipx01CFHYxtS1F/NXYRXdCKQZwa54CzFdCNTb/ZHetF8TyQVrOn3YIU97xsRFuefbmBrDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:15:56.917765Z","bundle_sha256":"8ca164635298b4f5d032b9712c30f5a7ad0359be3b32a054e99b0f292baab3f6"}}