{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FDBMX4V2SFPCVJNC6L7LUKCQYL","short_pith_number":"pith:FDBMX4V2","canonical_record":{"source":{"id":"1102.3988","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-02-19T13:07:01Z","cross_cats_sorted":["math.AP","math.RT"],"title_canon_sha256":"26ac8605a525c448e89acbe8251c00f8e05b32f4c61df718c9ebe959cb0d7724","abstract_canon_sha256":"731f0bebaabb616662ef7183ee3596d0b4f74629b4c4e3f300b7fd25e4a3a00d"},"schema_version":"1.0"},"canonical_sha256":"28c2cbf2ba915e2aa5a2f2feba2850c2fb62193bf57f588f0a8be32176e2f606","source":{"kind":"arxiv","id":"1102.3988","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3988","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3988v3","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3988","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"FDBMX4V2SFPC","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FDBMX4V2SFPCVJNC","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FDBMX4V2","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FDBMX4V2SFPCVJNC6L7LUKCQYL","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3988","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-02-19T13:07:01Z","cross_cats_sorted":["math.AP","math.RT"],"title_canon_sha256":"26ac8605a525c448e89acbe8251c00f8e05b32f4c61df718c9ebe959cb0d7724","abstract_canon_sha256":"731f0bebaabb616662ef7183ee3596d0b4f74629b4c4e3f300b7fd25e4a3a00d"},"schema_version":"1.0"},"canonical_sha256":"28c2cbf2ba915e2aa5a2f2feba2850c2fb62193bf57f588f0a8be32176e2f606","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:08.722187Z","signature_b64":"izU5XQGsMauWUqYhVbCXcNZGq21+g0YblQ8CSO1zlvXKnD2Gebms0wbvphh5QB5RAfI+n2engmW7gMRlONOjDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28c2cbf2ba915e2aa5a2f2feba2850c2fb62193bf57f588f0a8be32176e2f606","last_reissued_at":"2026-05-18T01:30:08.721678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:08.721678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3988","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":"2026-05-18T01:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1g8TVLU177Hau9rKaX5FT8i5YOJ0cFBe+Ddbo+ybCu5uLdk+4QTwTrrVSxM6HTvbC+FEkRKe4khSYlJACSmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:19:25.488272Z"},"content_sha256":"a8990e0b07cc130008ccec9a42dc818819583c4659f3cc817cdc00cf4738b288","schema_version":"1.0","event_id":"sha256:a8990e0b07cc130008ccec9a42dc818819583c4659f3cc817cdc00cf4738b288"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FDBMX4V2SFPCVJNC6L7LUKCQYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lp Fourier multipliers on compact Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.RT"],"primary_cat":"math.FA","authors_text":"Jens Wirth, Michael Ruzhansky","submitted_at":"2011-02-19T13:07:01Z","abstract_excerpt":"In this paper we prove Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give applications to a-priori estimates for non-hypoelliptic operators. Already in the case of tori we get an interesting refinement of the classical multiplier theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3988","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":"2026-05-18T01:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BI6Jm6Tcw0XqlZNcDI7FzKHsklarTa/J+T2lo7Ptymf+Ln54zyrFASQTVd6/d9uNVW9aNaxuM/MUP3rUbAIJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:19:25.488639Z"},"content_sha256":"0f4f4b19b43ed48e33426a9d0f0779142ccbb9906b133c2e20666a43a3e7f0fd","schema_version":"1.0","event_id":"sha256:0f4f4b19b43ed48e33426a9d0f0779142ccbb9906b133c2e20666a43a3e7f0fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FDBMX4V2SFPCVJNC6L7LUKCQYL/bundle.json","state_url":"https://pith.science/pith/FDBMX4V2SFPCVJNC6L7LUKCQYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FDBMX4V2SFPCVJNC6L7LUKCQYL/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":"2026-06-05T10:19:25Z","links":{"resolver":"https://pith.science/pith/FDBMX4V2SFPCVJNC6L7LUKCQYL","bundle":"https://pith.science/pith/FDBMX4V2SFPCVJNC6L7LUKCQYL/bundle.json","state":"https://pith.science/pith/FDBMX4V2SFPCVJNC6L7LUKCQYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FDBMX4V2SFPCVJNC6L7LUKCQYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FDBMX4V2SFPCVJNC6L7LUKCQYL","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":"731f0bebaabb616662ef7183ee3596d0b4f74629b4c4e3f300b7fd25e4a3a00d","cross_cats_sorted":["math.AP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-02-19T13:07:01Z","title_canon_sha256":"26ac8605a525c448e89acbe8251c00f8e05b32f4c61df718c9ebe959cb0d7724"},"schema_version":"1.0","source":{"id":"1102.3988","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3988","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3988v3","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3988","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"FDBMX4V2SFPC","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FDBMX4V2SFPCVJNC","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FDBMX4V2","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:0f4f4b19b43ed48e33426a9d0f0779142ccbb9906b133c2e20666a43a3e7f0fd","target":"graph","created_at":"2026-05-18T01:30:08Z","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":"In this paper we prove Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give applications to a-priori estimates for non-hypoelliptic operators. Already in the case of tori we get an interesting refinement of the classical multiplier theorem.","authors_text":"Jens Wirth, Michael Ruzhansky","cross_cats":["math.AP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-02-19T13:07:01Z","title":"Lp Fourier multipliers on compact Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3988","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:a8990e0b07cc130008ccec9a42dc818819583c4659f3cc817cdc00cf4738b288","target":"record","created_at":"2026-05-18T01:30:08Z","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":"731f0bebaabb616662ef7183ee3596d0b4f74629b4c4e3f300b7fd25e4a3a00d","cross_cats_sorted":["math.AP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-02-19T13:07:01Z","title_canon_sha256":"26ac8605a525c448e89acbe8251c00f8e05b32f4c61df718c9ebe959cb0d7724"},"schema_version":"1.0","source":{"id":"1102.3988","kind":"arxiv","version":3}},"canonical_sha256":"28c2cbf2ba915e2aa5a2f2feba2850c2fb62193bf57f588f0a8be32176e2f606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28c2cbf2ba915e2aa5a2f2feba2850c2fb62193bf57f588f0a8be32176e2f606","first_computed_at":"2026-05-18T01:30:08.721678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:08.721678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"izU5XQGsMauWUqYhVbCXcNZGq21+g0YblQ8CSO1zlvXKnD2Gebms0wbvphh5QB5RAfI+n2engmW7gMRlONOjDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:08.722187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3988","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8990e0b07cc130008ccec9a42dc818819583c4659f3cc817cdc00cf4738b288","sha256:0f4f4b19b43ed48e33426a9d0f0779142ccbb9906b133c2e20666a43a3e7f0fd"],"state_sha256":"46add9a62fa171d548d5bdb7800b8f5bfa8e7339a1ffc30dcc4cd635f6881e73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4KEE4g0WLF2DDzuXcfUi14lyQcCrB2erPsZ41zd35O3VHsl3z7EH03ERu4T72XzzfU0uUs/xPkdjJ9cZ1C3zCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:19:25.490539Z","bundle_sha256":"573731028e43ab1b941159868c9e6e93c8ff4b75c14c9e8dd42b2ae2723b5216"}}