{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:54UW5DTXBJVWY6MJAJLLCG6EM2","short_pith_number":"pith:54UW5DTX","canonical_record":{"source":{"id":"2412.15026","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-12-19T16:38:38Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"cf2b3886e3b11088de1ca7be0ba5fac7ab2105d4e6d94421055a8583bf599195","abstract_canon_sha256":"72a886f67742fd35b4f765c42a0caaf8a28fe21b555c9be5e209fd7882f8cc9f"},"schema_version":"1.0"},"canonical_sha256":"ef296e8e770a6b6c79890256b11bc466bd20ecff376e8c89965a387c6caf67d3","source":{"kind":"arxiv","id":"2412.15026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15026","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15026v1","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15026","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"54UW5DTXBJVW","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"pith_short_16","alias_value":"54UW5DTXBJVWY6MJ","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"pith_short_8","alias_value":"54UW5DTX","created_at":"2026-07-05T09:51:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:54UW5DTXBJVWY6MJAJLLCG6EM2","target":"record","payload":{"canonical_record":{"source":{"id":"2412.15026","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-12-19T16:38:38Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"cf2b3886e3b11088de1ca7be0ba5fac7ab2105d4e6d94421055a8583bf599195","abstract_canon_sha256":"72a886f67742fd35b4f765c42a0caaf8a28fe21b555c9be5e209fd7882f8cc9f"},"schema_version":"1.0"},"canonical_sha256":"ef296e8e770a6b6c79890256b11bc466bd20ecff376e8c89965a387c6caf67d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:51:57.093553Z","signature_b64":"MSZh4sd8xKIBjXnOuiDnsSnyHRCOdYvv/km+EiprnHDpNisSNi0w89qz9MtHxxXf9ATuJYNjJwPmNA6L4YkzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef296e8e770a6b6c79890256b11bc466bd20ecff376e8c89965a387c6caf67d3","last_reissued_at":"2026-07-05T09:51:57.092880Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:51:57.092880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.15026","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":"2026-07-05T09:51:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3BxfM3Q/GFQxoJIx/Gydtq6u0iPKzScwFGzhZ+NoUkcVEzqMOyLAt9QgV+zjSa4NV1QaaXGK6FBR6oiYYMQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T01:04:42.183683Z"},"content_sha256":"b11b293f5c2403a7dbd383963709b84a9f3ec9ea9ffbb780b73b3d3f5e6eb1e6","schema_version":"1.0","event_id":"sha256:b11b293f5c2403a7dbd383963709b84a9f3ec9ea9ffbb780b73b3d3f5e6eb1e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:54UW5DTXBJVWY6MJAJLLCG6EM2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multilinear matrix weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Spyridon Kakaroumpas, Zoe Nieraeth","submitted_at":"2024-12-19T16:38:38Z","abstract_excerpt":"In this work we fully characterize the classes of matrix weights for which multilinear Calder\\'on-Zygmund operators extend to bounded operators on matrix weighted Lebesgue spaces. To this end, we develop the theory of multilinear singular integrals taking values in tensor products of finite dimensional Hilbert spaces. On the one hand, we establish quantitative bounds in terms of multilinear Muckenhoupt matrix weight characteristics and scalar Fujii-Wilson conditions of a tensor product analogue of the convex body sparse operator, of a convex-set valued tensor product analogue of the Hardy-Litt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15026","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.15026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:51:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r9C+V9/aYTJJmATSedaBVhSod/SBOQunPagN4KtMQs3Uh5p4Y7ltzIQpor329fWKAELCjlEsspZOUrwlqrgxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T01:04:42.184197Z"},"content_sha256":"99ad52544b45200eaff604ed37e3bfd255bbe653aa6f92b24765bcfe97df62f8","schema_version":"1.0","event_id":"sha256:99ad52544b45200eaff604ed37e3bfd255bbe653aa6f92b24765bcfe97df62f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/54UW5DTXBJVWY6MJAJLLCG6EM2/bundle.json","state_url":"https://pith.science/pith/54UW5DTXBJVWY6MJAJLLCG6EM2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/54UW5DTXBJVWY6MJAJLLCG6EM2/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":"2026-08-19T01:04:42Z","links":{"resolver":"https://pith.science/pith/54UW5DTXBJVWY6MJAJLLCG6EM2","bundle":"https://pith.science/pith/54UW5DTXBJVWY6MJAJLLCG6EM2/bundle.json","state":"https://pith.science/pith/54UW5DTXBJVWY6MJAJLLCG6EM2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/54UW5DTXBJVWY6MJAJLLCG6EM2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:54UW5DTXBJVWY6MJAJLLCG6EM2","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":"72a886f67742fd35b4f765c42a0caaf8a28fe21b555c9be5e209fd7882f8cc9f","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-12-19T16:38:38Z","title_canon_sha256":"cf2b3886e3b11088de1ca7be0ba5fac7ab2105d4e6d94421055a8583bf599195"},"schema_version":"1.0","source":{"id":"2412.15026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15026","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15026v1","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15026","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"54UW5DTXBJVW","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"pith_short_16","alias_value":"54UW5DTXBJVWY6MJ","created_at":"2026-07-05T09:51:57Z"},{"alias_kind":"pith_short_8","alias_value":"54UW5DTX","created_at":"2026-07-05T09:51:57Z"}],"graph_snapshots":[{"event_id":"sha256:99ad52544b45200eaff604ed37e3bfd255bbe653aa6f92b24765bcfe97df62f8","target":"graph","created_at":"2026-07-05T09:51:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.15026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we fully characterize the classes of matrix weights for which multilinear Calder\\'on-Zygmund operators extend to bounded operators on matrix weighted Lebesgue spaces. To this end, we develop the theory of multilinear singular integrals taking values in tensor products of finite dimensional Hilbert spaces. On the one hand, we establish quantitative bounds in terms of multilinear Muckenhoupt matrix weight characteristics and scalar Fujii-Wilson conditions of a tensor product analogue of the convex body sparse operator, of a convex-set valued tensor product analogue of the Hardy-Litt","authors_text":"Spyridon Kakaroumpas, Zoe Nieraeth","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-12-19T16:38:38Z","title":"Multilinear matrix weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15026","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:b11b293f5c2403a7dbd383963709b84a9f3ec9ea9ffbb780b73b3d3f5e6eb1e6","target":"record","created_at":"2026-07-05T09:51:57Z","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":"72a886f67742fd35b4f765c42a0caaf8a28fe21b555c9be5e209fd7882f8cc9f","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-12-19T16:38:38Z","title_canon_sha256":"cf2b3886e3b11088de1ca7be0ba5fac7ab2105d4e6d94421055a8583bf599195"},"schema_version":"1.0","source":{"id":"2412.15026","kind":"arxiv","version":1}},"canonical_sha256":"ef296e8e770a6b6c79890256b11bc466bd20ecff376e8c89965a387c6caf67d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef296e8e770a6b6c79890256b11bc466bd20ecff376e8c89965a387c6caf67d3","first_computed_at":"2026-07-05T09:51:57.092880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:51:57.092880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MSZh4sd8xKIBjXnOuiDnsSnyHRCOdYvv/km+EiprnHDpNisSNi0w89qz9MtHxxXf9ATuJYNjJwPmNA6L4YkzCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:51:57.093553Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.15026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b11b293f5c2403a7dbd383963709b84a9f3ec9ea9ffbb780b73b3d3f5e6eb1e6","sha256:99ad52544b45200eaff604ed37e3bfd255bbe653aa6f92b24765bcfe97df62f8"],"state_sha256":"d29bcfac77a389319de40b98d4d109e97e860e6c8ab7cdadc43b8ffb6beb15e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+i2yLufZm3Antw8doW/8V29G/ipOKsLUyp7urOQKopBbEARx9tAkPHscm+eJJR9aIYD3mDTgcDgK/wx9M+XAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T01:04:42.189080Z","bundle_sha256":"51309e7fabf77c18ac4c134739e26d8cc4ba4847c0c1ead10f50dc1879fa8af3"}}