{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:C4HXWI3GRVYRZMEJVCV4SMK7JM","short_pith_number":"pith:C4HXWI3G","canonical_record":{"source":{"id":"1702.04569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-15T12:10:01Z","cross_cats_sorted":[],"title_canon_sha256":"5b8ebcb478430fb1016f0e8190c9e1d81111efaef7d811396033491ccfc27940","abstract_canon_sha256":"2e33d66ba9b50d3d56024fb6f9b078f64accd619b1e00511b1638f537471f839"},"schema_version":"1.0"},"canonical_sha256":"170f7b23668d711cb089a8abc9315f4b340c95c1c5d2035b0023c81d13ac0964","source":{"kind":"arxiv","id":"1702.04569","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04569","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04569v2","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04569","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"C4HXWI3GRVYR","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4HXWI3GRVYRZMEJ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4HXWI3G","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:C4HXWI3GRVYRZMEJVCV4SMK7JM","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-15T12:10:01Z","cross_cats_sorted":[],"title_canon_sha256":"5b8ebcb478430fb1016f0e8190c9e1d81111efaef7d811396033491ccfc27940","abstract_canon_sha256":"2e33d66ba9b50d3d56024fb6f9b078f64accd619b1e00511b1638f537471f839"},"schema_version":"1.0"},"canonical_sha256":"170f7b23668d711cb089a8abc9315f4b340c95c1c5d2035b0023c81d13ac0964","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:53.293936Z","signature_b64":"hC5o+ud2bfeWKTpED/kTc4MknQPNSVaEiizUIOlEb9D725tWkotPHD/dGouDXR9awwOKfpWTgUJNJ1d/sB/iDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"170f7b23668d711cb089a8abc9315f4b340c95c1c5d2035b0023c81d13ac0964","last_reissued_at":"2026-05-17T23:49:53.293516Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:53.293516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04569","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQMTLErsDrNipKABpJEiccJe5GiBTO2ddOghg8d3trwbLSxnsElwy0Eh20yAFisVadVG8+e3zxcLNgIrqyKzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:15:11.820198Z"},"content_sha256":"45428fac814b62218f2c7a9b589e1959a9694c1c4c31f11f26dba698d6f12cd6","schema_version":"1.0","event_id":"sha256:45428fac814b62218f2c7a9b589e1959a9694c1c4c31f11f26dba698d6f12cd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:C4HXWI3GRVYRZMEJVCV4SMK7JM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The sharp square function estimate with matrix weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander Volberg, Stefanie Petermichl, Tuomas Hyt\\\"onen","submitted_at":"2017-02-15T12:10:01Z","abstract_excerpt":"We prove the matrix $A_2$ conjecture for the dyadic square function, that is, a norm estimate of the matrix weighted square function, where the focus is on the sharp linear dependence on the matrix $A_2$ constant in the estimate. Moreover, we give a mixed estimate in terms of $A_2$ and $A_{\\infty}$ constants. Key is a sparse domination of a process inspired by the integrated form of the matrix--weighted square function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04569","kind":"arxiv","version":2},"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":"2026-05-17T23:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nxAym6bPfO2RGcqK/hogITsf4ofzf/6dcITKStpPtYONEe9MB9FhBfJqbETY3zu7xUPmLD4EoaTKOjmy394vAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:15:11.820569Z"},"content_sha256":"11032362cec7afa021c229426217dd006d94fc5887d0c8c2234090770a73fb9a","schema_version":"1.0","event_id":"sha256:11032362cec7afa021c229426217dd006d94fc5887d0c8c2234090770a73fb9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4HXWI3GRVYRZMEJVCV4SMK7JM/bundle.json","state_url":"https://pith.science/pith/C4HXWI3GRVYRZMEJVCV4SMK7JM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4HXWI3GRVYRZMEJVCV4SMK7JM/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":"2026-05-26T21:15:11Z","links":{"resolver":"https://pith.science/pith/C4HXWI3GRVYRZMEJVCV4SMK7JM","bundle":"https://pith.science/pith/C4HXWI3GRVYRZMEJVCV4SMK7JM/bundle.json","state":"https://pith.science/pith/C4HXWI3GRVYRZMEJVCV4SMK7JM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4HXWI3GRVYRZMEJVCV4SMK7JM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C4HXWI3GRVYRZMEJVCV4SMK7JM","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":"2e33d66ba9b50d3d56024fb6f9b078f64accd619b1e00511b1638f537471f839","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-15T12:10:01Z","title_canon_sha256":"5b8ebcb478430fb1016f0e8190c9e1d81111efaef7d811396033491ccfc27940"},"schema_version":"1.0","source":{"id":"1702.04569","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04569","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04569v2","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04569","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"C4HXWI3GRVYR","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4HXWI3GRVYRZMEJ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4HXWI3G","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:11032362cec7afa021c229426217dd006d94fc5887d0c8c2234090770a73fb9a","target":"graph","created_at":"2026-05-17T23:49:53Z","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 the matrix $A_2$ conjecture for the dyadic square function, that is, a norm estimate of the matrix weighted square function, where the focus is on the sharp linear dependence on the matrix $A_2$ constant in the estimate. Moreover, we give a mixed estimate in terms of $A_2$ and $A_{\\infty}$ constants. Key is a sparse domination of a process inspired by the integrated form of the matrix--weighted square function.","authors_text":"Alexander Volberg, Stefanie Petermichl, Tuomas Hyt\\\"onen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-15T12:10:01Z","title":"The sharp square function estimate with matrix weight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04569","kind":"arxiv","version":2},"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":"sha256:45428fac814b62218f2c7a9b589e1959a9694c1c4c31f11f26dba698d6f12cd6","target":"record","created_at":"2026-05-17T23:49:53Z","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":"2e33d66ba9b50d3d56024fb6f9b078f64accd619b1e00511b1638f537471f839","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-15T12:10:01Z","title_canon_sha256":"5b8ebcb478430fb1016f0e8190c9e1d81111efaef7d811396033491ccfc27940"},"schema_version":"1.0","source":{"id":"1702.04569","kind":"arxiv","version":2}},"canonical_sha256":"170f7b23668d711cb089a8abc9315f4b340c95c1c5d2035b0023c81d13ac0964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"170f7b23668d711cb089a8abc9315f4b340c95c1c5d2035b0023c81d13ac0964","first_computed_at":"2026-05-17T23:49:53.293516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:53.293516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hC5o+ud2bfeWKTpED/kTc4MknQPNSVaEiizUIOlEb9D725tWkotPHD/dGouDXR9awwOKfpWTgUJNJ1d/sB/iDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:53.293936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04569","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45428fac814b62218f2c7a9b589e1959a9694c1c4c31f11f26dba698d6f12cd6","sha256:11032362cec7afa021c229426217dd006d94fc5887d0c8c2234090770a73fb9a"],"state_sha256":"d31ed7a19d9727f4bc51ca5ff82311638e8176a5d8c2d7d760dd1dcd4fedd3eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TIB2kn20Es41mwDZgujWAfGB4j77izEeoCM7tJvDMJ1vHkPTsJJdF13CCetzuzIWoCI39Whszy6A5WW2/mCwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:15:11.822794Z","bundle_sha256":"e66ce8422ba878b96092cf39e7e0acb0086332ac8a31c0d46cf5ba612fe7e788"}}