{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EAFTOCR7BRC6CCMUGZAQPRX47P","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":"dfb4f2c1b3aa31427f951ba11a23ce86ba81295d8ae07482d16fce8dea025234","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-19T18:03:43Z","title_canon_sha256":"d5f5879cff507f586be6b10b1759b40fc382a734848f9139eaa7244d48e91ad6"},"schema_version":"1.0","source":{"id":"1605.06071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06071","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06071v1","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06071","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"EAFTOCR7BRC6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EAFTOCR7BRC6CCMU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EAFTOCR7","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:57376e4dd184c5ab0611c44d70f31187792d64eca22dd52e681e5e49283621c9","target":"graph","created_at":"2026-05-18T01:14:26Z","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 the scalar setting, the power functions $|x|^{\\gamma}$, for $-1 < \\gamma<1$, are the canonical examples of $A_2$ weights. In this paper, we study two types of power functions in the matrix setting, with the goal of obtaining canonical examples of $A_2$ matrix weights. We first study Type 1 matrix power functions, which are $n\\times n$ matrix functions whose entries are of the form $a|x|^{\\gamma}.$ Our main result characterizes when these power functions are $A_2$ matrix weights and has two extensions to Type $1$ power functions of several variables. We also study Type 2 matrix power functio","authors_text":"Katherine Lunceford, Kelly Bickel, Naba Mukhtar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-19T18:03:43Z","title":"Characterizations of $A_2$ Matrix Power Weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06071","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:dd175a6d74bbe0544f55b385502ee171c644d4fb2a58ed2df4521f0cf0c2e9cb","target":"record","created_at":"2026-05-18T01:14:26Z","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":"dfb4f2c1b3aa31427f951ba11a23ce86ba81295d8ae07482d16fce8dea025234","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-19T18:03:43Z","title_canon_sha256":"d5f5879cff507f586be6b10b1759b40fc382a734848f9139eaa7244d48e91ad6"},"schema_version":"1.0","source":{"id":"1605.06071","kind":"arxiv","version":1}},"canonical_sha256":"200b370a3f0c45e10994364107c6fcfbc6ba79d998b052e0658263d2eb5da4be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"200b370a3f0c45e10994364107c6fcfbc6ba79d998b052e0658263d2eb5da4be","first_computed_at":"2026-05-18T01:14:26.591524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:26.591524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3vSJeqT+IJZbFgz+qJkS0DpQpvuidmIGzPrSp/ZkblhjPBsTyUDrUBi9LvRj8Q+FcVFP3U591TbO4+xWrkXtCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:26.592062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd175a6d74bbe0544f55b385502ee171c644d4fb2a58ed2df4521f0cf0c2e9cb","sha256:57376e4dd184c5ab0611c44d70f31187792d64eca22dd52e681e5e49283621c9"],"state_sha256":"4167b385f8fe3e152acc5e03c894e3acdc89585388bb24d03d2193fb8465411a"}