{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XPVKYM6ZK3OEYHNS7SEFDW6ZTR","short_pith_number":"pith:XPVKYM6Z","canonical_record":{"source":{"id":"1511.02981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-10T03:11:42Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"6f0a820f9e0e512bb9a882a3c042d79c54e675935a63b43161a575c31a98d411","abstract_canon_sha256":"3a80729091fd1f60512575f2072b26289907076aa31558072342bf692dd6f06e"},"schema_version":"1.0"},"canonical_sha256":"bbeaac33d956dc4c1db2fc8851dbd99c55e527615df91c7da75a3a59ffe0a47e","source":{"kind":"arxiv","id":"1511.02981","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02981","created_at":"2026-05-18T01:15:14Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02981v2","created_at":"2026-05-18T01:15:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02981","created_at":"2026-05-18T01:15:14Z"},{"alias_kind":"pith_short_12","alias_value":"XPVKYM6ZK3OE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XPVKYM6ZK3OEYHNS","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XPVKYM6Z","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XPVKYM6ZK3OEYHNS7SEFDW6ZTR","target":"record","payload":{"canonical_record":{"source":{"id":"1511.02981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-10T03:11:42Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"6f0a820f9e0e512bb9a882a3c042d79c54e675935a63b43161a575c31a98d411","abstract_canon_sha256":"3a80729091fd1f60512575f2072b26289907076aa31558072342bf692dd6f06e"},"schema_version":"1.0"},"canonical_sha256":"bbeaac33d956dc4c1db2fc8851dbd99c55e527615df91c7da75a3a59ffe0a47e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:14.783546Z","signature_b64":"xWKra23H/dkvVEPk6pIuzuQXDTWEJPZ/EieGu6wxSbs2oJZYssyccHhkTS8ZW5+i0C67wBa2ti1h5E5clEjoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbeaac33d956dc4c1db2fc8851dbd99c55e527615df91c7da75a3a59ffe0a47e","last_reissued_at":"2026-05-18T01:15:14.782888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:14.782888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.02981","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":"2026-05-18T01:15:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWS1wAwtuPHc9QAjZEAZnpDfLozGMPw1C2PfCjdIV05eKFGQwVKozjBZyyeGWRooLzkAEfPnIRTUu4uwgORJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:14:42.743199Z"},"content_sha256":"d1babaf698431075ac27db10c1d22e44d26b04439f72b6034befd4630882d8f8","schema_version":"1.0","event_id":"sha256:d1babaf698431075ac27db10c1d22e44d26b04439f72b6034befd4630882d8f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XPVKYM6ZK3OEYHNS7SEFDW6ZTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absolute continuity for commuting row contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Kenneth R. Davidson, Rapha\\\"el Clou\\^atre","submitted_at":"2015-11-10T03:11:42Z","abstract_excerpt":"Absolutely continuous commuting row contractions admit a weak-$*$ continuous functional calculus. Building on recent work describing the first and second dual spaces of the closure of the polynomial multipliers on the Drury-Arveson space, we give a complete characterization of these commuting row contractions in measure theoretic terms. We also establish that completely non-unitary row contractions are necessarily absolutely continuous, in direct parallel with the case of a single contraction. Finally, we consider refinements of this question for row contractions that are annihilated by a give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02981","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":"2026-05-18T01:15:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e+DWKYY3OTtOUnHsQF8THXWI/Yyy0G5oy6oqxfcyZ7pdv8G+Z9glH9fWYMlsA7XlKW0ieRYLNHRMkQg08SNBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:14:42.743862Z"},"content_sha256":"e174d4d82a2aaa073f77299880fbef1da193e2d8da668b65e1e8fb7d086c838f","schema_version":"1.0","event_id":"sha256:e174d4d82a2aaa073f77299880fbef1da193e2d8da668b65e1e8fb7d086c838f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XPVKYM6ZK3OEYHNS7SEFDW6ZTR/bundle.json","state_url":"https://pith.science/pith/XPVKYM6ZK3OEYHNS7SEFDW6ZTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XPVKYM6ZK3OEYHNS7SEFDW6ZTR/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":"2026-06-11T05:14:42Z","links":{"resolver":"https://pith.science/pith/XPVKYM6ZK3OEYHNS7SEFDW6ZTR","bundle":"https://pith.science/pith/XPVKYM6ZK3OEYHNS7SEFDW6ZTR/bundle.json","state":"https://pith.science/pith/XPVKYM6ZK3OEYHNS7SEFDW6ZTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XPVKYM6ZK3OEYHNS7SEFDW6ZTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XPVKYM6ZK3OEYHNS7SEFDW6ZTR","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":"3a80729091fd1f60512575f2072b26289907076aa31558072342bf692dd6f06e","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-10T03:11:42Z","title_canon_sha256":"6f0a820f9e0e512bb9a882a3c042d79c54e675935a63b43161a575c31a98d411"},"schema_version":"1.0","source":{"id":"1511.02981","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02981","created_at":"2026-05-18T01:15:14Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02981v2","created_at":"2026-05-18T01:15:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02981","created_at":"2026-05-18T01:15:14Z"},{"alias_kind":"pith_short_12","alias_value":"XPVKYM6ZK3OE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XPVKYM6ZK3OEYHNS","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XPVKYM6Z","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:e174d4d82a2aaa073f77299880fbef1da193e2d8da668b65e1e8fb7d086c838f","target":"graph","created_at":"2026-05-18T01:15:14Z","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":"Absolutely continuous commuting row contractions admit a weak-$*$ continuous functional calculus. Building on recent work describing the first and second dual spaces of the closure of the polynomial multipliers on the Drury-Arveson space, we give a complete characterization of these commuting row contractions in measure theoretic terms. We also establish that completely non-unitary row contractions are necessarily absolutely continuous, in direct parallel with the case of a single contraction. Finally, we consider refinements of this question for row contractions that are annihilated by a give","authors_text":"Kenneth R. Davidson, Rapha\\\"el Clou\\^atre","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-10T03:11:42Z","title":"Absolute continuity for commuting row contractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02981","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:d1babaf698431075ac27db10c1d22e44d26b04439f72b6034befd4630882d8f8","target":"record","created_at":"2026-05-18T01:15:14Z","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":"3a80729091fd1f60512575f2072b26289907076aa31558072342bf692dd6f06e","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-10T03:11:42Z","title_canon_sha256":"6f0a820f9e0e512bb9a882a3c042d79c54e675935a63b43161a575c31a98d411"},"schema_version":"1.0","source":{"id":"1511.02981","kind":"arxiv","version":2}},"canonical_sha256":"bbeaac33d956dc4c1db2fc8851dbd99c55e527615df91c7da75a3a59ffe0a47e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbeaac33d956dc4c1db2fc8851dbd99c55e527615df91c7da75a3a59ffe0a47e","first_computed_at":"2026-05-18T01:15:14.782888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:14.782888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xWKra23H/dkvVEPk6pIuzuQXDTWEJPZ/EieGu6wxSbs2oJZYssyccHhkTS8ZW5+i0C67wBa2ti1h5E5clEjoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:14.783546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02981","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1babaf698431075ac27db10c1d22e44d26b04439f72b6034befd4630882d8f8","sha256:e174d4d82a2aaa073f77299880fbef1da193e2d8da668b65e1e8fb7d086c838f"],"state_sha256":"aaeb118da76aff791f14a21dd5fc4d288270b10dc40428a6b45f2c7d31f0b26e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ui6vrpLm4QHEWUbSvmCkEVqqv9PIkgzF7Z6jOOPKXvXSz+yqJPK7Tf78NlU3rZwIyWd4OlY1xjSg0Q0bqzzgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T05:14:42.747294Z","bundle_sha256":"d9f37d8470460d9a231e9d50b2dbae6768eb56f3e9322103556a5f85cc2ba36d"}}