{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FFNDII6BTEPX7D7E4K5CK53ZUX","short_pith_number":"pith:FFNDII6B","canonical_record":{"source":{"id":"1305.4272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-18T15:03:03Z","cross_cats_sorted":[],"title_canon_sha256":"5648884bae08af153a32be965c68da884251efe9e1c566064d52c9eabbedb961","abstract_canon_sha256":"eed0cf411c6dc80741bb6e46a7ad9a68f258d3c1b318cb376e960e038a5391af"},"schema_version":"1.0"},"canonical_sha256":"295a3423c1991f7f8fe4e2ba257779a5e196769d792aaf31cafc03ae28e61d92","source":{"kind":"arxiv","id":"1305.4272","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4272","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4272v2","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4272","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"FFNDII6BTEPX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FFNDII6BTEPX7D7E","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FFNDII6B","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FFNDII6BTEPX7D7E4K5CK53ZUX","target":"record","payload":{"canonical_record":{"source":{"id":"1305.4272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-18T15:03:03Z","cross_cats_sorted":[],"title_canon_sha256":"5648884bae08af153a32be965c68da884251efe9e1c566064d52c9eabbedb961","abstract_canon_sha256":"eed0cf411c6dc80741bb6e46a7ad9a68f258d3c1b318cb376e960e038a5391af"},"schema_version":"1.0"},"canonical_sha256":"295a3423c1991f7f8fe4e2ba257779a5e196769d792aaf31cafc03ae28e61d92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:14.304382Z","signature_b64":"9nCGDN7IReH9M1s8olcJYJmS/+bbhivI95ohWCCraK05PDHffYbjwz/ts8TK4G0YVfp8B8IRhiSG3fSAdd4fAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"295a3423c1991f7f8fe4e2ba257779a5e196769d792aaf31cafc03ae28e61d92","last_reissued_at":"2026-05-18T03:10:14.303699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:14.303699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.4272","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":"2026-05-18T03:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DnFi0nXoMWWw0uq8I1BRB5yXN0s7VDrtDfn9sw36iUGpRV9pWxStCH//pdw3LTUOO/g/Jh7XvlLZmj/jqo9OAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:40:41.391851Z"},"content_sha256":"ee4301f28e23b7036764554cd023ca88fd14f99d40fab80ba0be9f57fe7c91ae","schema_version":"1.0","event_id":"sha256:ee4301f28e23b7036764554cd023ca88fd14f99d40fab80ba0be9f57fe7c91ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FFNDII6BTEPX7D7E4K5CK53ZUX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dilations and constrained algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Michael A. Dritschel, Michael T. Jury, Scott McCullough","submitted_at":"2013-05-18T15:03:03Z","abstract_excerpt":"It is well known that unital contractive representations of the disk algebra are completely contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f whose first derivative vanishes at 0. We prove that there are unital contractive representations of A which are not completely contractive, and furthermore provide a Kaiser and Varopoulos inspired example for A and present a characterization of those contractive representations of A which are completely contractive. In the positive direction, for the algebra of rational functions with poles off the distinguished"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4272","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":"2026-05-18T03:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4L0C7WUAyqaJUrlNUOnWAQkh7YHOu3UtTGx8/JDk9CTEDr3yq3ljWCx/qsLGtdsdhvSaM1TzBS1rXPWOO6eNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:40:41.392586Z"},"content_sha256":"9668be27fe352a17ad0aa5841faa1094f363e5ee3ec08e0d98a690b152737ca0","schema_version":"1.0","event_id":"sha256:9668be27fe352a17ad0aa5841faa1094f363e5ee3ec08e0d98a690b152737ca0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFNDII6BTEPX7D7E4K5CK53ZUX/bundle.json","state_url":"https://pith.science/pith/FFNDII6BTEPX7D7E4K5CK53ZUX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFNDII6BTEPX7D7E4K5CK53ZUX/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":"2026-05-30T02:40:41Z","links":{"resolver":"https://pith.science/pith/FFNDII6BTEPX7D7E4K5CK53ZUX","bundle":"https://pith.science/pith/FFNDII6BTEPX7D7E4K5CK53ZUX/bundle.json","state":"https://pith.science/pith/FFNDII6BTEPX7D7E4K5CK53ZUX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFNDII6BTEPX7D7E4K5CK53ZUX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FFNDII6BTEPX7D7E4K5CK53ZUX","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":"eed0cf411c6dc80741bb6e46a7ad9a68f258d3c1b318cb376e960e038a5391af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-18T15:03:03Z","title_canon_sha256":"5648884bae08af153a32be965c68da884251efe9e1c566064d52c9eabbedb961"},"schema_version":"1.0","source":{"id":"1305.4272","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4272","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4272v2","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4272","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"FFNDII6BTEPX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FFNDII6BTEPX7D7E","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FFNDII6B","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:9668be27fe352a17ad0aa5841faa1094f363e5ee3ec08e0d98a690b152737ca0","target":"graph","created_at":"2026-05-18T03:10:14Z","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":"It is well known that unital contractive representations of the disk algebra are completely contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f whose first derivative vanishes at 0. We prove that there are unital contractive representations of A which are not completely contractive, and furthermore provide a Kaiser and Varopoulos inspired example for A and present a characterization of those contractive representations of A which are completely contractive. In the positive direction, for the algebra of rational functions with poles off the distinguished","authors_text":"Michael A. Dritschel, Michael T. Jury, Scott McCullough","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-18T15:03:03Z","title":"Dilations and constrained algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4272","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:ee4301f28e23b7036764554cd023ca88fd14f99d40fab80ba0be9f57fe7c91ae","target":"record","created_at":"2026-05-18T03:10:14Z","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":"eed0cf411c6dc80741bb6e46a7ad9a68f258d3c1b318cb376e960e038a5391af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-18T15:03:03Z","title_canon_sha256":"5648884bae08af153a32be965c68da884251efe9e1c566064d52c9eabbedb961"},"schema_version":"1.0","source":{"id":"1305.4272","kind":"arxiv","version":2}},"canonical_sha256":"295a3423c1991f7f8fe4e2ba257779a5e196769d792aaf31cafc03ae28e61d92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"295a3423c1991f7f8fe4e2ba257779a5e196769d792aaf31cafc03ae28e61d92","first_computed_at":"2026-05-18T03:10:14.303699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:14.303699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9nCGDN7IReH9M1s8olcJYJmS/+bbhivI95ohWCCraK05PDHffYbjwz/ts8TK4G0YVfp8B8IRhiSG3fSAdd4fAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:14.304382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4272","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee4301f28e23b7036764554cd023ca88fd14f99d40fab80ba0be9f57fe7c91ae","sha256:9668be27fe352a17ad0aa5841faa1094f363e5ee3ec08e0d98a690b152737ca0"],"state_sha256":"77f5315675d77169faff8c4f745d14892010e4fa068f0ba2b07467646ba522b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vX+TD5rpHAAld0G+0LhLpY9XultKh39/k5LBxUj5gMl4iy1L9W6QRudiLBB8SP6FMarh8xFmLczxf2BuOzoeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:40:41.396880Z","bundle_sha256":"c7e8e8789ce81d942eeadbb252e4b4c3dadafad19af7b0bedb4e10e001ced696"}}