{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MCTXBATFBMMWNRIEJKYR3EOSKZ","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":"9ad2984f15777ab66bb333f54f927eaaac2475a5ee96431e8ae803e259266e88","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-12-20T22:10:59Z","title_canon_sha256":"6ca656cea1cb388f163dc5f8920c45f47050aae775414f9e24042d047bb0eb09"},"schema_version":"1.0","source":{"id":"1212.5282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5282","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5282v1","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5282","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"pith_short_12","alias_value":"MCTXBATFBMMW","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MCTXBATFBMMWNRIE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MCTXBATF","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:8635659952e6090c08bcadbe0bb8dc8281152241d418af1dd9f82deb14840fff","target":"graph","created_at":"2026-05-18T03:38:02Z","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":"For $\\delta$ an $m$-tuple of analytic functions, we define an algebra $\\hidg$, contained in the bounded analytic functions on the analytic polyhedron $ {|\\delta^l(z)| < 1, \\ 1 \\leq l \\leq m}$, and prove a representation formula for it. We give conditions whereby every function that is analytic on a neighborhood of $ {|\\delta^l(z)| \\leq 1, \\ 1 \\leq l \\leq m}$ is actually in $\\hidg$. We use this to give a proof of the Oka extension theorem with bounds. We define an $\\hidg$ functional calculus for operators.","authors_text":"Jim Agler, John E. McCarthy","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-12-20T22:10:59Z","title":"Operator theory and the Oka extension theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5282","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":"sha256:7957480183ce9459f099bac132af6821452c4f82c32dff66acf19509d42208be","target":"record","created_at":"2026-05-18T03:38:02Z","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":"9ad2984f15777ab66bb333f54f927eaaac2475a5ee96431e8ae803e259266e88","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-12-20T22:10:59Z","title_canon_sha256":"6ca656cea1cb388f163dc5f8920c45f47050aae775414f9e24042d047bb0eb09"},"schema_version":"1.0","source":{"id":"1212.5282","kind":"arxiv","version":1}},"canonical_sha256":"60a77082650b1966c5044ab11d91d25669147d5418e864a67c1c35105da7226d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60a77082650b1966c5044ab11d91d25669147d5418e864a67c1c35105da7226d","first_computed_at":"2026-05-18T03:38:02.282461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:02.282461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XEWwgc7pqNUcwR3byHsiQP8LEeKXrqwFlypGXLLNexTjEv2zxMVvKO+0BE6C0wpx2Syn+guKXuy/W8Bspru+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:02.282979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7957480183ce9459f099bac132af6821452c4f82c32dff66acf19509d42208be","sha256:8635659952e6090c08bcadbe0bb8dc8281152241d418af1dd9f82deb14840fff"],"state_sha256":"fb94e85b8751ebbec91876e5e9fed50d8d0a746de53125eb276f6dad2c59ea08"}