{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YL6T7T6IBQ2KOWD5HT3LZ62IOX","short_pith_number":"pith:YL6T7T6I","canonical_record":{"source":{"id":"1908.05949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-16T12:40:31Z","cross_cats_sorted":[],"title_canon_sha256":"48a5a419f31a0bea42d118e908356f25e2c9a18e5da4e5105d90ac89a7568d19","abstract_canon_sha256":"587fd5ef371e41139c586ee91bf99c45236b09489c8cb876681cf0c44313dd7f"},"schema_version":"1.0"},"canonical_sha256":"c2fd3fcfc80c34a7587d3cf6bcfb4875ce45e094a17876a71bea069c743c07af","source":{"kind":"arxiv","id":"1908.05949","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05949","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05949v1","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05949","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"YL6T7T6IBQ2K","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"pith_short_16","alias_value":"YL6T7T6IBQ2KOWD5","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"pith_short_8","alias_value":"YL6T7T6I","created_at":"2026-07-05T02:45:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YL6T7T6IBQ2KOWD5HT3LZ62IOX","target":"record","payload":{"canonical_record":{"source":{"id":"1908.05949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-16T12:40:31Z","cross_cats_sorted":[],"title_canon_sha256":"48a5a419f31a0bea42d118e908356f25e2c9a18e5da4e5105d90ac89a7568d19","abstract_canon_sha256":"587fd5ef371e41139c586ee91bf99c45236b09489c8cb876681cf0c44313dd7f"},"schema_version":"1.0"},"canonical_sha256":"c2fd3fcfc80c34a7587d3cf6bcfb4875ce45e094a17876a71bea069c743c07af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:45:31.113471Z","signature_b64":"BqZF4pN1U5xPcD59KPZlAMB+Kj6DN5awtin0BqJtku4/BQs4LQXSxuMEgEnhpsTRPxjGJ9IxhQirHvL7hR6OBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2fd3fcfc80c34a7587d3cf6bcfb4875ce45e094a17876a71bea069c743c07af","last_reissued_at":"2026-07-05T02:45:31.112698Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:45:31.112698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.05949","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:45:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJMXc1R7LXBAZkyXACvrZ8WcdSJR7FURdTWVejoPmmV6eyK4vzoOFv5GzEeavGXG6MzuuT9CDNDu2KDzAVrdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:01:04.208779Z"},"content_sha256":"a190274d550a88b0335f98cd8d9cdb60f3a47f727366c5befce97da22167ddce","schema_version":"1.0","event_id":"sha256:a190274d550a88b0335f98cd8d9cdb60f3a47f727366c5befce97da22167ddce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YL6T7T6IBQ2KOWD5HT3LZ62IOX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative partial convexity via $\\Gamma$-convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Igor Klep, James Eldred Pascoe, Mark E. Mancuso, Michael Jury, Scott McCullough","submitted_at":"2019-08-16T12:40:31Z","abstract_excerpt":"Motivated by classical notions of partial convexity, biconvexity, and bilinear matrix inequalities, we investigate the theory of free sets that are defined by (low degree) noncommutative matrix polynomials with constrained terms. Given a tuple of symmetric polynomials $\\Gamma$, a free set is called $\\Gamma$-convex if it closed under isometric conjugation by isometries intertwining $\\Gamma$. We establish an Effros-Winkler Hahn-Banach separation theorem for $\\Gamma$-convex sets; they are delineated by linear pencils in the coordinates of $\\Gamma$ and the variables $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05949","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05949/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:45:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/qHYYg/StEzOiZidd3kWYNFmTiali8zLxGSRsPB2GcfzHc7eaSFgBpxoTdy1KDwCsJ9J7JP59ErSo9E1sI3/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:01:04.209278Z"},"content_sha256":"6ce133bfda2927547d945cbaca4dd4f9e56848d4e90536c16068a30970d31e39","schema_version":"1.0","event_id":"sha256:6ce133bfda2927547d945cbaca4dd4f9e56848d4e90536c16068a30970d31e39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YL6T7T6IBQ2KOWD5HT3LZ62IOX/bundle.json","state_url":"https://pith.science/pith/YL6T7T6IBQ2KOWD5HT3LZ62IOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YL6T7T6IBQ2KOWD5HT3LZ62IOX/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":"2026-08-16T20:01:04Z","links":{"resolver":"https://pith.science/pith/YL6T7T6IBQ2KOWD5HT3LZ62IOX","bundle":"https://pith.science/pith/YL6T7T6IBQ2KOWD5HT3LZ62IOX/bundle.json","state":"https://pith.science/pith/YL6T7T6IBQ2KOWD5HT3LZ62IOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YL6T7T6IBQ2KOWD5HT3LZ62IOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YL6T7T6IBQ2KOWD5HT3LZ62IOX","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":"587fd5ef371e41139c586ee91bf99c45236b09489c8cb876681cf0c44313dd7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-16T12:40:31Z","title_canon_sha256":"48a5a419f31a0bea42d118e908356f25e2c9a18e5da4e5105d90ac89a7568d19"},"schema_version":"1.0","source":{"id":"1908.05949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05949","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05949v1","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05949","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"YL6T7T6IBQ2K","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"pith_short_16","alias_value":"YL6T7T6IBQ2KOWD5","created_at":"2026-07-05T02:45:31Z"},{"alias_kind":"pith_short_8","alias_value":"YL6T7T6I","created_at":"2026-07-05T02:45:31Z"}],"graph_snapshots":[{"event_id":"sha256:6ce133bfda2927547d945cbaca4dd4f9e56848d4e90536c16068a30970d31e39","target":"graph","created_at":"2026-07-05T02:45:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.05949/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by classical notions of partial convexity, biconvexity, and bilinear matrix inequalities, we investigate the theory of free sets that are defined by (low degree) noncommutative matrix polynomials with constrained terms. Given a tuple of symmetric polynomials $\\Gamma$, a free set is called $\\Gamma$-convex if it closed under isometric conjugation by isometries intertwining $\\Gamma$. We establish an Effros-Winkler Hahn-Banach separation theorem for $\\Gamma$-convex sets; they are delineated by linear pencils in the coordinates of $\\Gamma$ and the variables $x$.","authors_text":"Igor Klep, James Eldred Pascoe, Mark E. Mancuso, Michael Jury, Scott McCullough","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-16T12:40:31Z","title":"Noncommutative partial convexity via $\\Gamma$-convexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05949","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:a190274d550a88b0335f98cd8d9cdb60f3a47f727366c5befce97da22167ddce","target":"record","created_at":"2026-07-05T02:45:31Z","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":"587fd5ef371e41139c586ee91bf99c45236b09489c8cb876681cf0c44313dd7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-16T12:40:31Z","title_canon_sha256":"48a5a419f31a0bea42d118e908356f25e2c9a18e5da4e5105d90ac89a7568d19"},"schema_version":"1.0","source":{"id":"1908.05949","kind":"arxiv","version":1}},"canonical_sha256":"c2fd3fcfc80c34a7587d3cf6bcfb4875ce45e094a17876a71bea069c743c07af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2fd3fcfc80c34a7587d3cf6bcfb4875ce45e094a17876a71bea069c743c07af","first_computed_at":"2026-07-05T02:45:31.112698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:45:31.112698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BqZF4pN1U5xPcD59KPZlAMB+Kj6DN5awtin0BqJtku4/BQs4LQXSxuMEgEnhpsTRPxjGJ9IxhQirHvL7hR6OBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:45:31.113471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a190274d550a88b0335f98cd8d9cdb60f3a47f727366c5befce97da22167ddce","sha256:6ce133bfda2927547d945cbaca4dd4f9e56848d4e90536c16068a30970d31e39"],"state_sha256":"64a2da8f3c28e7065ba1e5b13beba9eb7c6a78254418e967c80dafdccbc3eb9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"we/IXJts7JrUl4j/DwyhgpX3WAv3NGVWRx7C9AtcFKCz5lNHviAaufiHERhCGYeoX7QH5uKhR2/pmkypx1PoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T20:01:04.214478Z","bundle_sha256":"2bf3a4744ffc683961f6e85ab8f0878928b709a0b7462b42bba7e7b2fa231970"}}