{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4QGOM7ABSFRKLWIDX7OFEEC3IM","short_pith_number":"pith:4QGOM7AB","canonical_record":{"source":{"id":"1703.06951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-20T20:20:18Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"af24e3431427428d71c4a4dff6bc4a1faae340a35cfc80b291efda54ab85a682","abstract_canon_sha256":"62fe274ff3cd4730ddc04b34f7e8761bf9c83c30d0e3eff9d0170c72ac48710b"},"schema_version":"1.0"},"canonical_sha256":"e40ce67c019162a5d903bfdc52105b430fc5f3a4f6977c9c6d9053bff5608fb4","source":{"kind":"arxiv","id":"1703.06951","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06951","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06951v1","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06951","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"pith_short_12","alias_value":"4QGOM7ABSFRK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4QGOM7ABSFRKLWID","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4QGOM7AB","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4QGOM7ABSFRKLWIDX7OFEEC3IM","target":"record","payload":{"canonical_record":{"source":{"id":"1703.06951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-20T20:20:18Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"af24e3431427428d71c4a4dff6bc4a1faae340a35cfc80b291efda54ab85a682","abstract_canon_sha256":"62fe274ff3cd4730ddc04b34f7e8761bf9c83c30d0e3eff9d0170c72ac48710b"},"schema_version":"1.0"},"canonical_sha256":"e40ce67c019162a5d903bfdc52105b430fc5f3a4f6977c9c6d9053bff5608fb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:11.776776Z","signature_b64":"2Z1S9AKaMCjxPNSvwSZtL+fitMcUV/qcelkDPhgPyBjQ9i+HDwryGvcSmc/7twlaAOzSWgrojB91OURA8XX5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e40ce67c019162a5d903bfdc52105b430fc5f3a4f6977c9c6d9053bff5608fb4","last_reissued_at":"2026-05-18T00:48:11.776208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:11.776208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.06951","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":"2026-05-18T00:48:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RNxY8WFM4WFlZ5WB4KapU8O/VpuZl8t/pniO1olGly2XZ6LAs8wuuM9EsY7i2lyvAwbSKUOC79ykcbuPK0sVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:38:12.670247Z"},"content_sha256":"97558cb1673bab6937bfee2a1c41f1cdb875d755e609985fe0d817d0d73df2a7","schema_version":"1.0","event_id":"sha256:97558cb1673bab6937bfee2a1c41f1cdb875d755e609985fe0d817d0d73df2a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4QGOM7ABSFRKLWIDX7OFEEC3IM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positivstellensatz\\\"e for noncommutative rational expressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.FA","authors_text":"J. E. Pascoe","submitted_at":"2017-03-20T20:20:18Z","abstract_excerpt":"We derive some Positivstellensatz\\\"e for noncommutative rational expressions from the Positivstellensatz\\\"e for noncommutative polynomials. Specifically, we show that if a noncommutative rational expression is positive on a polynomially convex set, then there is an algebraic certificate witnessing that fact. As in the case of noncommutative polynomials, our results are nicer when we additionally assume positivity on a convex set-- that is, we obtain a so-called \"perfect Positivstellensatz\" on convex sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06951","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":""},"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":"2026-05-18T00:48:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nRlsAFC41SDkOoPBH+JEOu5aRmOIfwjLM1ltBkyJ2CbLJ8AR5JnWD+mkw94v7yqsrVv38g6w1iejWnvfqpicDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:38:12.670603Z"},"content_sha256":"3f68b9c0622bd17401d143fb007fa72077260609d2bf7515a00a41d13db368ef","schema_version":"1.0","event_id":"sha256:3f68b9c0622bd17401d143fb007fa72077260609d2bf7515a00a41d13db368ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4QGOM7ABSFRKLWIDX7OFEEC3IM/bundle.json","state_url":"https://pith.science/pith/4QGOM7ABSFRKLWIDX7OFEEC3IM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4QGOM7ABSFRKLWIDX7OFEEC3IM/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":"2026-06-22T12:38:12Z","links":{"resolver":"https://pith.science/pith/4QGOM7ABSFRKLWIDX7OFEEC3IM","bundle":"https://pith.science/pith/4QGOM7ABSFRKLWIDX7OFEEC3IM/bundle.json","state":"https://pith.science/pith/4QGOM7ABSFRKLWIDX7OFEEC3IM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4QGOM7ABSFRKLWIDX7OFEEC3IM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4QGOM7ABSFRKLWIDX7OFEEC3IM","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":"62fe274ff3cd4730ddc04b34f7e8761bf9c83c30d0e3eff9d0170c72ac48710b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-20T20:20:18Z","title_canon_sha256":"af24e3431427428d71c4a4dff6bc4a1faae340a35cfc80b291efda54ab85a682"},"schema_version":"1.0","source":{"id":"1703.06951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06951","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06951v1","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06951","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"pith_short_12","alias_value":"4QGOM7ABSFRK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4QGOM7ABSFRKLWID","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4QGOM7AB","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:3f68b9c0622bd17401d143fb007fa72077260609d2bf7515a00a41d13db368ef","target":"graph","created_at":"2026-05-18T00:48:11Z","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":"We derive some Positivstellensatz\\\"e for noncommutative rational expressions from the Positivstellensatz\\\"e for noncommutative polynomials. Specifically, we show that if a noncommutative rational expression is positive on a polynomially convex set, then there is an algebraic certificate witnessing that fact. As in the case of noncommutative polynomials, our results are nicer when we additionally assume positivity on a convex set-- that is, we obtain a so-called \"perfect Positivstellensatz\" on convex sets.","authors_text":"J. E. Pascoe","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-20T20:20:18Z","title":"Positivstellensatz\\\"e for noncommutative rational expressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06951","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":"sha256:97558cb1673bab6937bfee2a1c41f1cdb875d755e609985fe0d817d0d73df2a7","target":"record","created_at":"2026-05-18T00:48:11Z","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":"62fe274ff3cd4730ddc04b34f7e8761bf9c83c30d0e3eff9d0170c72ac48710b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-20T20:20:18Z","title_canon_sha256":"af24e3431427428d71c4a4dff6bc4a1faae340a35cfc80b291efda54ab85a682"},"schema_version":"1.0","source":{"id":"1703.06951","kind":"arxiv","version":1}},"canonical_sha256":"e40ce67c019162a5d903bfdc52105b430fc5f3a4f6977c9c6d9053bff5608fb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e40ce67c019162a5d903bfdc52105b430fc5f3a4f6977c9c6d9053bff5608fb4","first_computed_at":"2026-05-18T00:48:11.776208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:11.776208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Z1S9AKaMCjxPNSvwSZtL+fitMcUV/qcelkDPhgPyBjQ9i+HDwryGvcSmc/7twlaAOzSWgrojB91OURA8XX5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:11.776776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97558cb1673bab6937bfee2a1c41f1cdb875d755e609985fe0d817d0d73df2a7","sha256:3f68b9c0622bd17401d143fb007fa72077260609d2bf7515a00a41d13db368ef"],"state_sha256":"21f12a2ce22a694f68ae31c94c648c9c0b2f4c66a831725112d2e5bcfaabd3ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PwBuzpgdXB6aBo1ZgJPQO20lEwkqdkXdvxRtYtd2J4GUqnl5wPgGwvjad/ZDypPgYqBBrvDf0Hu3h57No/6HBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:38:12.672484Z","bundle_sha256":"4d476437cb2f4a7eeb1a1a1be67a8c59d0265a8066ec31c622cc213c176b60c1"}}