{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2HXG4ZR3VA5VF4GUSN6WOVTEDU","short_pith_number":"pith:2HXG4ZR3","canonical_record":{"source":{"id":"2607.09339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-10T12:20:16Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"98f79c807708bcc33179ff1c428c3fae9e85a939a43e5817c141da7e09011a09","abstract_canon_sha256":"0611996e96114c30f444c3ae83dd4e3be43eafe176f70c00f9c7fbee0b883693"},"schema_version":"1.0"},"canonical_sha256":"d1ee6e663ba83b52f0d4937d6756641d37f3649507fb676ff3c83bc5359eb5f6","source":{"kind":"arxiv","id":"2607.09339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09339","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09339v1","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09339","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"2HXG4ZR3VA5V","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"pith_short_16","alias_value":"2HXG4ZR3VA5VF4GU","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"pith_short_8","alias_value":"2HXG4ZR3","created_at":"2026-07-13T01:19:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2HXG4ZR3VA5VF4GUSN6WOVTEDU","target":"record","payload":{"canonical_record":{"source":{"id":"2607.09339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-10T12:20:16Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"98f79c807708bcc33179ff1c428c3fae9e85a939a43e5817c141da7e09011a09","abstract_canon_sha256":"0611996e96114c30f444c3ae83dd4e3be43eafe176f70c00f9c7fbee0b883693"},"schema_version":"1.0"},"canonical_sha256":"d1ee6e663ba83b52f0d4937d6756641d37f3649507fb676ff3c83bc5359eb5f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:19:03.772798Z","signature_b64":"KTKeUnhH/6LcdSPiD3lr1Y5HQ4n1BCfFwzA3LKmME+xNXbahO/n2bZTu/3vUzcr/GyZjx9CVvJW21TuIAZfsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1ee6e663ba83b52f0d4937d6756641d37f3649507fb676ff3c83bc5359eb5f6","last_reissued_at":"2026-07-13T01:19:03.769614Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:19:03.769614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.09339","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":"2026-07-13T01:19:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQbyMKKOUNIelSRkE8axAq8uKGT24yyqbgCP1m09DgaPh1CwBn42U0Lz7wCBeq6N/emVz5hYWyDdRhygYVJuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:08:46.720255Z"},"content_sha256":"f6394aecef6748b4740dcebe68958df653024d7bb81eb08c498ce761be03c912","schema_version":"1.0","event_id":"sha256:f6394aecef6748b4740dcebe68958df653024d7bb81eb08c498ce761be03c912"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2HXG4ZR3VA5VF4GUSN6WOVTEDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PCPOP.jl: A Julia package for partially commutative polynomial optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"quant-ph","authors_text":"Abhishek Mishra, Mois\\'es Bermejo Mor\\'an","submitted_at":"2026-07-10T12:20:16Z","abstract_excerpt":"Here we present PCPOP, a Julia package for polynomial optimization that supports non-commutative optimization, tracial polynomial optimization, trace polynomial optimization and state polynomial optimization. PCPOP fully supports exact arithmetic computations and incorporates convenient functionalities such as algebraic reductions based on Gr\\\"obner basis methods, automatized symmetrization via Wedderburn decompositions, and Jordan algebra reductions. As a distinguished feature, PCPOP implements a specialized framework for polynomial computations in partially commutative variables that provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09339","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/2607.09339/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":"2026-07-13T01:19:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WYoIPCSIhF9QiRkV1ge2YMSTC/F5rYD7gIlSHHVBxkXmtNlTAsgHO0nWHTGMk7Omhwywabd2hS8cgAdcvoufDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:08:46.721202Z"},"content_sha256":"f2b9f880fc942c3827c24227c77018897be4eca0af79e018a848cbef2037bb21","schema_version":"1.0","event_id":"sha256:f2b9f880fc942c3827c24227c77018897be4eca0af79e018a848cbef2037bb21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HXG4ZR3VA5VF4GUSN6WOVTEDU/bundle.json","state_url":"https://pith.science/pith/2HXG4ZR3VA5VF4GUSN6WOVTEDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HXG4ZR3VA5VF4GUSN6WOVTEDU/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":"2026-08-04T19:08:46Z","links":{"resolver":"https://pith.science/pith/2HXG4ZR3VA5VF4GUSN6WOVTEDU","bundle":"https://pith.science/pith/2HXG4ZR3VA5VF4GUSN6WOVTEDU/bundle.json","state":"https://pith.science/pith/2HXG4ZR3VA5VF4GUSN6WOVTEDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HXG4ZR3VA5VF4GUSN6WOVTEDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2HXG4ZR3VA5VF4GUSN6WOVTEDU","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":"0611996e96114c30f444c3ae83dd4e3be43eafe176f70c00f9c7fbee0b883693","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-10T12:20:16Z","title_canon_sha256":"98f79c807708bcc33179ff1c428c3fae9e85a939a43e5817c141da7e09011a09"},"schema_version":"1.0","source":{"id":"2607.09339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09339","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09339v1","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09339","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"2HXG4ZR3VA5V","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"pith_short_16","alias_value":"2HXG4ZR3VA5VF4GU","created_at":"2026-07-13T01:19:03Z"},{"alias_kind":"pith_short_8","alias_value":"2HXG4ZR3","created_at":"2026-07-13T01:19:03Z"}],"graph_snapshots":[{"event_id":"sha256:f2b9f880fc942c3827c24227c77018897be4eca0af79e018a848cbef2037bb21","target":"graph","created_at":"2026-07-13T01:19:03Z","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/2607.09339/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Here we present PCPOP, a Julia package for polynomial optimization that supports non-commutative optimization, tracial polynomial optimization, trace polynomial optimization and state polynomial optimization. PCPOP fully supports exact arithmetic computations and incorporates convenient functionalities such as algebraic reductions based on Gr\\\"obner basis methods, automatized symmetrization via Wedderburn decompositions, and Jordan algebra reductions. As a distinguished feature, PCPOP implements a specialized framework for polynomial computations in partially commutative variables that provide","authors_text":"Abhishek Mishra, Mois\\'es Bermejo Mor\\'an","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-10T12:20:16Z","title":"PCPOP.jl: A Julia package for partially commutative polynomial optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09339","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:f6394aecef6748b4740dcebe68958df653024d7bb81eb08c498ce761be03c912","target":"record","created_at":"2026-07-13T01:19:03Z","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":"0611996e96114c30f444c3ae83dd4e3be43eafe176f70c00f9c7fbee0b883693","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-10T12:20:16Z","title_canon_sha256":"98f79c807708bcc33179ff1c428c3fae9e85a939a43e5817c141da7e09011a09"},"schema_version":"1.0","source":{"id":"2607.09339","kind":"arxiv","version":1}},"canonical_sha256":"d1ee6e663ba83b52f0d4937d6756641d37f3649507fb676ff3c83bc5359eb5f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1ee6e663ba83b52f0d4937d6756641d37f3649507fb676ff3c83bc5359eb5f6","first_computed_at":"2026-07-13T01:19:03.769614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:19:03.769614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KTKeUnhH/6LcdSPiD3lr1Y5HQ4n1BCfFwzA3LKmME+xNXbahO/n2bZTu/3vUzcr/GyZjx9CVvJW21TuIAZfsBg==","signature_status":"signed_v1","signed_at":"2026-07-13T01:19:03.772798Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6394aecef6748b4740dcebe68958df653024d7bb81eb08c498ce761be03c912","sha256:f2b9f880fc942c3827c24227c77018897be4eca0af79e018a848cbef2037bb21"],"state_sha256":"7e647a2b2945a9c84928b739ff1bd3687ecfc426d56ab7399c6d2829fa08bce7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8i+ipVVjLYvNv4wfKn8/BPaY6kT8QghPwM+A54zp3V+i8M+JzJEM7z8YXV9cZA8bKg3RURJlna1Sj4s55IoDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:08:46.729062Z","bundle_sha256":"b80b6010fa2216ccdfab95a8cc5e6ad92ad695f96f4c3492ff3871057d08df9b"}}