{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MJWRNWHQZ7P7FYT3N3NRHLZ3DT","short_pith_number":"pith:MJWRNWHQ","schema_version":"1.0","canonical_sha256":"626d16d8f0cfdff2e27b6edb13af3b1ce8e15431da5f94f379b5a32ff5529891","source":{"kind":"arxiv","id":"2605.23830","version":1},"attestation_state":"computed","paper":{"title":"IntegrateUnitary.jl: A Julia package for symbolic integration over Haar measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.MS"],"primary_cat":"quant-ph","authors_text":"{\\L}ukasz Pawela, Zbigniew Pucha{\\l}a","submitted_at":"2026-05-22T16:36:35Z","abstract_excerpt":"Symbolic integration over the Haar measure of compact groups is a computational cornerstone in quantum information science and random matrix theory. We present \\texttt{IntegrateUnitary.jl}, a comprehensive Julia package for computing exact expectations of polynomial functions over a wide range of compact groups ($U(d)$, $O(d)$, $Sp(d)$, and $SU(d)$ for balanced polynomials), circular and Gaussian ensembles, Ginibre ensembles, permutation groups, random pure states, and unitary $t$-designs. The package provides a fully open-source implementation of the Weingarten calculus and Wick contractions "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.23830","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-05-22T16:36:35Z","cross_cats_sorted":["cs.MS"],"title_canon_sha256":"0336a654733a4e2108187ee184b436d7e8838b978f76fbfed73a4b7a154a3aae","abstract_canon_sha256":"461acca6158206b61440aa81d7453f7b37472f2ce7de091bee57385a2adcc37b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:34.467833Z","signature_b64":"tsgDK0OlkdZsviThyTouOH7MM8IkxRUs875GznCPiyMemM3nhk1z6FDwoxEGCBXgytoV+Z9Fru59ViCxmeObBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"626d16d8f0cfdff2e27b6edb13af3b1ce8e15431da5f94f379b5a32ff5529891","last_reissued_at":"2026-05-25T02:02:34.467059Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:34.467059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"IntegrateUnitary.jl: A Julia package for symbolic integration over Haar measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.MS"],"primary_cat":"quant-ph","authors_text":"{\\L}ukasz Pawela, Zbigniew Pucha{\\l}a","submitted_at":"2026-05-22T16:36:35Z","abstract_excerpt":"Symbolic integration over the Haar measure of compact groups is a computational cornerstone in quantum information science and random matrix theory. We present \\texttt{IntegrateUnitary.jl}, a comprehensive Julia package for computing exact expectations of polynomial functions over a wide range of compact groups ($U(d)$, $O(d)$, $Sp(d)$, and $SU(d)$ for balanced polynomials), circular and Gaussian ensembles, Ginibre ensembles, permutation groups, random pure states, and unitary $t$-designs. The package provides a fully open-source implementation of the Weingarten calculus and Wick contractions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23830","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/2605.23830/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.23830","created_at":"2026-05-25T02:02:34.467193+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.23830v1","created_at":"2026-05-25T02:02:34.467193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23830","created_at":"2026-05-25T02:02:34.467193+00:00"},{"alias_kind":"pith_short_12","alias_value":"MJWRNWHQZ7P7","created_at":"2026-05-25T02:02:34.467193+00:00"},{"alias_kind":"pith_short_16","alias_value":"MJWRNWHQZ7P7FYT3","created_at":"2026-05-25T02:02:34.467193+00:00"},{"alias_kind":"pith_short_8","alias_value":"MJWRNWHQ","created_at":"2026-05-25T02:02:34.467193+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT","json":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT.json","graph_json":"https://pith.science/api/pith-number/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/graph.json","events_json":"https://pith.science/api/pith-number/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/events.json","paper":"https://pith.science/paper/MJWRNWHQ"},"agent_actions":{"view_html":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT","download_json":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT.json","view_paper":"https://pith.science/paper/MJWRNWHQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.23830&json=true","fetch_graph":"https://pith.science/api/pith-number/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/graph.json","fetch_events":"https://pith.science/api/pith-number/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/action/storage_attestation","attest_author":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/action/author_attestation","sign_citation":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/action/citation_signature","submit_replication":"https://pith.science/pith/MJWRNWHQZ7P7FYT3N3NRHLZ3DT/action/replication_record"}},"created_at":"2026-05-25T02:02:34.467193+00:00","updated_at":"2026-05-25T02:02:34.467193+00:00"}