{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YVYZQA6OKRDXPJJDNE6EV3LBGX","short_pith_number":"pith:YVYZQA6O","schema_version":"1.0","canonical_sha256":"c5719803ce544777a523693c4aed6135d0367f42cc2a657fb43b2cbf0d9367ed","source":{"kind":"arxiv","id":"1509.00930","version":1},"attestation_state":"computed","paper":{"title":"Testing Properties of Functions on Finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kenta Oono, Yuichi Yoshida","submitted_at":"2015-09-03T03:27:55Z","abstract_excerpt":"We study testing properties of functions on finite groups. First we consider functions of the form $f:G \\to \\mathbb{C}$, where $G$ is a finite group. We show that conjugate invariance, homomorphism, and the property of being proportional to an irreducible character is testable with a constant number of queries to $f$, where a character is a crucial notion in representation theory. Our proof relies on representation theory and harmonic analysis on finite groups. Next we consider functions of the form $f: G \\to M_d(\\mathbb{C})$, where $d$ is a fixed constant and $M_d(\\mathbb{C})$ is the family o"},"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":"1509.00930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-03T03:27:55Z","cross_cats_sorted":[],"title_canon_sha256":"9937fd0667b8055779b92b0c8b84b4492c8d095c7a18b012a1997fbb5c600b3f","abstract_canon_sha256":"38c95ee4648a75e3e1ad3b3a53253748eece2c125e34adb0ffde6de0c75b6bd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:04.755871Z","signature_b64":"1LEJAQuQx4R/iLaIccycLUnvUnh+E95XFAsGaudTTncxyQIVQSy5shJKKbCvSP5tOUmQQ0sB9JYkqn2nyHUaBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5719803ce544777a523693c4aed6135d0367f42cc2a657fb43b2cbf0d9367ed","last_reissued_at":"2026-05-18T01:34:04.755433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:04.755433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Testing Properties of Functions on Finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kenta Oono, Yuichi Yoshida","submitted_at":"2015-09-03T03:27:55Z","abstract_excerpt":"We study testing properties of functions on finite groups. First we consider functions of the form $f:G \\to \\mathbb{C}$, where $G$ is a finite group. We show that conjugate invariance, homomorphism, and the property of being proportional to an irreducible character is testable with a constant number of queries to $f$, where a character is a crucial notion in representation theory. Our proof relies on representation theory and harmonic analysis on finite groups. Next we consider functions of the form $f: G \\to M_d(\\mathbb{C})$, where $d$ is a fixed constant and $M_d(\\mathbb{C})$ is the family o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00930","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.00930","created_at":"2026-05-18T01:34:04.755513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.00930v1","created_at":"2026-05-18T01:34:04.755513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00930","created_at":"2026-05-18T01:34:04.755513+00:00"},{"alias_kind":"pith_short_12","alias_value":"YVYZQA6OKRDX","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YVYZQA6OKRDXPJJD","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YVYZQA6O","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.05871","citing_title":"A General Framework for Low Soundness Homomorphism Testing","ref_index":2016,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX","json":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX.json","graph_json":"https://pith.science/api/pith-number/YVYZQA6OKRDXPJJDNE6EV3LBGX/graph.json","events_json":"https://pith.science/api/pith-number/YVYZQA6OKRDXPJJDNE6EV3LBGX/events.json","paper":"https://pith.science/paper/YVYZQA6O"},"agent_actions":{"view_html":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX","download_json":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX.json","view_paper":"https://pith.science/paper/YVYZQA6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.00930&json=true","fetch_graph":"https://pith.science/api/pith-number/YVYZQA6OKRDXPJJDNE6EV3LBGX/graph.json","fetch_events":"https://pith.science/api/pith-number/YVYZQA6OKRDXPJJDNE6EV3LBGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX/action/storage_attestation","attest_author":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX/action/author_attestation","sign_citation":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX/action/citation_signature","submit_replication":"https://pith.science/pith/YVYZQA6OKRDXPJJDNE6EV3LBGX/action/replication_record"}},"created_at":"2026-05-18T01:34:04.755513+00:00","updated_at":"2026-05-18T01:34:04.755513+00:00"}