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The d-dimensional WL-algorithm can distinguish many pairs of graphs, but the pairs of non-isomorphic graphs constructed by Cai, Furer and Immerman it cannot distinguish. If d is fixed, then the WL-algorithm runs in polynomial time. We will formulate the Graph Isomorphism Problem as an Orbit Problem: Given a representation V of an algebraic group G and two elements v_1,v_2 in V, decide whether v_1 and v_2 lie i"},"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":"1012.2081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-09T19:02:45Z","cross_cats_sorted":["cs.CC","math.AC","math.RA"],"title_canon_sha256":"0d660731a57f2da607942848674fe7d52d8901e2b453b757b8131e859c47762e","abstract_canon_sha256":"1e9a95051c1a67bd88d9402ac8df018a3208e10c369fc85a825a8bd1a8939217"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:49.033693Z","signature_b64":"b5iHtStFzvVho3C4z2tbiqvlaLHlQx4JvMhmbBJu16ZZHgbZZqmEA3HWPjFIB/okCnd/nnaZmXm9jeZ+JQqmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5510cc74524b6dc93e432d9159febb95b1c5e2324eedec8a31f2176f23c100d1","last_reissued_at":"2026-05-18T04:33:49.033164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:49.033164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Graph Isomorphism Problem and approximate categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AC","math.RA"],"primary_cat":"math.CO","authors_text":"Harm Derksen","submitted_at":"2010-12-09T19:02:45Z","abstract_excerpt":"It is unknown whether two graphs can be tested for isomorphism in polynomial time. 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