{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7YRIAA7RVAEFBLLNCBL322SSUS","short_pith_number":"pith:7YRIAA7R","canonical_record":{"source":{"id":"1106.6191","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:27:48Z","cross_cats_sorted":["cs.SC","math.NT"],"title_canon_sha256":"2ac5154d2852fea5adf0b9285c22fda988028298b7c3c4c255261d49e05e715a","abstract_canon_sha256":"d29899e61c71908771820453b78a0d0d6a7a76197ceb8f36ebfbc0d4ca8f721b"},"schema_version":"1.0"},"canonical_sha256":"fe228003f1a80850ad6d1057bd6a52a4bbbf299ce8b775e1253df18f3b196b31","source":{"kind":"arxiv","id":"1106.6191","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6191","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6191v3","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6191","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"7YRIAA7RVAEF","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7YRIAA7RVAEFBLLN","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7YRIAA7R","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7YRIAA7RVAEFBLLNCBL322SSUS","target":"record","payload":{"canonical_record":{"source":{"id":"1106.6191","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:27:48Z","cross_cats_sorted":["cs.SC","math.NT"],"title_canon_sha256":"2ac5154d2852fea5adf0b9285c22fda988028298b7c3c4c255261d49e05e715a","abstract_canon_sha256":"d29899e61c71908771820453b78a0d0d6a7a76197ceb8f36ebfbc0d4ca8f721b"},"schema_version":"1.0"},"canonical_sha256":"fe228003f1a80850ad6d1057bd6a52a4bbbf299ce8b775e1253df18f3b196b31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:57.610557Z","signature_b64":"F6TjVdCDTU+CU+0Ld7M/glY6KvM42aZ7LlciHkTWz6asFH0ImW7oPDes30Bo594rBvA6u0qDOZ85P2EOy5BpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe228003f1a80850ad6d1057bd6a52a4bbbf299ce8b775e1253df18f3b196b31","last_reissued_at":"2026-05-18T04:05:57.609999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:57.609999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.6191","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GmIQW1fKaQwAilWimNkj7GoYAaffrhUEHW0gnVLjFn/+oR55EQJxfwlpk/JLvTDqb/1jB2Zj4Qn5SYBvg3MYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:50:23.087056Z"},"content_sha256":"751547ab7e68a5b9cfca5fff8c44bccedcc2192626e6b57752f98404ff10becb","schema_version":"1.0","event_id":"sha256:751547ab7e68a5b9cfca5fff8c44bccedcc2192626e6b57752f98404ff10becb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7YRIAA7RVAEFBLLNCBL322SSUS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Splitting full matrix algebras over algebraic number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NT"],"primary_cat":"math.RA","authors_text":"G\\'abor Ivanyos, Josef Schicho, Lajos R\\'onyai","submitted_at":"2011-06-30T11:27:48Z","abstract_excerpt":"Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(K) can be constructed by a polynomial time ff-algorithm. (An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.)\n  As a consequence, we obtain a polynomial time ff-algorithm to com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6191","kind":"arxiv","version":3},"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":"2026-05-18T04:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7PamLo8xWVuCQJtUKR99R+zEC2cIwjlO3PZCAcvHVCd6Pt+JnguPtnhCfrc43BUBvUiOKHPPz7KJmmGfjrT9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:50:23.087780Z"},"content_sha256":"fadf6fc948a8244b21e761e15cd9fbedaa38f1905fdbb56cee117e0e60ab3286","schema_version":"1.0","event_id":"sha256:fadf6fc948a8244b21e761e15cd9fbedaa38f1905fdbb56cee117e0e60ab3286"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7YRIAA7RVAEFBLLNCBL322SSUS/bundle.json","state_url":"https://pith.science/pith/7YRIAA7RVAEFBLLNCBL322SSUS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7YRIAA7RVAEFBLLNCBL322SSUS/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":"2026-05-29T15:50:23Z","links":{"resolver":"https://pith.science/pith/7YRIAA7RVAEFBLLNCBL322SSUS","bundle":"https://pith.science/pith/7YRIAA7RVAEFBLLNCBL322SSUS/bundle.json","state":"https://pith.science/pith/7YRIAA7RVAEFBLLNCBL322SSUS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7YRIAA7RVAEFBLLNCBL322SSUS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7YRIAA7RVAEFBLLNCBL322SSUS","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":"d29899e61c71908771820453b78a0d0d6a7a76197ceb8f36ebfbc0d4ca8f721b","cross_cats_sorted":["cs.SC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:27:48Z","title_canon_sha256":"2ac5154d2852fea5adf0b9285c22fda988028298b7c3c4c255261d49e05e715a"},"schema_version":"1.0","source":{"id":"1106.6191","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6191","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6191v3","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6191","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"7YRIAA7RVAEF","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7YRIAA7RVAEFBLLN","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7YRIAA7R","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:fadf6fc948a8244b21e761e15cd9fbedaa38f1905fdbb56cee117e0e60ab3286","target":"graph","created_at":"2026-05-18T04:05:57Z","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":"Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(K) can be constructed by a polynomial time ff-algorithm. (An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.)\n  As a consequence, we obtain a polynomial time ff-algorithm to com","authors_text":"G\\'abor Ivanyos, Josef Schicho, Lajos R\\'onyai","cross_cats":["cs.SC","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:27:48Z","title":"Splitting full matrix algebras over algebraic number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6191","kind":"arxiv","version":3},"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":"sha256:751547ab7e68a5b9cfca5fff8c44bccedcc2192626e6b57752f98404ff10becb","target":"record","created_at":"2026-05-18T04:05:57Z","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":"d29899e61c71908771820453b78a0d0d6a7a76197ceb8f36ebfbc0d4ca8f721b","cross_cats_sorted":["cs.SC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-30T11:27:48Z","title_canon_sha256":"2ac5154d2852fea5adf0b9285c22fda988028298b7c3c4c255261d49e05e715a"},"schema_version":"1.0","source":{"id":"1106.6191","kind":"arxiv","version":3}},"canonical_sha256":"fe228003f1a80850ad6d1057bd6a52a4bbbf299ce8b775e1253df18f3b196b31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe228003f1a80850ad6d1057bd6a52a4bbbf299ce8b775e1253df18f3b196b31","first_computed_at":"2026-05-18T04:05:57.609999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:57.609999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F6TjVdCDTU+CU+0Ld7M/glY6KvM42aZ7LlciHkTWz6asFH0ImW7oPDes30Bo594rBvA6u0qDOZ85P2EOy5BpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:57.610557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.6191","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:751547ab7e68a5b9cfca5fff8c44bccedcc2192626e6b57752f98404ff10becb","sha256:fadf6fc948a8244b21e761e15cd9fbedaa38f1905fdbb56cee117e0e60ab3286"],"state_sha256":"68dbb67ce545d24d497dba1389be2512dcd2a778e5dfb64862fd611a0a60c757"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7oCL3g7RuCMcy1oaPnST2fO+Iu634smh07t1WooUz2CD5IPkJWxv6TLsy372K2bgTLqrad/8UNq4s9TDk3ohBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:50:23.090849Z","bundle_sha256":"36d8ab0c58c5d174c0cbfe5d75fad519818658a2072e08129f48f04705876295"}}