{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BJW7QOQMBNIMGAX5QNOYRNWKBK","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":"3c09b110ca66cf845dadf7d19ad4a17d1e6262a04bf04cd1496c3c6493513372","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-22T10:42:07Z","title_canon_sha256":"40faf4a039b7e59451a7de00d26f913ebad8d291998bb2a72c3a38d1978f3bca"},"schema_version":"1.0","source":{"id":"1409.6136","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6136","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6136v2","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6136","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"pith_short_12","alias_value":"BJW7QOQMBNIM","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BJW7QOQMBNIMGAX5","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BJW7QOQM","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:e47a661d4be970b63b28f6295a38f10de64abdf6cd4b18f44959167e9c4d6e99","target":"graph","created_at":"2026-05-18T01:27:54Z","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":"Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate that.","authors_text":"Anupam Singh, Ayan Mahalanobis","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-22T10:42:07Z","title":"Gaussian elimination in unitary groups with an application to cryptography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6136","kind":"arxiv","version":2},"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":"sha256:8badb4ca76e3e2c3c494456221df7051d4c804e9d66176a6b2043cd6c5405850","target":"record","created_at":"2026-05-18T01:27:54Z","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":"3c09b110ca66cf845dadf7d19ad4a17d1e6262a04bf04cd1496c3c6493513372","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-22T10:42:07Z","title_canon_sha256":"40faf4a039b7e59451a7de00d26f913ebad8d291998bb2a72c3a38d1978f3bca"},"schema_version":"1.0","source":{"id":"1409.6136","kind":"arxiv","version":2}},"canonical_sha256":"0a6df83a0c0b50c302fd835d88b6ca0a8c0748caa5a6487840cc9b161169370d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a6df83a0c0b50c302fd835d88b6ca0a8c0748caa5a6487840cc9b161169370d","first_computed_at":"2026-05-18T01:27:54.639921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:54.639921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j+ICpqRhwWG5pVr700AJ7dpV0LdVc7YTCkg48ME9uZlKrIORt7riI3jrWu5ZkKVU5YvdLxNmf5vtzhp5KD44Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:54.640571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6136","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8badb4ca76e3e2c3c494456221df7051d4c804e9d66176a6b2043cd6c5405850","sha256:e47a661d4be970b63b28f6295a38f10de64abdf6cd4b18f44959167e9c4d6e99"],"state_sha256":"55ba4e4445d6bb659abe0185a024adb37778b7786e229b950949135e54aed53a"}