{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QA3Y343DWLQYUKKRLTEXPMSS2P","short_pith_number":"pith:QA3Y343D","canonical_record":{"source":{"id":"1209.6544","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-28T15:29:57Z","cross_cats_sorted":[],"title_canon_sha256":"c0365f300fe1238c727cb217c6f9707c59b13f30da0852f32b0c266447f43d14","abstract_canon_sha256":"37b2687088e26c829d7fe61899d9a9c9c82592956dbf02bfac19ff6a228dc3ba"},"schema_version":"1.0"},"canonical_sha256":"80378df363b2e18a29515cc977b252d3dd37d84c8286e815f134639d2380f484","source":{"kind":"arxiv","id":"1209.6544","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6544","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6544v4","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6544","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"QA3Y343DWLQY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QA3Y343DWLQYUKKR","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QA3Y343D","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QA3Y343DWLQYUKKRLTEXPMSS2P","target":"record","payload":{"canonical_record":{"source":{"id":"1209.6544","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-28T15:29:57Z","cross_cats_sorted":[],"title_canon_sha256":"c0365f300fe1238c727cb217c6f9707c59b13f30da0852f32b0c266447f43d14","abstract_canon_sha256":"37b2687088e26c829d7fe61899d9a9c9c82592956dbf02bfac19ff6a228dc3ba"},"schema_version":"1.0"},"canonical_sha256":"80378df363b2e18a29515cc977b252d3dd37d84c8286e815f134639d2380f484","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:34.872390Z","signature_b64":"Y+uHMqUjWfnw6u5QVXmXG0mmF1ys63Zk6hHTojeqQidQy2W3JvajeSts1vNx/BEltKgDPWk+TqAie+pzqfQsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80378df363b2e18a29515cc977b252d3dd37d84c8286e815f134639d2380f484","last_reissued_at":"2026-05-18T00:05:34.871820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:34.871820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.6544","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"08xv5FsKLwq+v8t7JFgyDH1pdgQEaoW5CTRV4WJE0Q2lDGnURh+mbDK6JgX+WnE2nScVRFidz7psuexTgJZPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:19:47.520229Z"},"content_sha256":"f70526682d11af0bb7f01e90c21e9bfad82e32d960e56322d50b4e88a3fe809d","schema_version":"1.0","event_id":"sha256:f70526682d11af0bb7f01e90c21e9bfad82e32d960e56322d50b4e88a3fe809d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QA3Y343DWLQYUKKRLTEXPMSS2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-generated algebras and standard-form congruence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jason Gaddis","submitted_at":"2012-09-28T15:29:57Z","abstract_excerpt":"Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic polynomials. Canonical forms under standard-form congruence for three-by-three matrices are derived. This is then used to give a classification of algebras defined by two generators and one degree two relation. We also apply standard-form congruence to classify homogenizations of these algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6544","kind":"arxiv","version":4},"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":"2026-05-18T00:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0p76lXw6sNT3tAfQiwX7F6EUzz6BslPkJ51xxIaaW8cOaTQQNeC6zpMf5AW9gJqsyPe++ZiXnlMBdvHGWcwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:19:47.520930Z"},"content_sha256":"20fadfd0d5dac17a4e35f2d01bb2c2757aa73021c348d328a50a448d786dc79e","schema_version":"1.0","event_id":"sha256:20fadfd0d5dac17a4e35f2d01bb2c2757aa73021c348d328a50a448d786dc79e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QA3Y343DWLQYUKKRLTEXPMSS2P/bundle.json","state_url":"https://pith.science/pith/QA3Y343DWLQYUKKRLTEXPMSS2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QA3Y343DWLQYUKKRLTEXPMSS2P/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":"2026-06-08T17:19:47Z","links":{"resolver":"https://pith.science/pith/QA3Y343DWLQYUKKRLTEXPMSS2P","bundle":"https://pith.science/pith/QA3Y343DWLQYUKKRLTEXPMSS2P/bundle.json","state":"https://pith.science/pith/QA3Y343DWLQYUKKRLTEXPMSS2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QA3Y343DWLQYUKKRLTEXPMSS2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QA3Y343DWLQYUKKRLTEXPMSS2P","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":"37b2687088e26c829d7fe61899d9a9c9c82592956dbf02bfac19ff6a228dc3ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-28T15:29:57Z","title_canon_sha256":"c0365f300fe1238c727cb217c6f9707c59b13f30da0852f32b0c266447f43d14"},"schema_version":"1.0","source":{"id":"1209.6544","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6544","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6544v4","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6544","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"QA3Y343DWLQY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QA3Y343DWLQYUKKR","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QA3Y343D","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:20fadfd0d5dac17a4e35f2d01bb2c2757aa73021c348d328a50a448d786dc79e","target":"graph","created_at":"2026-05-18T00:05:34Z","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":"Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic polynomials. Canonical forms under standard-form congruence for three-by-three matrices are derived. This is then used to give a classification of algebras defined by two generators and one degree two relation. We also apply standard-form congruence to classify homogenizations of these algebras.","authors_text":"Jason Gaddis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-28T15:29:57Z","title":"Two-generated algebras and standard-form congruence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6544","kind":"arxiv","version":4},"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:f70526682d11af0bb7f01e90c21e9bfad82e32d960e56322d50b4e88a3fe809d","target":"record","created_at":"2026-05-18T00:05:34Z","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":"37b2687088e26c829d7fe61899d9a9c9c82592956dbf02bfac19ff6a228dc3ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-28T15:29:57Z","title_canon_sha256":"c0365f300fe1238c727cb217c6f9707c59b13f30da0852f32b0c266447f43d14"},"schema_version":"1.0","source":{"id":"1209.6544","kind":"arxiv","version":4}},"canonical_sha256":"80378df363b2e18a29515cc977b252d3dd37d84c8286e815f134639d2380f484","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80378df363b2e18a29515cc977b252d3dd37d84c8286e815f134639d2380f484","first_computed_at":"2026-05-18T00:05:34.871820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:34.871820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y+uHMqUjWfnw6u5QVXmXG0mmF1ys63Zk6hHTojeqQidQy2W3JvajeSts1vNx/BEltKgDPWk+TqAie+pzqfQsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:34.872390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.6544","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f70526682d11af0bb7f01e90c21e9bfad82e32d960e56322d50b4e88a3fe809d","sha256:20fadfd0d5dac17a4e35f2d01bb2c2757aa73021c348d328a50a448d786dc79e"],"state_sha256":"b51e550c5b37f23b5ef39ce3cabd777bee613bc63acdc21a9d67007ae611888a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4o+x845wybkAipDBqkzLQMZkwwV3o7Z2YwTyD9iE+w/XrVVt2HwLM14oBwAy2sSqYVfkCtiXxwIaZRGTp95JBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:19:47.524875Z","bundle_sha256":"db10069c7a82764507849ca0f3f02c65d818b65140a6e2a76d9eb8144a83676a"}}