{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YESF3TRFZBBYHMNRTKBG62BOIB","short_pith_number":"pith:YESF3TRF","canonical_record":{"source":{"id":"1612.01582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-12-05T22:43:38Z","cross_cats_sorted":[],"title_canon_sha256":"f2e5a3d4ce4c9f6d7d7cd765052c53e840f54987edc803ad7733d7a8b503ecbd","abstract_canon_sha256":"6f94b80a193a326b41b8c4ea98d2b9323905249034f738eb31a170a0603c525e"},"schema_version":"1.0"},"canonical_sha256":"c1245dce25c84383b1b19a826f682e4047014657ef4d46b2ee4203f1456535c3","source":{"kind":"arxiv","id":"1612.01582","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01582","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01582v1","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01582","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"pith_short_12","alias_value":"YESF3TRFZBBY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YESF3TRFZBBYHMNR","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YESF3TRF","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YESF3TRFZBBYHMNRTKBG62BOIB","target":"record","payload":{"canonical_record":{"source":{"id":"1612.01582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-12-05T22:43:38Z","cross_cats_sorted":[],"title_canon_sha256":"f2e5a3d4ce4c9f6d7d7cd765052c53e840f54987edc803ad7733d7a8b503ecbd","abstract_canon_sha256":"6f94b80a193a326b41b8c4ea98d2b9323905249034f738eb31a170a0603c525e"},"schema_version":"1.0"},"canonical_sha256":"c1245dce25c84383b1b19a826f682e4047014657ef4d46b2ee4203f1456535c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:48.134211Z","signature_b64":"FwO/UtdZzYE6/Ki9b0hvQbkueWjX/EX65qH78I6PnnFBZlJbPzLrPJ3X+b87UaTiaKNIgoGmNdCkmTaLVduhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1245dce25c84383b1b19a826f682e4047014657ef4d46b2ee4203f1456535c3","last_reissued_at":"2026-05-18T00:55:48.133499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:48.133499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.01582","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M97yiazPB9Niru6DI6ALc4vSxYQvKpb6gNgJUtf4OWB7kPJrpjo1sTCE+rPU7G0NzGAIV/+xgu7IlV5LY+YzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:52:20.247864Z"},"content_sha256":"ef1f072ddb70eb9223d5ee4d40322acae4d6bff44dc5e00ebe1dc031d75e359c","schema_version":"1.0","event_id":"sha256:ef1f072ddb70eb9223d5ee4d40322acae4d6bff44dc5e00ebe1dc031d75e359c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YESF3TRFZBBYHMNRTKBG62BOIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isomorphisms of Discriminant Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alberto Gioia, Owen Biesel","submitted_at":"2016-12-05T22:43:38Z","abstract_excerpt":"For each natural number $n$, we define a category whose objects are discriminant algebras in rank $n$, i.e. functorial means of attaching to each rank-$n$ algebra a quadratic algebra with the same discriminant. We show that the discriminant algebras defined in [2], [6], and [10] are all isomorphic in this category, and prove furthermore that in ranks $n \\leq 3$ discriminant algebras are unique up to unique isomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01582","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doCz67BnbWwROJKa0XtjosyDr9+jZ6Y5sVvP1XR1I7+zC2s9tclWjfi15wv1rYQgl1BRV8X6RBz8pKBkiNGdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:52:20.248209Z"},"content_sha256":"cb335725404c9977e6482d06f87aff547e67e45f3b79ed262eebd1b52f741924","schema_version":"1.0","event_id":"sha256:cb335725404c9977e6482d06f87aff547e67e45f3b79ed262eebd1b52f741924"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YESF3TRFZBBYHMNRTKBG62BOIB/bundle.json","state_url":"https://pith.science/pith/YESF3TRFZBBYHMNRTKBG62BOIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YESF3TRFZBBYHMNRTKBG62BOIB/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":"2026-06-08T12:52:20Z","links":{"resolver":"https://pith.science/pith/YESF3TRFZBBYHMNRTKBG62BOIB","bundle":"https://pith.science/pith/YESF3TRFZBBYHMNRTKBG62BOIB/bundle.json","state":"https://pith.science/pith/YESF3TRFZBBYHMNRTKBG62BOIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YESF3TRFZBBYHMNRTKBG62BOIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YESF3TRFZBBYHMNRTKBG62BOIB","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":"6f94b80a193a326b41b8c4ea98d2b9323905249034f738eb31a170a0603c525e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-12-05T22:43:38Z","title_canon_sha256":"f2e5a3d4ce4c9f6d7d7cd765052c53e840f54987edc803ad7733d7a8b503ecbd"},"schema_version":"1.0","source":{"id":"1612.01582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01582","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01582v1","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01582","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"pith_short_12","alias_value":"YESF3TRFZBBY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YESF3TRFZBBYHMNR","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YESF3TRF","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:cb335725404c9977e6482d06f87aff547e67e45f3b79ed262eebd1b52f741924","target":"graph","created_at":"2026-05-18T00:55:48Z","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":"For each natural number $n$, we define a category whose objects are discriminant algebras in rank $n$, i.e. functorial means of attaching to each rank-$n$ algebra a quadratic algebra with the same discriminant. We show that the discriminant algebras defined in [2], [6], and [10] are all isomorphic in this category, and prove furthermore that in ranks $n \\leq 3$ discriminant algebras are unique up to unique isomorphism.","authors_text":"Alberto Gioia, Owen Biesel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-12-05T22:43:38Z","title":"Isomorphisms of Discriminant Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01582","kind":"arxiv","version":1},"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:ef1f072ddb70eb9223d5ee4d40322acae4d6bff44dc5e00ebe1dc031d75e359c","target":"record","created_at":"2026-05-18T00:55:48Z","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":"6f94b80a193a326b41b8c4ea98d2b9323905249034f738eb31a170a0603c525e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-12-05T22:43:38Z","title_canon_sha256":"f2e5a3d4ce4c9f6d7d7cd765052c53e840f54987edc803ad7733d7a8b503ecbd"},"schema_version":"1.0","source":{"id":"1612.01582","kind":"arxiv","version":1}},"canonical_sha256":"c1245dce25c84383b1b19a826f682e4047014657ef4d46b2ee4203f1456535c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1245dce25c84383b1b19a826f682e4047014657ef4d46b2ee4203f1456535c3","first_computed_at":"2026-05-18T00:55:48.133499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:48.133499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FwO/UtdZzYE6/Ki9b0hvQbkueWjX/EX65qH78I6PnnFBZlJbPzLrPJ3X+b87UaTiaKNIgoGmNdCkmTaLVduhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:48.134211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef1f072ddb70eb9223d5ee4d40322acae4d6bff44dc5e00ebe1dc031d75e359c","sha256:cb335725404c9977e6482d06f87aff547e67e45f3b79ed262eebd1b52f741924"],"state_sha256":"e721c3b293e192d6373e14126c663708d64202050d09a808182793d5ea021d9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uo72Qt69LBf5n28wksvc1l4q1l1slDapDb3lfSP+Vea26xeBc/pwKTFynRNh3o4gIq2wQ32RiJOa9MkKiYTsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:52:20.250445Z","bundle_sha256":"4a71c43c9a95938b09d4a0c4cd026646fc318ee31c8594f2bd39650e4d7b19ce"}}