{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FNMQLV4L3K4JR4ZF2SE2LNSM72","short_pith_number":"pith:FNMQLV4L","canonical_record":{"source":{"id":"2211.13156","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-11-23T17:32:10Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e31867a2bca14e3e1968eb505f1ff911022229305c5eb4342eef83f87c23ce53","abstract_canon_sha256":"111148a1ef02caf8fb3b323e8d0ed4ee5d4e8a01aefdff3dde682bd17921445e"},"schema_version":"1.0"},"canonical_sha256":"2b5905d78bdab898f325d489a5b64cfebbd499b518016223ea3d4f60c15ecb58","source":{"kind":"arxiv","id":"2211.13156","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.13156","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"arxiv_version","alias_value":"2211.13156v3","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.13156","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"pith_short_12","alias_value":"FNMQLV4L3K4J","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"pith_short_16","alias_value":"FNMQLV4L3K4JR4ZF","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"pith_short_8","alias_value":"FNMQLV4L","created_at":"2026-07-05T10:20:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FNMQLV4L3K4JR4ZF2SE2LNSM72","target":"record","payload":{"canonical_record":{"source":{"id":"2211.13156","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-11-23T17:32:10Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e31867a2bca14e3e1968eb505f1ff911022229305c5eb4342eef83f87c23ce53","abstract_canon_sha256":"111148a1ef02caf8fb3b323e8d0ed4ee5d4e8a01aefdff3dde682bd17921445e"},"schema_version":"1.0"},"canonical_sha256":"2b5905d78bdab898f325d489a5b64cfebbd499b518016223ea3d4f60c15ecb58","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:34.317597Z","signature_b64":"sKbvxZdk4+VaqmxlIXSbNMkPhfNB8gX4J7dy0pMR1co6HUkyg9wppmnU7bhaVwPMuL0UIHnbDVigk9PJtdIJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b5905d78bdab898f325d489a5b64cfebbd499b518016223ea3d4f60c15ecb58","last_reissued_at":"2026-07-05T10:20:34.317157Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:34.317157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.13156","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":"2026-07-05T10:20:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVyK55bZNuHHcxN04oy6UMk/lGVC3D+Q4hVdY8DaJ1cTdsKUpg4rwdmf7c9cs55TFKkIEKt9QKqroKj+CgPnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T20:18:21.965739Z"},"content_sha256":"bf89527496cd4cfa55ab470d8438b67044a45f064e590fdc5d5b56cd7597b757","schema_version":"1.0","event_id":"sha256:bf89527496cd4cfa55ab470d8438b67044a45f064e590fdc5d5b56cd7597b757"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FNMQLV4L3K4JR4ZF2SE2LNSM72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ideal classes of orders in quaternion algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Harry Smit, Stefano Marseglia","submitted_at":"2022-11-23T17:32:10Z","abstract_excerpt":"We provide an algorithm that, given any order $O$ in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right $O$-ideals, including the non-invertible ones. The theory is developed for a more general kind of algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.13156","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.13156/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:20:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wv0R5kY7TZ8o7uppXAzmYfKt+OB7uyyMwGWPzwfDmB2Sg1d0GXJY61srhUA8oQPKGEQoZOZG4HV9QQ1YIfpNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T20:18:21.966565Z"},"content_sha256":"e756dc36e0a81e5944ea68cd951ce78a18a90fef766115bea1cd8379679f48d8","schema_version":"1.0","event_id":"sha256:e756dc36e0a81e5944ea68cd951ce78a18a90fef766115bea1cd8379679f48d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FNMQLV4L3K4JR4ZF2SE2LNSM72/bundle.json","state_url":"https://pith.science/pith/FNMQLV4L3K4JR4ZF2SE2LNSM72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FNMQLV4L3K4JR4ZF2SE2LNSM72/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":"2026-08-22T20:18:21Z","links":{"resolver":"https://pith.science/pith/FNMQLV4L3K4JR4ZF2SE2LNSM72","bundle":"https://pith.science/pith/FNMQLV4L3K4JR4ZF2SE2LNSM72/bundle.json","state":"https://pith.science/pith/FNMQLV4L3K4JR4ZF2SE2LNSM72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FNMQLV4L3K4JR4ZF2SE2LNSM72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FNMQLV4L3K4JR4ZF2SE2LNSM72","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":"111148a1ef02caf8fb3b323e8d0ed4ee5d4e8a01aefdff3dde682bd17921445e","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-11-23T17:32:10Z","title_canon_sha256":"e31867a2bca14e3e1968eb505f1ff911022229305c5eb4342eef83f87c23ce53"},"schema_version":"1.0","source":{"id":"2211.13156","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.13156","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"arxiv_version","alias_value":"2211.13156v3","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.13156","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"pith_short_12","alias_value":"FNMQLV4L3K4J","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"pith_short_16","alias_value":"FNMQLV4L3K4JR4ZF","created_at":"2026-07-05T10:20:34Z"},{"alias_kind":"pith_short_8","alias_value":"FNMQLV4L","created_at":"2026-07-05T10:20:34Z"}],"graph_snapshots":[{"event_id":"sha256:e756dc36e0a81e5944ea68cd951ce78a18a90fef766115bea1cd8379679f48d8","target":"graph","created_at":"2026-07-05T10:20:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.13156/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide an algorithm that, given any order $O$ in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right $O$-ideals, including the non-invertible ones. The theory is developed for a more general kind of algebras.","authors_text":"Harry Smit, Stefano Marseglia","cross_cats":["math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-11-23T17:32:10Z","title":"Ideal classes of orders in quaternion algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.13156","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:bf89527496cd4cfa55ab470d8438b67044a45f064e590fdc5d5b56cd7597b757","target":"record","created_at":"2026-07-05T10:20:34Z","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":"111148a1ef02caf8fb3b323e8d0ed4ee5d4e8a01aefdff3dde682bd17921445e","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-11-23T17:32:10Z","title_canon_sha256":"e31867a2bca14e3e1968eb505f1ff911022229305c5eb4342eef83f87c23ce53"},"schema_version":"1.0","source":{"id":"2211.13156","kind":"arxiv","version":3}},"canonical_sha256":"2b5905d78bdab898f325d489a5b64cfebbd499b518016223ea3d4f60c15ecb58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b5905d78bdab898f325d489a5b64cfebbd499b518016223ea3d4f60c15ecb58","first_computed_at":"2026-07-05T10:20:34.317157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:20:34.317157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sKbvxZdk4+VaqmxlIXSbNMkPhfNB8gX4J7dy0pMR1co6HUkyg9wppmnU7bhaVwPMuL0UIHnbDVigk9PJtdIJCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:20:34.317597Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.13156","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf89527496cd4cfa55ab470d8438b67044a45f064e590fdc5d5b56cd7597b757","sha256:e756dc36e0a81e5944ea68cd951ce78a18a90fef766115bea1cd8379679f48d8"],"state_sha256":"0479b4eecf6e5a88459e6f3c5ab398823c9cf74f6615679a85215bd81982fc76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UVGkL99F8XaLDSKyFmiBhHJjqbBZMa0+ncc5XmJLwJ7d+F1m6Sf9QIxJFOf6lyLX6vQtcF+qefyzbh9QNtQwDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T20:18:21.973304Z","bundle_sha256":"cbee321e1501a716977695fec09cc0d9031a5714d58f24b3712643ea7f57e5c6"}}