{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YEGDMJZ7U52JVM6UELZQPGXLRR","short_pith_number":"pith:YEGDMJZ7","canonical_record":{"source":{"id":"2608.04668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-08-05T10:28:08Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"30ba81656a78150c4cae107f57c7a9617a6188abf41bf3273ada2c7cf697e300","abstract_canon_sha256":"059eed9f3bc47b6f51419f11b835a450165142d6e2b1ac68d6f48ac3905d0da4"},"schema_version":"1.0"},"canonical_sha256":"c10c36273fa7749ab3d422f3079aeb8c4854f670c7dce148d05a8b1f75e921d6","source":{"kind":"arxiv","id":"2608.04668","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04668","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04668v1","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04668","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"YEGDMJZ7U52J","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"pith_short_16","alias_value":"YEGDMJZ7U52JVM6U","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"pith_short_8","alias_value":"YEGDMJZ7","created_at":"2026-08-06T01:46:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YEGDMJZ7U52JVM6UELZQPGXLRR","target":"record","payload":{"canonical_record":{"source":{"id":"2608.04668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-08-05T10:28:08Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"30ba81656a78150c4cae107f57c7a9617a6188abf41bf3273ada2c7cf697e300","abstract_canon_sha256":"059eed9f3bc47b6f51419f11b835a450165142d6e2b1ac68d6f48ac3905d0da4"},"schema_version":"1.0"},"canonical_sha256":"c10c36273fa7749ab3d422f3079aeb8c4854f670c7dce148d05a8b1f75e921d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:46:07.968646Z","signature_b64":"6HdEnaSEJ2SWsViRDogYYcPgd2FwWmbOlyJZ3N1TXBO2N6zLPUoFLXpbFTdcSM3ZpCybY/EDzz0Xw7nU9p2KBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c10c36273fa7749ab3d422f3079aeb8c4854f670c7dce148d05a8b1f75e921d6","last_reissued_at":"2026-08-06T01:46:07.967088Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:46:07.967088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.04668","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":"2026-08-06T01:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"trSNePnwS9uF9CdvjWmzVw5TjPcESgV0xkMDRWn2bDOUkJE1fdQFGLNaNHIAl+MvVqbng5LRuYH8l7FcmXelDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T05:51:57.163201Z"},"content_sha256":"b04624ab9ef07924eb44f372c3f269b5ca1b744e25645aa852322b07433242cb","schema_version":"1.0","event_id":"sha256:b04624ab9ef07924eb44f372c3f269b5ca1b744e25645aa852322b07433242cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YEGDMJZ7U52JVM6UELZQPGXLRR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Composition algebras in symmetric tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Alberto Elduque, Javier R\\'andez-Ib\\'a\\~nez","submitted_at":"2026-08-05T10:28:08Z","abstract_excerpt":"Composition algebras in symmetric tensor categories are defined. The classical results on standard unital composition algebras, as well as the classification of the unital composition superalgebras, are reviewed in light of this definition, and the unital composition algebras in the category $Ver_4^+$ (the counterpart to the category of vector superspaces in characteristic 2) are classified."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04668","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04668/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":"2026-08-06T01:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E6WfvaUH5JyO+5RL8Kzln8sXFstPAWtmCvsz/EqakNN3VarRowVYEgnco4GDbGSFdnC7VykXCmWE6CNnVnONAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T05:51:57.163718Z"},"content_sha256":"ca1996dfcdb69628aeb7df84af563162425d37eee3d76aa89dd04cc9700706d7","schema_version":"1.0","event_id":"sha256:ca1996dfcdb69628aeb7df84af563162425d37eee3d76aa89dd04cc9700706d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YEGDMJZ7U52JVM6UELZQPGXLRR/bundle.json","state_url":"https://pith.science/pith/YEGDMJZ7U52JVM6UELZQPGXLRR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YEGDMJZ7U52JVM6UELZQPGXLRR/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":"2026-08-19T05:51:57Z","links":{"resolver":"https://pith.science/pith/YEGDMJZ7U52JVM6UELZQPGXLRR","bundle":"https://pith.science/pith/YEGDMJZ7U52JVM6UELZQPGXLRR/bundle.json","state":"https://pith.science/pith/YEGDMJZ7U52JVM6UELZQPGXLRR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YEGDMJZ7U52JVM6UELZQPGXLRR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YEGDMJZ7U52JVM6UELZQPGXLRR","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":"059eed9f3bc47b6f51419f11b835a450165142d6e2b1ac68d6f48ac3905d0da4","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-08-05T10:28:08Z","title_canon_sha256":"30ba81656a78150c4cae107f57c7a9617a6188abf41bf3273ada2c7cf697e300"},"schema_version":"1.0","source":{"id":"2608.04668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04668","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04668v1","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04668","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"YEGDMJZ7U52J","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"pith_short_16","alias_value":"YEGDMJZ7U52JVM6U","created_at":"2026-08-06T01:46:07Z"},{"alias_kind":"pith_short_8","alias_value":"YEGDMJZ7","created_at":"2026-08-06T01:46:07Z"}],"graph_snapshots":[{"event_id":"sha256:ca1996dfcdb69628aeb7df84af563162425d37eee3d76aa89dd04cc9700706d7","target":"graph","created_at":"2026-08-06T01:46:07Z","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/2608.04668/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Composition algebras in symmetric tensor categories are defined. The classical results on standard unital composition algebras, as well as the classification of the unital composition superalgebras, are reviewed in light of this definition, and the unital composition algebras in the category $Ver_4^+$ (the counterpart to the category of vector superspaces in characteristic 2) are classified.","authors_text":"Alberto Elduque, Javier R\\'andez-Ib\\'a\\~nez","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-08-05T10:28:08Z","title":"Composition algebras in symmetric tensor categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04668","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:b04624ab9ef07924eb44f372c3f269b5ca1b744e25645aa852322b07433242cb","target":"record","created_at":"2026-08-06T01:46:07Z","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":"059eed9f3bc47b6f51419f11b835a450165142d6e2b1ac68d6f48ac3905d0da4","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-08-05T10:28:08Z","title_canon_sha256":"30ba81656a78150c4cae107f57c7a9617a6188abf41bf3273ada2c7cf697e300"},"schema_version":"1.0","source":{"id":"2608.04668","kind":"arxiv","version":1}},"canonical_sha256":"c10c36273fa7749ab3d422f3079aeb8c4854f670c7dce148d05a8b1f75e921d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c10c36273fa7749ab3d422f3079aeb8c4854f670c7dce148d05a8b1f75e921d6","first_computed_at":"2026-08-06T01:46:07.967088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-06T01:46:07.967088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6HdEnaSEJ2SWsViRDogYYcPgd2FwWmbOlyJZ3N1TXBO2N6zLPUoFLXpbFTdcSM3ZpCybY/EDzz0Xw7nU9p2KBQ==","signature_status":"signed_v1","signed_at":"2026-08-06T01:46:07.968646Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.04668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b04624ab9ef07924eb44f372c3f269b5ca1b744e25645aa852322b07433242cb","sha256:ca1996dfcdb69628aeb7df84af563162425d37eee3d76aa89dd04cc9700706d7"],"state_sha256":"a3b67a9b1c5d787bdc49f546f3ad5fb1c7f54b1782192f45cf62ab725693343c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3zSuza2+53ydVVMw5wu3Gcyz5x8Lz9Rq2ymY7N0NnefcbQr0S/5em5Klvd/AOKaP73Ep1h87tZKM2zB7hXPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T05:51:57.170007Z","bundle_sha256":"1ad7e6ecbb457a97eb1f893561f3eb8893a35dfad1d9884f0da8bfa09d00145d"}}