{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RDRREBRANOVEGQDLV7Z5UD5W6C","short_pith_number":"pith:RDRREBRA","canonical_record":{"source":{"id":"1003.1864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-03-09T13:04:11Z","cross_cats_sorted":[],"title_canon_sha256":"dd7659e8f3ae7f1b6032d7bd5b2344bb520a61f8a24db1ce9d7ba180c5357eae","abstract_canon_sha256":"c3112bdaa5afb37c8354d323ded33c8fc4d7ce334703a27ea9d9ed44b9b2e139"},"schema_version":"1.0"},"canonical_sha256":"88e31206206baa43406baff3da0fb6f0b370fd3cd99b497789708618e60e8688","source":{"kind":"arxiv","id":"1003.1864","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1864","created_at":"2026-05-18T01:23:39Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1864v1","created_at":"2026-05-18T01:23:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1864","created_at":"2026-05-18T01:23:39Z"},{"alias_kind":"pith_short_12","alias_value":"RDRREBRANOVE","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RDRREBRANOVEGQDL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RDRREBRA","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RDRREBRANOVEGQDLV7Z5UD5W6C","target":"record","payload":{"canonical_record":{"source":{"id":"1003.1864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-03-09T13:04:11Z","cross_cats_sorted":[],"title_canon_sha256":"dd7659e8f3ae7f1b6032d7bd5b2344bb520a61f8a24db1ce9d7ba180c5357eae","abstract_canon_sha256":"c3112bdaa5afb37c8354d323ded33c8fc4d7ce334703a27ea9d9ed44b9b2e139"},"schema_version":"1.0"},"canonical_sha256":"88e31206206baa43406baff3da0fb6f0b370fd3cd99b497789708618e60e8688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:39.399734Z","signature_b64":"YXVaHSm5km5omiOCEjqXaeOcVTGYomJwlYFqFaZ1qyL13ThcYyQJZqrLYVFfRabN63AkidZIo+0TdmLu8wQeDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88e31206206baa43406baff3da0fb6f0b370fd3cd99b497789708618e60e8688","last_reissued_at":"2026-05-18T01:23:39.399082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:39.399082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.1864","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":"2026-05-18T01:23:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7E6M50sXC609ocurK6WaMpIVCo6jC+3Oua2PGVxu7gxzMwkvut7AYAvTTyvxYiIXa6ZvDYHDdzbhkVKVolKOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:46:54.923364Z"},"content_sha256":"78e102c84adaeb69b59611a350ad07f11c153adc80ae5374b90847d9db9a65bf","schema_version":"1.0","event_id":"sha256:78e102c84adaeb69b59611a350ad07f11c153adc80ae5374b90847d9db9a65bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RDRREBRANOVEGQDLV7Z5UD5W6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the tensor rank of multiplication in any extension of $\\F_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Julia Pieltant, St\\'ephane Ballet","submitted_at":"2010-03-09T13:04:11Z","abstract_excerpt":"In this paper, we obtain new bounds for the tensor rank of multiplication in any extension of $\\F_2$. In particular, it also enables us to obtain the best known asymptotic bound. In this aim, we use the generalized algorithm of type Chudnovsky with derivative evaluations on places of degree one, two and four applied on  the descent over $\\F_2$ of a Garcia-Stichtenoth tower of algebraic function fields defined over $\\F_{2^4}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1864","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":"2026-05-18T01:23:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e2R3yyZLFpAEdxcqu6k4r0hmmtMBqhdcswrdvMrEjXn2us0q6EIx/DJd80DaNX/9vo5VfZ1NdmCD1Oc65ktGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:46:54.924005Z"},"content_sha256":"1acf3724a2d20a5669f48f0582acd8099f9f602f945e2a000e428dd0783eb970","schema_version":"1.0","event_id":"sha256:1acf3724a2d20a5669f48f0582acd8099f9f602f945e2a000e428dd0783eb970"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDRREBRANOVEGQDLV7Z5UD5W6C/bundle.json","state_url":"https://pith.science/pith/RDRREBRANOVEGQDLV7Z5UD5W6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDRREBRANOVEGQDLV7Z5UD5W6C/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":"2026-05-28T17:46:54Z","links":{"resolver":"https://pith.science/pith/RDRREBRANOVEGQDLV7Z5UD5W6C","bundle":"https://pith.science/pith/RDRREBRANOVEGQDLV7Z5UD5W6C/bundle.json","state":"https://pith.science/pith/RDRREBRANOVEGQDLV7Z5UD5W6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDRREBRANOVEGQDLV7Z5UD5W6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RDRREBRANOVEGQDLV7Z5UD5W6C","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":"c3112bdaa5afb37c8354d323ded33c8fc4d7ce334703a27ea9d9ed44b9b2e139","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-03-09T13:04:11Z","title_canon_sha256":"dd7659e8f3ae7f1b6032d7bd5b2344bb520a61f8a24db1ce9d7ba180c5357eae"},"schema_version":"1.0","source":{"id":"1003.1864","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1864","created_at":"2026-05-18T01:23:39Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1864v1","created_at":"2026-05-18T01:23:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1864","created_at":"2026-05-18T01:23:39Z"},{"alias_kind":"pith_short_12","alias_value":"RDRREBRANOVE","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RDRREBRANOVEGQDL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RDRREBRA","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:1acf3724a2d20a5669f48f0582acd8099f9f602f945e2a000e428dd0783eb970","target":"graph","created_at":"2026-05-18T01:23:39Z","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":"In this paper, we obtain new bounds for the tensor rank of multiplication in any extension of $\\F_2$. In particular, it also enables us to obtain the best known asymptotic bound. In this aim, we use the generalized algorithm of type Chudnovsky with derivative evaluations on places of degree one, two and four applied on  the descent over $\\F_2$ of a Garcia-Stichtenoth tower of algebraic function fields defined over $\\F_{2^4}$.","authors_text":"Julia Pieltant, St\\'ephane Ballet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-03-09T13:04:11Z","title":"On the tensor rank of multiplication in any extension of $\\F_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1864","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":"sha256:78e102c84adaeb69b59611a350ad07f11c153adc80ae5374b90847d9db9a65bf","target":"record","created_at":"2026-05-18T01:23:39Z","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":"c3112bdaa5afb37c8354d323ded33c8fc4d7ce334703a27ea9d9ed44b9b2e139","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-03-09T13:04:11Z","title_canon_sha256":"dd7659e8f3ae7f1b6032d7bd5b2344bb520a61f8a24db1ce9d7ba180c5357eae"},"schema_version":"1.0","source":{"id":"1003.1864","kind":"arxiv","version":1}},"canonical_sha256":"88e31206206baa43406baff3da0fb6f0b370fd3cd99b497789708618e60e8688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88e31206206baa43406baff3da0fb6f0b370fd3cd99b497789708618e60e8688","first_computed_at":"2026-05-18T01:23:39.399082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:39.399082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXVaHSm5km5omiOCEjqXaeOcVTGYomJwlYFqFaZ1qyL13ThcYyQJZqrLYVFfRabN63AkidZIo+0TdmLu8wQeDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:39.399734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1864","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78e102c84adaeb69b59611a350ad07f11c153adc80ae5374b90847d9db9a65bf","sha256:1acf3724a2d20a5669f48f0582acd8099f9f602f945e2a000e428dd0783eb970"],"state_sha256":"a8ccc9b269797f789f1890736a228780d6c0ffc0e2f5305f4d2e381a29dfb5eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1QkKkwPiDpKRCY+vvUYMlP7ZJtNQHCLHrJBfhWkuLqzGRbUxD7H0hUd4LJHWfIflmMglxjXEocRgThzhc1TIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:46:54.927669Z","bundle_sha256":"a64e8119ae11be1ee928004e0dc2ef1558887a994a7f42b436f15d021e1a72c7"}}