{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:LKHMDJ7QZJD2VB44FXVASIORSQ","short_pith_number":"pith:LKHMDJ7Q","canonical_record":{"source":{"id":"1002.1664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-08T17:44:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bc010f5bf5ccb5860a1b9bc68f7970621aa1c9d597391576fc10933261629d5f","abstract_canon_sha256":"8558ea00617e93f5245482ddfcc6aeb7b4ea134c243c4ccb8ac5d90b52b8fb93"},"schema_version":"1.0"},"canonical_sha256":"5a8ec1a7f0ca47aa879c2dea0921d1940b7141c69e46cb461aa08b7f186b77d4","source":{"kind":"arxiv","id":"1002.1664","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1664","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1664v2","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1664","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"LKHMDJ7QZJD2","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LKHMDJ7QZJD2VB44","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LKHMDJ7Q","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:LKHMDJ7QZJD2VB44FXVASIORSQ","target":"record","payload":{"canonical_record":{"source":{"id":"1002.1664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-08T17:44:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bc010f5bf5ccb5860a1b9bc68f7970621aa1c9d597391576fc10933261629d5f","abstract_canon_sha256":"8558ea00617e93f5245482ddfcc6aeb7b4ea134c243c4ccb8ac5d90b52b8fb93"},"schema_version":"1.0"},"canonical_sha256":"5a8ec1a7f0ca47aa879c2dea0921d1940b7141c69e46cb461aa08b7f186b77d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:23.820149Z","signature_b64":"PqV8aa9l5fRcXM0VfVTpzfYbgbjb8kRRtAs6irCa2Vm7KxpiRRc8ygh5DN4nw4yKJ26i5jAAeRjsdSi5RszrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a8ec1a7f0ca47aa879c2dea0921d1940b7141c69e46cb461aa08b7f186b77d4","last_reissued_at":"2026-05-18T02:44:23.819545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:23.819545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.1664","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3hiAJBEas9Q4EI28dOM+Ud+nA71lIj6bBO1lCodG53S7PM5QlqEqQ7VkzEVyXjc/hoIjC/CyR542mco+vZt2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:41:16.063229Z"},"content_sha256":"ea7d36533e93fa260b87a90f588bf84fc7a5936c60f523939f3cbd5822779bb6","schema_version":"1.0","event_id":"sha256:ea7d36533e93fa260b87a90f588bf84fc7a5936c60f523939f3cbd5822779bb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:LKHMDJ7QZJD2VB44FXVASIORSQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Alexander Yong, Edward Clifford, Hugh Thomas","submitted_at":"2010-02-08T17:44:45Z","abstract_excerpt":"We present a proof of a Littlewood-Richardson rule for the K-theory of odd orthogonal Grassmannians OG(n,2n+1), as conjectured in [Thomas-Yong '09]. Specifically, we prove that rectification using the jeu de taquin for increasing shifted tableaux introduced there, is well-defined and gives rise to an associative product. Recently, [Buch-Ravikumar '09] proved a Pieri rule for OG(n,2n+1) that [Feigenbaum-Sergel '09] showed confirms a special case of the conjecture. Together, these results imply the aforementioned conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1664","kind":"arxiv","version":2},"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":"2026-05-18T02:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dlrz2AWtZj/JtsGkvhLAQ8mDlppSBeDF3B+APoMTWeWZlFHF9qxgrb4Kn13ZFEEBolMFs/nGuK1PbheZyUCYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:41:16.063928Z"},"content_sha256":"dd5805bd5876161e77e555ad609aa40f45b76f56d106b9b104f15af0996decea","schema_version":"1.0","event_id":"sha256:dd5805bd5876161e77e555ad609aa40f45b76f56d106b9b104f15af0996decea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LKHMDJ7QZJD2VB44FXVASIORSQ/bundle.json","state_url":"https://pith.science/pith/LKHMDJ7QZJD2VB44FXVASIORSQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LKHMDJ7QZJD2VB44FXVASIORSQ/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":"2026-05-25T12:41:16Z","links":{"resolver":"https://pith.science/pith/LKHMDJ7QZJD2VB44FXVASIORSQ","bundle":"https://pith.science/pith/LKHMDJ7QZJD2VB44FXVASIORSQ/bundle.json","state":"https://pith.science/pith/LKHMDJ7QZJD2VB44FXVASIORSQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LKHMDJ7QZJD2VB44FXVASIORSQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LKHMDJ7QZJD2VB44FXVASIORSQ","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":"8558ea00617e93f5245482ddfcc6aeb7b4ea134c243c4ccb8ac5d90b52b8fb93","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-08T17:44:45Z","title_canon_sha256":"bc010f5bf5ccb5860a1b9bc68f7970621aa1c9d597391576fc10933261629d5f"},"schema_version":"1.0","source":{"id":"1002.1664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1664","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1664v2","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1664","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"LKHMDJ7QZJD2","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LKHMDJ7QZJD2VB44","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LKHMDJ7Q","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:dd5805bd5876161e77e555ad609aa40f45b76f56d106b9b104f15af0996decea","target":"graph","created_at":"2026-05-18T02:44:23Z","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":"We present a proof of a Littlewood-Richardson rule for the K-theory of odd orthogonal Grassmannians OG(n,2n+1), as conjectured in [Thomas-Yong '09]. Specifically, we prove that rectification using the jeu de taquin for increasing shifted tableaux introduced there, is well-defined and gives rise to an associative product. Recently, [Buch-Ravikumar '09] proved a Pieri rule for OG(n,2n+1) that [Feigenbaum-Sergel '09] showed confirms a special case of the conjecture. Together, these results imply the aforementioned conjecture.","authors_text":"Alexander Yong, Edward Clifford, Hugh Thomas","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-08T17:44:45Z","title":"K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1664","kind":"arxiv","version":2},"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:ea7d36533e93fa260b87a90f588bf84fc7a5936c60f523939f3cbd5822779bb6","target":"record","created_at":"2026-05-18T02:44:23Z","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":"8558ea00617e93f5245482ddfcc6aeb7b4ea134c243c4ccb8ac5d90b52b8fb93","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-08T17:44:45Z","title_canon_sha256":"bc010f5bf5ccb5860a1b9bc68f7970621aa1c9d597391576fc10933261629d5f"},"schema_version":"1.0","source":{"id":"1002.1664","kind":"arxiv","version":2}},"canonical_sha256":"5a8ec1a7f0ca47aa879c2dea0921d1940b7141c69e46cb461aa08b7f186b77d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a8ec1a7f0ca47aa879c2dea0921d1940b7141c69e46cb461aa08b7f186b77d4","first_computed_at":"2026-05-18T02:44:23.819545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:23.819545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PqV8aa9l5fRcXM0VfVTpzfYbgbjb8kRRtAs6irCa2Vm7KxpiRRc8ygh5DN4nw4yKJ26i5jAAeRjsdSi5RszrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:23.820149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea7d36533e93fa260b87a90f588bf84fc7a5936c60f523939f3cbd5822779bb6","sha256:dd5805bd5876161e77e555ad609aa40f45b76f56d106b9b104f15af0996decea"],"state_sha256":"5a946a5cb6c7af0852e956db79842313c8ec41c4e58274f9e5f7da3d2a28a26b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPrB/WB6UJld07XnkHZ0aGCdQF/+mlZ1+uFFInn/Q/JU+cpXQmTSV6weVsr7fvXDgJSSVGksBKxV/o1A/rsgCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:41:16.067826Z","bundle_sha256":"b49cbdaa664c71d706281f679fe101128d64dd7f95147141976d2626bf1f7d8d"}}