{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:V3JUGEF7I6HB6WSMXKKR43FNI5","short_pith_number":"pith:V3JUGEF7","canonical_record":{"source":{"id":"2201.12951","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-01-31T01:21:33Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"05c6f93bfb7e196d556797ad58fd3771c476df242a85d19c429394f45c36ce3b","abstract_canon_sha256":"abae686e693cb631ade41bdae5923103a992c86ab7fc8cf4c586aa196175d8ba"},"schema_version":"1.0"},"canonical_sha256":"aed34310bf478e1f5a4cba951e6cad474418a04185589c0e45cf2608f644054e","source":{"kind":"arxiv","id":"2201.12951","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.12951","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"arxiv_version","alias_value":"2201.12951v1","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.12951","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"pith_short_12","alias_value":"V3JUGEF7I6HB","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"pith_short_16","alias_value":"V3JUGEF7I6HB6WSM","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"pith_short_8","alias_value":"V3JUGEF7","created_at":"2026-07-05T03:52:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:V3JUGEF7I6HB6WSMXKKR43FNI5","target":"record","payload":{"canonical_record":{"source":{"id":"2201.12951","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-01-31T01:21:33Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"05c6f93bfb7e196d556797ad58fd3771c476df242a85d19c429394f45c36ce3b","abstract_canon_sha256":"abae686e693cb631ade41bdae5923103a992c86ab7fc8cf4c586aa196175d8ba"},"schema_version":"1.0"},"canonical_sha256":"aed34310bf478e1f5a4cba951e6cad474418a04185589c0e45cf2608f644054e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:52:41.276584Z","signature_b64":"jRoDP9piKUUn8VfDTD7dvJlutaC6dg3Zuy1iI0Zk1JIddMPQKPv4HFwfdkwM5NU8BFrfFd/6P8sIqXY2dkaDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aed34310bf478e1f5a4cba951e6cad474418a04185589c0e45cf2608f644054e","last_reissued_at":"2026-07-05T03:52:41.276111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:52:41.276111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.12951","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":"2026-07-05T03:52:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OapCm1xAWHQbw/u4AAkdnXzNCSUo8pkeIRaemo8hia2o9hpJ24MFFmqc9uKhTNDE9Fbbaxed+AA2pYHQLAjHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:32:40.465462Z"},"content_sha256":"62284dda237fd3b896eebfe06690a6b7a8b7d6f9a432a2379a1ec877e4fc80a3","schema_version":"1.0","event_id":"sha256:62284dda237fd3b896eebfe06690a6b7a8b7d6f9a432a2379a1ec877e4fc80a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:V3JUGEF7I6HB6WSMXKKR43FNI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum $K$-theory of $G/P$ and $K$-homology of affine Grassmannian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Chi Hong Chow, Naichung Conan Leung","submitted_at":"2022-01-31T01:21:33Z","abstract_excerpt":"This paper is the $K$-theoretic analogue of a recent new proof, given by the first named author, of Peterson-Lam-Shimozono's theorem via Savelyev's generalization of Seidel representations. The outcome is a new proof of Lam-Li-Mihalcea-Shimozono's conjecture, including its extension to the parabolic case, which was first verified by Kato."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.12951","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/2201.12951/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":"2026-07-05T03:52:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pyEjnOF9hCjqgYQdjx0w1RDYhY2D8v4ZTsrx+F5h9edZE2PsomWBbT6GzDdmW75f4oh/ike67hW0OsgQl6cYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:32:40.466383Z"},"content_sha256":"f870caaed8a90fb65685904417557fd95f1d12730593c6e33ad7ae2a0a0b1715","schema_version":"1.0","event_id":"sha256:f870caaed8a90fb65685904417557fd95f1d12730593c6e33ad7ae2a0a0b1715"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3JUGEF7I6HB6WSMXKKR43FNI5/bundle.json","state_url":"https://pith.science/pith/V3JUGEF7I6HB6WSMXKKR43FNI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3JUGEF7I6HB6WSMXKKR43FNI5/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":"2026-08-10T13:32:40Z","links":{"resolver":"https://pith.science/pith/V3JUGEF7I6HB6WSMXKKR43FNI5","bundle":"https://pith.science/pith/V3JUGEF7I6HB6WSMXKKR43FNI5/bundle.json","state":"https://pith.science/pith/V3JUGEF7I6HB6WSMXKKR43FNI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3JUGEF7I6HB6WSMXKKR43FNI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:V3JUGEF7I6HB6WSMXKKR43FNI5","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":"abae686e693cb631ade41bdae5923103a992c86ab7fc8cf4c586aa196175d8ba","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-01-31T01:21:33Z","title_canon_sha256":"05c6f93bfb7e196d556797ad58fd3771c476df242a85d19c429394f45c36ce3b"},"schema_version":"1.0","source":{"id":"2201.12951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.12951","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"arxiv_version","alias_value":"2201.12951v1","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.12951","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"pith_short_12","alias_value":"V3JUGEF7I6HB","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"pith_short_16","alias_value":"V3JUGEF7I6HB6WSM","created_at":"2026-07-05T03:52:41Z"},{"alias_kind":"pith_short_8","alias_value":"V3JUGEF7","created_at":"2026-07-05T03:52:41Z"}],"graph_snapshots":[{"event_id":"sha256:f870caaed8a90fb65685904417557fd95f1d12730593c6e33ad7ae2a0a0b1715","target":"graph","created_at":"2026-07-05T03:52:41Z","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/2201.12951/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is the $K$-theoretic analogue of a recent new proof, given by the first named author, of Peterson-Lam-Shimozono's theorem via Savelyev's generalization of Seidel representations. The outcome is a new proof of Lam-Li-Mihalcea-Shimozono's conjecture, including its extension to the parabolic case, which was first verified by Kato.","authors_text":"Chi Hong Chow, Naichung Conan Leung","cross_cats":["math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-01-31T01:21:33Z","title":"Quantum $K$-theory of $G/P$ and $K$-homology of affine Grassmannian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.12951","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":"sha256:62284dda237fd3b896eebfe06690a6b7a8b7d6f9a432a2379a1ec877e4fc80a3","target":"record","created_at":"2026-07-05T03:52:41Z","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":"abae686e693cb631ade41bdae5923103a992c86ab7fc8cf4c586aa196175d8ba","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-01-31T01:21:33Z","title_canon_sha256":"05c6f93bfb7e196d556797ad58fd3771c476df242a85d19c429394f45c36ce3b"},"schema_version":"1.0","source":{"id":"2201.12951","kind":"arxiv","version":1}},"canonical_sha256":"aed34310bf478e1f5a4cba951e6cad474418a04185589c0e45cf2608f644054e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aed34310bf478e1f5a4cba951e6cad474418a04185589c0e45cf2608f644054e","first_computed_at":"2026-07-05T03:52:41.276111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:52:41.276111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jRoDP9piKUUn8VfDTD7dvJlutaC6dg3Zuy1iI0Zk1JIddMPQKPv4HFwfdkwM5NU8BFrfFd/6P8sIqXY2dkaDAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:52:41.276584Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.12951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62284dda237fd3b896eebfe06690a6b7a8b7d6f9a432a2379a1ec877e4fc80a3","sha256:f870caaed8a90fb65685904417557fd95f1d12730593c6e33ad7ae2a0a0b1715"],"state_sha256":"c7fd343a01275bc9a146435ea898001c074e23d1f15bb4b93c00600edc174b01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"81cEY7qBRxza4m0yzxAbuVYzBHrcMI+TEMJF4Wg/Rr0CC8IjeXkCqSxOfp1ixU3vPRdJLHvYyWiaxCUJIHfSCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T13:32:40.476575Z","bundle_sha256":"001512f366ff6c0f1822725d381e032f5f73d8c42308864fcc031680d2a42949"}}