{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LSYUBXWJCEHTKRTRJJVCPI5FSX","short_pith_number":"pith:LSYUBXWJ","canonical_record":{"source":{"id":"2502.05618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-08T15:52:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"96b73689025e8f5bf174e34d4fc95fcb07bb2f444b5dea71b64e80225d3bec65","abstract_canon_sha256":"52fd77691d5cfa514fc160b7e01267206284e23b990801b77a449adacbe40253"},"schema_version":"1.0"},"canonical_sha256":"5cb140dec9110f3546714a6a27a3a595d32d80ebc25cf3165230bbd812cff720","source":{"kind":"arxiv","id":"2502.05618","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05618","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05618v1","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05618","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"LSYUBXWJCEHT","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"pith_short_16","alias_value":"LSYUBXWJCEHTKRTR","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"pith_short_8","alias_value":"LSYUBXWJ","created_at":"2026-07-05T10:11:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LSYUBXWJCEHTKRTRJJVCPI5FSX","target":"record","payload":{"canonical_record":{"source":{"id":"2502.05618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-08T15:52:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"96b73689025e8f5bf174e34d4fc95fcb07bb2f444b5dea71b64e80225d3bec65","abstract_canon_sha256":"52fd77691d5cfa514fc160b7e01267206284e23b990801b77a449adacbe40253"},"schema_version":"1.0"},"canonical_sha256":"5cb140dec9110f3546714a6a27a3a595d32d80ebc25cf3165230bbd812cff720","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:40.656815Z","signature_b64":"YNduEvkKJr98fb/UWHtzdIpxwP7J5Azen9bh6K4p2WwR1H+HyyjE0ytVOyzU8clSZM/KgIDUMDBuk2y2SedZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cb140dec9110f3546714a6a27a3a595d32d80ebc25cf3165230bbd812cff720","last_reissued_at":"2026-07-05T10:11:40.656394Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:40.656394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.05618","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":"2026-07-05T10:11:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mCX6aHDTs7wmZCVgU+yOqvXb3csJfbt1/fbCd4p8D5xaWlYr6MLigdaWyIIZQgyscYDe72KGJKI3+OTH+K3uCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T14:44:15.773120Z"},"content_sha256":"0db8d2ce2618db7211ace02800975c9bd798c2022a131984b839f7f6d5f14325","schema_version":"1.0","event_id":"sha256:0db8d2ce2618db7211ace02800975c9bd798c2022a131984b839f7f6d5f14325"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LSYUBXWJCEHTKRTRJJVCPI5FSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lowering operators on $K$-$k$-Schur functions and a lowering operator formula for closed $K$-$k$-Schur functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Li Guo, Xing Gao, Yaozhou Fang","submitted_at":"2025-02-08T15:52:23Z","abstract_excerpt":"This paper gives a systematic study of the lowering operators acting on the $K$-$k$-Schur functions, motivated by the pivotal role played by the operators in the definition and study of Katalan functions. A lowering operator formula for closed $K$-$k$-Schur functions is obtained. As an application, a combinatorial proof is provided to a conjecture on closed $k$-Schur Katalan functions, posed by Blasiak, Morse and Seelinger, and recently proved by Ikeda, Iwao and Naito by a different method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05618","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/2502.05618/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":"2026-07-05T10:11:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ro/Kq7eHyH25K0D3iI8wzi/KVEP7LOZAt0E/12MQidKWjxWfsRbPxyr297YohP+JzarhGd/n5d4+O235QwZfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T14:44:15.774104Z"},"content_sha256":"7b2bd19f394e7109f0bf6b627fd42ed5d4f0ec6b348fe7cc750c0b9936f0d44f","schema_version":"1.0","event_id":"sha256:7b2bd19f394e7109f0bf6b627fd42ed5d4f0ec6b348fe7cc750c0b9936f0d44f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LSYUBXWJCEHTKRTRJJVCPI5FSX/bundle.json","state_url":"https://pith.science/pith/LSYUBXWJCEHTKRTRJJVCPI5FSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LSYUBXWJCEHTKRTRJJVCPI5FSX/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":"2026-08-11T14:44:15Z","links":{"resolver":"https://pith.science/pith/LSYUBXWJCEHTKRTRJJVCPI5FSX","bundle":"https://pith.science/pith/LSYUBXWJCEHTKRTRJJVCPI5FSX/bundle.json","state":"https://pith.science/pith/LSYUBXWJCEHTKRTRJJVCPI5FSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LSYUBXWJCEHTKRTRJJVCPI5FSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LSYUBXWJCEHTKRTRJJVCPI5FSX","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":"52fd77691d5cfa514fc160b7e01267206284e23b990801b77a449adacbe40253","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-08T15:52:23Z","title_canon_sha256":"96b73689025e8f5bf174e34d4fc95fcb07bb2f444b5dea71b64e80225d3bec65"},"schema_version":"1.0","source":{"id":"2502.05618","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05618","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05618v1","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05618","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"LSYUBXWJCEHT","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"pith_short_16","alias_value":"LSYUBXWJCEHTKRTR","created_at":"2026-07-05T10:11:40Z"},{"alias_kind":"pith_short_8","alias_value":"LSYUBXWJ","created_at":"2026-07-05T10:11:40Z"}],"graph_snapshots":[{"event_id":"sha256:7b2bd19f394e7109f0bf6b627fd42ed5d4f0ec6b348fe7cc750c0b9936f0d44f","target":"graph","created_at":"2026-07-05T10:11:40Z","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/2502.05618/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper gives a systematic study of the lowering operators acting on the $K$-$k$-Schur functions, motivated by the pivotal role played by the operators in the definition and study of Katalan functions. A lowering operator formula for closed $K$-$k$-Schur functions is obtained. As an application, a combinatorial proof is provided to a conjecture on closed $k$-Schur Katalan functions, posed by Blasiak, Morse and Seelinger, and recently proved by Ikeda, Iwao and Naito by a different method.","authors_text":"Li Guo, Xing Gao, Yaozhou Fang","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-08T15:52:23Z","title":"Lowering operators on $K$-$k$-Schur functions and a lowering operator formula for closed $K$-$k$-Schur functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05618","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":"sha256:0db8d2ce2618db7211ace02800975c9bd798c2022a131984b839f7f6d5f14325","target":"record","created_at":"2026-07-05T10:11:40Z","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":"52fd77691d5cfa514fc160b7e01267206284e23b990801b77a449adacbe40253","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-08T15:52:23Z","title_canon_sha256":"96b73689025e8f5bf174e34d4fc95fcb07bb2f444b5dea71b64e80225d3bec65"},"schema_version":"1.0","source":{"id":"2502.05618","kind":"arxiv","version":1}},"canonical_sha256":"5cb140dec9110f3546714a6a27a3a595d32d80ebc25cf3165230bbd812cff720","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cb140dec9110f3546714a6a27a3a595d32d80ebc25cf3165230bbd812cff720","first_computed_at":"2026-07-05T10:11:40.656394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:40.656394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YNduEvkKJr98fb/UWHtzdIpxwP7J5Azen9bh6K4p2WwR1H+HyyjE0ytVOyzU8clSZM/KgIDUMDBuk2y2SedZDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:40.656815Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.05618","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db8d2ce2618db7211ace02800975c9bd798c2022a131984b839f7f6d5f14325","sha256:7b2bd19f394e7109f0bf6b627fd42ed5d4f0ec6b348fe7cc750c0b9936f0d44f"],"state_sha256":"4fbd8213e8701370555baa1b06e4cf6a477c29ec1cd99717735d1caacab601e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L92vo6f2VIlzO/PIMlgkPGSKrochYc5Lsll7F6O6Ha7IY6iB4qyJ6ld7lmNoYvuAQMPzAWM9/mJYx1tXS+aTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T14:44:15.781381Z","bundle_sha256":"8d379aec5d135bdb4d46e6c94b016be47bc0b1fcd01e4b049e44d15280733991"}}