{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EUAR6AZ5YVKCAYRNKUAU3WGBD2","short_pith_number":"pith:EUAR6AZ5","canonical_record":{"source":{"id":"1703.08664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-25T08:24:33Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"546b8748a6816bbea63e971c30b2773dbfb68a085a3ebae1ba52012f9e9378c9","abstract_canon_sha256":"5c4e7eb28af3dfceb6c16ae7458a5271d8a189f067eb56870f4dbfcee979bf79"},"schema_version":"1.0"},"canonical_sha256":"25011f033dc55420622d55014dd8c11ebe86a19a47dcada29fd525b578395111","source":{"kind":"arxiv","id":"1703.08664","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08664","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08664v2","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08664","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"EUAR6AZ5YVKC","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EUAR6AZ5YVKCAYRN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EUAR6AZ5","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EUAR6AZ5YVKCAYRNKUAU3WGBD2","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-25T08:24:33Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"546b8748a6816bbea63e971c30b2773dbfb68a085a3ebae1ba52012f9e9378c9","abstract_canon_sha256":"5c4e7eb28af3dfceb6c16ae7458a5271d8a189f067eb56870f4dbfcee979bf79"},"schema_version":"1.0"},"canonical_sha256":"25011f033dc55420622d55014dd8c11ebe86a19a47dcada29fd525b578395111","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:06.302576Z","signature_b64":"TuMDpaNMGVMQuwvzh+vHvK/Y5XZ/MFGU4iucp7CXqPkFOMLhhb72w8M10bvDJ7dBeDx43FG28AXZivEpC66aAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25011f033dc55420622d55014dd8c11ebe86a19a47dcada29fd525b578395111","last_reissued_at":"2026-05-18T00:22:06.302029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:06.302029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08664","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":"2026-05-18T00:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAYfx6CgmYFgvNA9yM97kr7mwS6j9bAB7nWnr9/Sv6zE2N0JkzVUAXyrcL1pzgIjCha6Y56jrgai2YefFuVQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:03:25.048178Z"},"content_sha256":"283bb22de341de8f4f2e5298cf70f6f6f793434258143a440d731c52c497d829","schema_version":"1.0","event_id":"sha256:283bb22de341de8f4f2e5298cf70f6f6f793434258143a440d731c52c497d829"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EUAR6AZ5YVKCAYRNKUAU3WGBD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Peterson Isomorphism in $K$-theory and Relativistic Toda Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AG","authors_text":"Shinsuke Iwao, Takeshi Ikeda, Toshiaki Maeno","submitted_at":"2017-03-25T08:24:33Z","abstract_excerpt":"The $K$-homology ring of the affine Grassmannian of $SL_n(C)$ was studied by Lam, Schilling, and Shimozono. It is realized as a certain concrete Hopf subring of the ring of symmetric functions. On the other hand, for the quantum $K$-theory of the flag variety $Fl_n$, Kirillov and Maeno provided a conjectural presentation based on the results obtained by Givental and Lee. We construct an explicit birational morphism between the spectrums of these two rings. Our method relies on Ruijsenaars's relativistic Toda lattice with unipotent initial condition. From this result, we obtain a $K$-theory ana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08664","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":"2026-05-18T00:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyxD81RDDZUEmARH26c3RPrZzFzfHX1+EwIjc6L1du/gLUmHMTbOo8p89UkyacGoMzbrrdVZJCfHHXXBea1pCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:03:25.048773Z"},"content_sha256":"5a2c1c251d2069bf42da2d8e1b07d72be5e52c1314759c31078c2ceaad128a0d","schema_version":"1.0","event_id":"sha256:5a2c1c251d2069bf42da2d8e1b07d72be5e52c1314759c31078c2ceaad128a0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUAR6AZ5YVKCAYRNKUAU3WGBD2/bundle.json","state_url":"https://pith.science/pith/EUAR6AZ5YVKCAYRNKUAU3WGBD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUAR6AZ5YVKCAYRNKUAU3WGBD2/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":"2026-05-26T22:03:25Z","links":{"resolver":"https://pith.science/pith/EUAR6AZ5YVKCAYRNKUAU3WGBD2","bundle":"https://pith.science/pith/EUAR6AZ5YVKCAYRNKUAU3WGBD2/bundle.json","state":"https://pith.science/pith/EUAR6AZ5YVKCAYRNKUAU3WGBD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUAR6AZ5YVKCAYRNKUAU3WGBD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EUAR6AZ5YVKCAYRNKUAU3WGBD2","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":"5c4e7eb28af3dfceb6c16ae7458a5271d8a189f067eb56870f4dbfcee979bf79","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-25T08:24:33Z","title_canon_sha256":"546b8748a6816bbea63e971c30b2773dbfb68a085a3ebae1ba52012f9e9378c9"},"schema_version":"1.0","source":{"id":"1703.08664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08664","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08664v2","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08664","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"EUAR6AZ5YVKC","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EUAR6AZ5YVKCAYRN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EUAR6AZ5","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:5a2c1c251d2069bf42da2d8e1b07d72be5e52c1314759c31078c2ceaad128a0d","target":"graph","created_at":"2026-05-18T00:22:06Z","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":"The $K$-homology ring of the affine Grassmannian of $SL_n(C)$ was studied by Lam, Schilling, and Shimozono. It is realized as a certain concrete Hopf subring of the ring of symmetric functions. On the other hand, for the quantum $K$-theory of the flag variety $Fl_n$, Kirillov and Maeno provided a conjectural presentation based on the results obtained by Givental and Lee. We construct an explicit birational morphism between the spectrums of these two rings. Our method relies on Ruijsenaars's relativistic Toda lattice with unipotent initial condition. From this result, we obtain a $K$-theory ana","authors_text":"Shinsuke Iwao, Takeshi Ikeda, Toshiaki Maeno","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-25T08:24:33Z","title":"Peterson Isomorphism in $K$-theory and Relativistic Toda Lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08664","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":"sha256:283bb22de341de8f4f2e5298cf70f6f6f793434258143a440d731c52c497d829","target":"record","created_at":"2026-05-18T00:22:06Z","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":"5c4e7eb28af3dfceb6c16ae7458a5271d8a189f067eb56870f4dbfcee979bf79","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-25T08:24:33Z","title_canon_sha256":"546b8748a6816bbea63e971c30b2773dbfb68a085a3ebae1ba52012f9e9378c9"},"schema_version":"1.0","source":{"id":"1703.08664","kind":"arxiv","version":2}},"canonical_sha256":"25011f033dc55420622d55014dd8c11ebe86a19a47dcada29fd525b578395111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25011f033dc55420622d55014dd8c11ebe86a19a47dcada29fd525b578395111","first_computed_at":"2026-05-18T00:22:06.302029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:06.302029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TuMDpaNMGVMQuwvzh+vHvK/Y5XZ/MFGU4iucp7CXqPkFOMLhhb72w8M10bvDJ7dBeDx43FG28AXZivEpC66aAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:06.302576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:283bb22de341de8f4f2e5298cf70f6f6f793434258143a440d731c52c497d829","sha256:5a2c1c251d2069bf42da2d8e1b07d72be5e52c1314759c31078c2ceaad128a0d"],"state_sha256":"65b0da812b9459218e7b4d8ee9b48cbc942a4a5be7842d81550d16da437f8100"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYO7bUH7Mf5Zlo+ueezsv/uoInjL/AhMvflcG/bHFW+lOXRS3KNvNMO4yS8p0rk2QhrtxtUpw13Ui8DPV2rIDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:03:25.051650Z","bundle_sha256":"648f96cbdac082b4dbd5100e7ca8311c01caabfb99681e213538ce204e34bce4"}}