{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MIPMIKECMEQFT2BQQQX2SHP7ES","short_pith_number":"pith:MIPMIKEC","canonical_record":{"source":{"id":"1406.1283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-05T07:36:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e667df625d7f907c9073f16dc6fa1179138476a2a3116a5996bcaeaf9abd3dc1","abstract_canon_sha256":"7550e8f494db34dac47c62444a7e43eefaf1dd7b92d90bd3f59bafc576d62499"},"schema_version":"1.0"},"canonical_sha256":"621ec42882612059e830842fa91dff24b9db3376bf09b23889546117b8d94692","source":{"kind":"arxiv","id":"1406.1283","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1283","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1283v2","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1283","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"MIPMIKECMEQF","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MIPMIKECMEQFT2BQ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MIPMIKEC","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MIPMIKECMEQFT2BQQQX2SHP7ES","target":"record","payload":{"canonical_record":{"source":{"id":"1406.1283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-05T07:36:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e667df625d7f907c9073f16dc6fa1179138476a2a3116a5996bcaeaf9abd3dc1","abstract_canon_sha256":"7550e8f494db34dac47c62444a7e43eefaf1dd7b92d90bd3f59bafc576d62499"},"schema_version":"1.0"},"canonical_sha256":"621ec42882612059e830842fa91dff24b9db3376bf09b23889546117b8d94692","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:40.581303Z","signature_b64":"5bFWaQO277EnOKyAa//DaijutogrMpBWH2O3OhTgs9YwC4gvNWDXnFQqlNq4sjvJAIZ7PT4XvXs9LqE+54SvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"621ec42882612059e830842fa91dff24b9db3376bf09b23889546117b8d94692","last_reissued_at":"2026-05-18T02:28:40.580847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:40.580847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.1283","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":"2026-05-18T02:28:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hnIY6Tm087unabsUWuSF6/uZ77HLJ9b4+gFcS/ksGhwYt8zUAQiZoKklx9t6zakyvNKp1OGqxjetfzvKC1OOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:47:55.780439Z"},"content_sha256":"6a0dac8122cfc753d72af5bd78a34d5ead4c71b2561616611d6b69eaca8f2b5b","schema_version":"1.0","event_id":"sha256:6a0dac8122cfc753d72af5bd78a34d5ead4c71b2561616611d6b69eaca8f2b5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MIPMIKECMEQFT2BQQQX2SHP7ES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric representations of the formal affine Hecke algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Changlong Zhong, Gufang Zhao","submitted_at":"2014-06-05T07:36:11Z","abstract_excerpt":"For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung, Malag\\'on-L\\'opez, Savage, and Zainoulline. Coming from this formal group law, there is also an oriented cohomology theory. We identify the formal affine Hecke algebra with a convolution algebra coming from the oriented cohomology theory applied to the Steinberg variety. As a consequence, this algebra acts on the corresponding cohomology of the Springer fibers. This generalizes the action of classical affine Hecke algebra on the $K$-theory of the Springer fibers constructed by Lusztig. We also give a residue "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1283","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":"2026-05-18T02:28:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N+vDs3nJIhiDRL/XNf3+HBlU/Gh9uZ2Y0yPA9XB6yxD5e8Iy28+bg+1NZQ0mYMQF/qNQJ509YXS7A3+bW45mAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:47:55.780824Z"},"content_sha256":"8b82007dbd7de2f25e66e387088bd6c153a70661020c0e3a90d5cd16abb073ed","schema_version":"1.0","event_id":"sha256:8b82007dbd7de2f25e66e387088bd6c153a70661020c0e3a90d5cd16abb073ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIPMIKECMEQFT2BQQQX2SHP7ES/bundle.json","state_url":"https://pith.science/pith/MIPMIKECMEQFT2BQQQX2SHP7ES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIPMIKECMEQFT2BQQQX2SHP7ES/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":"2026-06-02T20:47:55Z","links":{"resolver":"https://pith.science/pith/MIPMIKECMEQFT2BQQQX2SHP7ES","bundle":"https://pith.science/pith/MIPMIKECMEQFT2BQQQX2SHP7ES/bundle.json","state":"https://pith.science/pith/MIPMIKECMEQFT2BQQQX2SHP7ES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIPMIKECMEQFT2BQQQX2SHP7ES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MIPMIKECMEQFT2BQQQX2SHP7ES","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":"7550e8f494db34dac47c62444a7e43eefaf1dd7b92d90bd3f59bafc576d62499","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-05T07:36:11Z","title_canon_sha256":"e667df625d7f907c9073f16dc6fa1179138476a2a3116a5996bcaeaf9abd3dc1"},"schema_version":"1.0","source":{"id":"1406.1283","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1283","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1283v2","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1283","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"MIPMIKECMEQF","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MIPMIKECMEQFT2BQ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MIPMIKEC","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:8b82007dbd7de2f25e66e387088bd6c153a70661020c0e3a90d5cd16abb073ed","target":"graph","created_at":"2026-05-18T02:28:40Z","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"},"paper":{"abstract_excerpt":"For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung, Malag\\'on-L\\'opez, Savage, and Zainoulline. Coming from this formal group law, there is also an oriented cohomology theory. We identify the formal affine Hecke algebra with a convolution algebra coming from the oriented cohomology theory applied to the Steinberg variety. As a consequence, this algebra acts on the corresponding cohomology of the Springer fibers. This generalizes the action of classical affine Hecke algebra on the $K$-theory of the Springer fibers constructed by Lusztig. We also give a residue ","authors_text":"Changlong Zhong, Gufang Zhao","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-05T07:36:11Z","title":"Geometric representations of the formal affine Hecke algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1283","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":"sha256:6a0dac8122cfc753d72af5bd78a34d5ead4c71b2561616611d6b69eaca8f2b5b","target":"record","created_at":"2026-05-18T02:28:40Z","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":"7550e8f494db34dac47c62444a7e43eefaf1dd7b92d90bd3f59bafc576d62499","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-05T07:36:11Z","title_canon_sha256":"e667df625d7f907c9073f16dc6fa1179138476a2a3116a5996bcaeaf9abd3dc1"},"schema_version":"1.0","source":{"id":"1406.1283","kind":"arxiv","version":2}},"canonical_sha256":"621ec42882612059e830842fa91dff24b9db3376bf09b23889546117b8d94692","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"621ec42882612059e830842fa91dff24b9db3376bf09b23889546117b8d94692","first_computed_at":"2026-05-18T02:28:40.580847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:40.580847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bFWaQO277EnOKyAa//DaijutogrMpBWH2O3OhTgs9YwC4gvNWDXnFQqlNq4sjvJAIZ7PT4XvXs9LqE+54SvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:40.581303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1283","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a0dac8122cfc753d72af5bd78a34d5ead4c71b2561616611d6b69eaca8f2b5b","sha256:8b82007dbd7de2f25e66e387088bd6c153a70661020c0e3a90d5cd16abb073ed"],"state_sha256":"2db07a3c67a8cc25eae76a20b087a1b48ddf9c6ac4824b94669045d428573b14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4iyfSR6nJK5UMyXDJpCC1ECPzhm1KiPPodafY5r6NpnuzAJuBdQIQ3RSkz+5JBtLx9ILBnuAV1BZRKudE0lFAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:47:55.783460Z","bundle_sha256":"6731aa7efbd68b087f1588356fc203c9a3af2ca37bfa130e4c877681d25e2fc2"}}