{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:72IMWDMISIZMRNVRMANNYAHLJ5","short_pith_number":"pith:72IMWDMI","canonical_record":{"source":{"id":"2309.09140","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-17T02:55:07Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"9a72fecb6f582693ef1dc07ea5b0badbd28c5c9285513d23d73cb35a198935e9","abstract_canon_sha256":"9b016ab8a8714b72a99e99f9261fa587ca16add9244c14a5810534c65b66aab7"},"schema_version":"1.0"},"canonical_sha256":"fe90cb0d889232c8b6b1601adc00eb4f6bef4557977fb3c8585cebed1e71f29d","source":{"kind":"arxiv","id":"2309.09140","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.09140","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"2309.09140v2","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.09140","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"72IMWDMISIZM","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_16","alias_value":"72IMWDMISIZMRNVR","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_8","alias_value":"72IMWDMI","created_at":"2026-06-19T16:11:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:72IMWDMISIZMRNVRMANNYAHLJ5","target":"record","payload":{"canonical_record":{"source":{"id":"2309.09140","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-17T02:55:07Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"9a72fecb6f582693ef1dc07ea5b0badbd28c5c9285513d23d73cb35a198935e9","abstract_canon_sha256":"9b016ab8a8714b72a99e99f9261fa587ca16add9244c14a5810534c65b66aab7"},"schema_version":"1.0"},"canonical_sha256":"fe90cb0d889232c8b6b1601adc00eb4f6bef4557977fb3c8585cebed1e71f29d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:07.743701Z","signature_b64":"suFJKvtUdngVYimXExK62v5RuHPYUfoOablug9hwcF18vrPRUcZyTtS72ozlA03C7f5Nv5zmjMYX9XCovYD1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe90cb0d889232c8b6b1601adc00eb4f6bef4557977fb3c8585cebed1e71f29d","last_reissued_at":"2026-06-19T16:11:07.743355Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:07.743355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.09140","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":"2026-06-19T16:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tQH52pptUwY9JdbuZd02iz7LTbCDMuHjV58z9aFtIOrDdwZ1hSI85OxboWA5v5EYX3dzX6h8Fhh/Z7FeRubFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:18:12.740326Z"},"content_sha256":"33bd02c4763b1e8930352fa7246dedd268f835fcbe2f5cc69c17f6a109b915ce","schema_version":"1.0","event_id":"sha256:33bd02c4763b1e8930352fa7246dedd268f835fcbe2f5cc69c17f6a109b915ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:72IMWDMISIZMRNVRMANNYAHLJ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic classes via the periodic Hecke module and its Langlands dual","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.AG","authors_text":"Changlong Zhong, Cristian Lenart, Gufang Zhao","submitted_at":"2023-09-17T02:55:07Z","abstract_excerpt":"This paper explores a construction of the elliptic classes of the Springer resolution using the periodic Hecke module. The module is established by employing the Poincar\\'e line bundle over the product of the abelian variety of elliptic cohomology and its dual. Additionally, we introduce the elliptic twisted group algebra, which acts on the periodic module. The construction of the elliptic twisted group algebra is such that the Demazure-Lusztig (DL) operators with dynamical parameters are rational sections. We define elliptic classes as rational sections of the periodic module, and give explic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09140","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.09140/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":"2026-06-19T16:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cv4lpW9BN0eCqiiuI0KXE8fYf6qqoFz+LR5vIfuSBNGF4uIt9iMWA7Fn+q2gN7KRaNB6Dql/gX95owgXkm1qCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:18:12.740699Z"},"content_sha256":"35e56ca0d7d4903e158044a0995c4f0774c18a28bad106dd5b8d2ddbd7eeb659","schema_version":"1.0","event_id":"sha256:35e56ca0d7d4903e158044a0995c4f0774c18a28bad106dd5b8d2ddbd7eeb659"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72IMWDMISIZMRNVRMANNYAHLJ5/bundle.json","state_url":"https://pith.science/pith/72IMWDMISIZMRNVRMANNYAHLJ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72IMWDMISIZMRNVRMANNYAHLJ5/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":"2026-06-20T07:18:12Z","links":{"resolver":"https://pith.science/pith/72IMWDMISIZMRNVRMANNYAHLJ5","bundle":"https://pith.science/pith/72IMWDMISIZMRNVRMANNYAHLJ5/bundle.json","state":"https://pith.science/pith/72IMWDMISIZMRNVRMANNYAHLJ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72IMWDMISIZMRNVRMANNYAHLJ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:72IMWDMISIZMRNVRMANNYAHLJ5","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":"9b016ab8a8714b72a99e99f9261fa587ca16add9244c14a5810534c65b66aab7","cross_cats_sorted":["math.KT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-17T02:55:07Z","title_canon_sha256":"9a72fecb6f582693ef1dc07ea5b0badbd28c5c9285513d23d73cb35a198935e9"},"schema_version":"1.0","source":{"id":"2309.09140","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.09140","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"2309.09140v2","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.09140","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"72IMWDMISIZM","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_16","alias_value":"72IMWDMISIZMRNVR","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_8","alias_value":"72IMWDMI","created_at":"2026-06-19T16:11:07Z"}],"graph_snapshots":[{"event_id":"sha256:35e56ca0d7d4903e158044a0995c4f0774c18a28bad106dd5b8d2ddbd7eeb659","target":"graph","created_at":"2026-06-19T16:11:07Z","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/2309.09140/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper explores a construction of the elliptic classes of the Springer resolution using the periodic Hecke module. The module is established by employing the Poincar\\'e line bundle over the product of the abelian variety of elliptic cohomology and its dual. Additionally, we introduce the elliptic twisted group algebra, which acts on the periodic module. The construction of the elliptic twisted group algebra is such that the Demazure-Lusztig (DL) operators with dynamical parameters are rational sections. We define elliptic classes as rational sections of the periodic module, and give explic","authors_text":"Changlong Zhong, Cristian Lenart, Gufang Zhao","cross_cats":["math.KT","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-17T02:55:07Z","title":"Elliptic classes via the periodic Hecke module and its Langlands dual"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09140","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":"sha256:33bd02c4763b1e8930352fa7246dedd268f835fcbe2f5cc69c17f6a109b915ce","target":"record","created_at":"2026-06-19T16:11:07Z","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":"9b016ab8a8714b72a99e99f9261fa587ca16add9244c14a5810534c65b66aab7","cross_cats_sorted":["math.KT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-17T02:55:07Z","title_canon_sha256":"9a72fecb6f582693ef1dc07ea5b0badbd28c5c9285513d23d73cb35a198935e9"},"schema_version":"1.0","source":{"id":"2309.09140","kind":"arxiv","version":2}},"canonical_sha256":"fe90cb0d889232c8b6b1601adc00eb4f6bef4557977fb3c8585cebed1e71f29d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe90cb0d889232c8b6b1601adc00eb4f6bef4557977fb3c8585cebed1e71f29d","first_computed_at":"2026-06-19T16:11:07.743355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:07.743355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"suFJKvtUdngVYimXExK62v5RuHPYUfoOablug9hwcF18vrPRUcZyTtS72ozlA03C7f5Nv5zmjMYX9XCovYD1CQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:07.743701Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.09140","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33bd02c4763b1e8930352fa7246dedd268f835fcbe2f5cc69c17f6a109b915ce","sha256:35e56ca0d7d4903e158044a0995c4f0774c18a28bad106dd5b8d2ddbd7eeb659"],"state_sha256":"e00fc8a2d955bfd0319bd7994357742fbe1c2889c870dcd8b9186ec79ffc25d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ug5pRAImJ+uGWG4/G/9llsMbmS4SSh0XTPYk5SfTOdKACbji/wp/5PYP4UjU67nvKQPHye8yLaSi5uUocSBsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:18:12.742636Z","bundle_sha256":"dcaa1df3a4f04853bf73edd80b787ce8d38ad7e38b7a1b18b6d725f03fe9c97a"}}