{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZXSTYNKKX4LBE2MFXPY6Q6WVFE","short_pith_number":"pith:ZXSTYNKK","canonical_record":{"source":{"id":"2501.18849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-31T02:06:21Z","cross_cats_sorted":["hep-th","math.SG"],"title_canon_sha256":"643e16e006f2d5fc85540719332cd01dca385258810519aecd86a14f861883b2","abstract_canon_sha256":"1cc406c3f51288ca37b3db045c6655fb71aa7a13b4ca7db07e05002adc8a8487"},"schema_version":"1.0"},"canonical_sha256":"cde53c354abf16126985bbf1e87ad529078c6f058448a1f3a3354f36121262f5","source":{"kind":"arxiv","id":"2501.18849","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.18849","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"2501.18849v2","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18849","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZXSTYNKKX4LB","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZXSTYNKKX4LBE2MF","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZXSTYNKK","created_at":"2026-07-05T11:57:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZXSTYNKKX4LBE2MFXPY6Q6WVFE","target":"record","payload":{"canonical_record":{"source":{"id":"2501.18849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-31T02:06:21Z","cross_cats_sorted":["hep-th","math.SG"],"title_canon_sha256":"643e16e006f2d5fc85540719332cd01dca385258810519aecd86a14f861883b2","abstract_canon_sha256":"1cc406c3f51288ca37b3db045c6655fb71aa7a13b4ca7db07e05002adc8a8487"},"schema_version":"1.0"},"canonical_sha256":"cde53c354abf16126985bbf1e87ad529078c6f058448a1f3a3354f36121262f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:57:54.601060Z","signature_b64":"jmLwFCeWLMKkOsHjtMq31FtV6d6va5hVHQ2zooYmf7uXou8S/uSvm5dvGu8+yvlYBdZNbSCxjKnpkI/iOLaKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cde53c354abf16126985bbf1e87ad529078c6f058448a1f3a3354f36121262f5","last_reissued_at":"2026-07-05T11:57:54.600635Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:57:54.600635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.18849","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":"2026-07-05T11:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QrFizIFjOLzqLTX88So3ai6XnkB16+U90JCNRE+qN01v2m0l5s5WX29x9Y/0xln0OYZHquDC3gvke847WOaeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T07:50:59.561108Z"},"content_sha256":"41e97c1e05a26c427ba47da0a56e2bbfae274a96c7ce442e63f00666fa945a8d","schema_version":"1.0","event_id":"sha256:41e97c1e05a26c427ba47da0a56e2bbfae274a96c7ce442e63f00666fa945a8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZXSTYNKKX4LBE2MFXPY6Q6WVFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier analysis of equivariant quantum cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.AG","authors_text":"Hiroshi Iritani","submitted_at":"2025-01-31T02:06:21Z","abstract_excerpt":"Equivariant quantum cohomology possesses the structure of a difference module by shift operators (Seidel representation) of equivariant parameters. Teleman's conjecture suggests that shift operators and equivariant parameters acting on QH_T(X) should be identified, respectively, with the Novikov variables and the quantum connection of the GIT quotient X//T. This can be interpreted as a form of Fourier duality between equivariant quantum cohomology (D-module) of X and quantum cohomology (D-module) of the GIT quotient X//T.\n  We introduce the notion of \"quantum volume,\" derived from Givental's p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18849","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/2501.18849/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":"2026-07-05T11:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vGhBE7myN3KKqBLZ3UwXIGziprLlHcy3kwi2CMVQi42dwsYVpBBP6TulSs7koIOnM9JfWqGOQYFj84MjUwn9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T07:50:59.561600Z"},"content_sha256":"8c71e707c718c0499cf3cd250b814a687dc79e85856578bf547b0d739da57222","schema_version":"1.0","event_id":"sha256:8c71e707c718c0499cf3cd250b814a687dc79e85856578bf547b0d739da57222"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZXSTYNKKX4LBE2MFXPY6Q6WVFE/bundle.json","state_url":"https://pith.science/pith/ZXSTYNKKX4LBE2MFXPY6Q6WVFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZXSTYNKKX4LBE2MFXPY6Q6WVFE/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":"2026-08-10T07:50:59Z","links":{"resolver":"https://pith.science/pith/ZXSTYNKKX4LBE2MFXPY6Q6WVFE","bundle":"https://pith.science/pith/ZXSTYNKKX4LBE2MFXPY6Q6WVFE/bundle.json","state":"https://pith.science/pith/ZXSTYNKKX4LBE2MFXPY6Q6WVFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZXSTYNKKX4LBE2MFXPY6Q6WVFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZXSTYNKKX4LBE2MFXPY6Q6WVFE","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":"1cc406c3f51288ca37b3db045c6655fb71aa7a13b4ca7db07e05002adc8a8487","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-31T02:06:21Z","title_canon_sha256":"643e16e006f2d5fc85540719332cd01dca385258810519aecd86a14f861883b2"},"schema_version":"1.0","source":{"id":"2501.18849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.18849","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"2501.18849v2","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18849","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZXSTYNKKX4LB","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZXSTYNKKX4LBE2MF","created_at":"2026-07-05T11:57:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZXSTYNKK","created_at":"2026-07-05T11:57:54Z"}],"graph_snapshots":[{"event_id":"sha256:8c71e707c718c0499cf3cd250b814a687dc79e85856578bf547b0d739da57222","target":"graph","created_at":"2026-07-05T11:57:54Z","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/2501.18849/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Equivariant quantum cohomology possesses the structure of a difference module by shift operators (Seidel representation) of equivariant parameters. Teleman's conjecture suggests that shift operators and equivariant parameters acting on QH_T(X) should be identified, respectively, with the Novikov variables and the quantum connection of the GIT quotient X//T. This can be interpreted as a form of Fourier duality between equivariant quantum cohomology (D-module) of X and quantum cohomology (D-module) of the GIT quotient X//T.\n  We introduce the notion of \"quantum volume,\" derived from Givental's p","authors_text":"Hiroshi Iritani","cross_cats":["hep-th","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-31T02:06:21Z","title":"Fourier analysis of equivariant quantum cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18849","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":"sha256:41e97c1e05a26c427ba47da0a56e2bbfae274a96c7ce442e63f00666fa945a8d","target":"record","created_at":"2026-07-05T11:57:54Z","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":"1cc406c3f51288ca37b3db045c6655fb71aa7a13b4ca7db07e05002adc8a8487","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-31T02:06:21Z","title_canon_sha256":"643e16e006f2d5fc85540719332cd01dca385258810519aecd86a14f861883b2"},"schema_version":"1.0","source":{"id":"2501.18849","kind":"arxiv","version":2}},"canonical_sha256":"cde53c354abf16126985bbf1e87ad529078c6f058448a1f3a3354f36121262f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cde53c354abf16126985bbf1e87ad529078c6f058448a1f3a3354f36121262f5","first_computed_at":"2026-07-05T11:57:54.600635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:57:54.600635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jmLwFCeWLMKkOsHjtMq31FtV6d6va5hVHQ2zooYmf7uXou8S/uSvm5dvGu8+yvlYBdZNbSCxjKnpkI/iOLaKDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:57:54.601060Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.18849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41e97c1e05a26c427ba47da0a56e2bbfae274a96c7ce442e63f00666fa945a8d","sha256:8c71e707c718c0499cf3cd250b814a687dc79e85856578bf547b0d739da57222"],"state_sha256":"bd557b805d043f55b87fb5d374dda24a571c153c3f591d11c987be9f8eca3866"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d92i2lwmkUm7RhRg0u7V6f8rBUyh5UPs8/m4SJExSn8qX0J9cKgvvbeKoxU2YvPE7dQ4OXrQlpWHPjBCIfE+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T07:50:59.566155Z","bundle_sha256":"23201c95c1dc2d13c6406969c88f5a8684800b6e17a049222b427f0f2ae7b666"}}