{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FRM7DUURO6N4G24PHQPEOIFXHB","short_pith_number":"pith:FRM7DUUR","canonical_record":{"source":{"id":"1512.08586","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-29T02:46:02Z","cross_cats_sorted":[],"title_canon_sha256":"576e2fb764e11ef54a2e8b34cac20cf740fefa390e86b656738a01db6d43d59b","abstract_canon_sha256":"ec59518ebefbdb5b78f4aecdeee75f070956ccd928756ced5ee7d6b307b890f6"},"schema_version":"1.0"},"canonical_sha256":"2c59f1d291779bc36b8f3c1e4720b7386ebdf23477fce644bc7604b8356dc8a5","source":{"kind":"arxiv","id":"1512.08586","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08586","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08586v3","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08586","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"pith_short_12","alias_value":"FRM7DUURO6N4","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FRM7DUURO6N4G24P","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FRM7DUUR","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FRM7DUURO6N4G24PHQPEOIFXHB","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08586","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-29T02:46:02Z","cross_cats_sorted":[],"title_canon_sha256":"576e2fb764e11ef54a2e8b34cac20cf740fefa390e86b656738a01db6d43d59b","abstract_canon_sha256":"ec59518ebefbdb5b78f4aecdeee75f070956ccd928756ced5ee7d6b307b890f6"},"schema_version":"1.0"},"canonical_sha256":"2c59f1d291779bc36b8f3c1e4720b7386ebdf23477fce644bc7604b8356dc8a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:37.495108Z","signature_b64":"QbERvlOJLIGafmxmtS7R0fE18DQg7WUcvUVGehLw3kjWaao2qcoj9bSQ8I+f1xdvtqihaEoKnXV9xoMyGeeaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c59f1d291779bc36b8f3c1e4720b7386ebdf23477fce644bc7604b8356dc8a5","last_reissued_at":"2026-05-18T00:48:37.494451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:37.494451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08586","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLOy/SAt3/W6wTQt7giXpLn1OksVFyeVbTeDb2Tv1JloRl3QNx9LpYIcxOT9+btJ7eQEtd629bwf9dHPraR6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:40:09.966110Z"},"content_sha256":"ee927e15027334abb95f7396c2d283129a5ba446442dbeb99d1855c30f2c6026","schema_version":"1.0","event_id":"sha256:ee927e15027334abb95f7396c2d283129a5ba446442dbeb99d1855c30f2c6026"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FRM7DUURO6N4G24PHQPEOIFXHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum sheaf cohomology on Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Eric Sharpe, Jirui Guo, Zhentao Lu","submitted_at":"2015-12-29T02:46:02Z","abstract_excerpt":"In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08586","kind":"arxiv","version":3},"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":"2026-05-18T00:48:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mSFlAeUBP5rv/fUeIt50ttg8jX4/LZ5EwZVhYIPBHAeYr7GDStHZU/KPYtBAApNOKSpPxtu+l/N+IwAGcpkBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:40:09.966733Z"},"content_sha256":"57d2a3c14260c70ee156ef174fe2ea978f246a65d63be4d1c250de102f40e3ea","schema_version":"1.0","event_id":"sha256:57d2a3c14260c70ee156ef174fe2ea978f246a65d63be4d1c250de102f40e3ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FRM7DUURO6N4G24PHQPEOIFXHB/bundle.json","state_url":"https://pith.science/pith/FRM7DUURO6N4G24PHQPEOIFXHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FRM7DUURO6N4G24PHQPEOIFXHB/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":"2026-06-06T20:40:09Z","links":{"resolver":"https://pith.science/pith/FRM7DUURO6N4G24PHQPEOIFXHB","bundle":"https://pith.science/pith/FRM7DUURO6N4G24PHQPEOIFXHB/bundle.json","state":"https://pith.science/pith/FRM7DUURO6N4G24PHQPEOIFXHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FRM7DUURO6N4G24PHQPEOIFXHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FRM7DUURO6N4G24PHQPEOIFXHB","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":"ec59518ebefbdb5b78f4aecdeee75f070956ccd928756ced5ee7d6b307b890f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-29T02:46:02Z","title_canon_sha256":"576e2fb764e11ef54a2e8b34cac20cf740fefa390e86b656738a01db6d43d59b"},"schema_version":"1.0","source":{"id":"1512.08586","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08586","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08586v3","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08586","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"pith_short_12","alias_value":"FRM7DUURO6N4","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FRM7DUURO6N4G24P","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FRM7DUUR","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:57d2a3c14260c70ee156ef174fe2ea978f246a65d63be4d1c250de102f40e3ea","target":"graph","created_at":"2026-05-18T00:48:37Z","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":"In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances","authors_text":"Eric Sharpe, Jirui Guo, Zhentao Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-29T02:46:02Z","title":"Quantum sheaf cohomology on Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08586","kind":"arxiv","version":3},"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:ee927e15027334abb95f7396c2d283129a5ba446442dbeb99d1855c30f2c6026","target":"record","created_at":"2026-05-18T00:48:37Z","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":"ec59518ebefbdb5b78f4aecdeee75f070956ccd928756ced5ee7d6b307b890f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-29T02:46:02Z","title_canon_sha256":"576e2fb764e11ef54a2e8b34cac20cf740fefa390e86b656738a01db6d43d59b"},"schema_version":"1.0","source":{"id":"1512.08586","kind":"arxiv","version":3}},"canonical_sha256":"2c59f1d291779bc36b8f3c1e4720b7386ebdf23477fce644bc7604b8356dc8a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c59f1d291779bc36b8f3c1e4720b7386ebdf23477fce644bc7604b8356dc8a5","first_computed_at":"2026-05-18T00:48:37.494451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:37.494451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QbERvlOJLIGafmxmtS7R0fE18DQg7WUcvUVGehLw3kjWaao2qcoj9bSQ8I+f1xdvtqihaEoKnXV9xoMyGeeaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:37.495108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08586","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee927e15027334abb95f7396c2d283129a5ba446442dbeb99d1855c30f2c6026","sha256:57d2a3c14260c70ee156ef174fe2ea978f246a65d63be4d1c250de102f40e3ea"],"state_sha256":"772a2eb7857381d130ea7bf303e36275a8ac7bb00e85da7a45a2665505a39a0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9qP1u0LZNwXUn817m7iCp168rQFNgfbxPvQcSKTMCdpttd7zNvL15j/DGXCN4jn/wuhii5CvZFQPciEmORzDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:40:09.969865Z","bundle_sha256":"20a6cca2f200cfe299e4b68c6b0c5aaeb1b0fe58123059f5e12945f39c9467ef"}}