{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WELKTTTU2VKTQIZKKTXENMEPLV","short_pith_number":"pith:WELKTTTU","canonical_record":{"source":{"id":"2507.00116","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-30T18:00:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2fd4d2a3f54812cb9f042dad717eb486415a51ad57185e586b8ebcba9c6796f8","abstract_canon_sha256":"e1d4609bc9703addc842edfaa131b533c21eded11d3a7e96e46228509c3aac7f"},"schema_version":"1.0"},"canonical_sha256":"b116a9ce74d55538232a54ee46b08f5d412ca7375cf99a30d8717b5fef08fca7","source":{"kind":"arxiv","id":"2507.00116","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.00116","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"arxiv_version","alias_value":"2507.00116v2","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00116","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"pith_short_12","alias_value":"WELKTTTU2VKT","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"pith_short_16","alias_value":"WELKTTTU2VKTQIZK","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"pith_short_8","alias_value":"WELKTTTU","created_at":"2026-07-05T11:37:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WELKTTTU2VKTQIZKKTXENMEPLV","target":"record","payload":{"canonical_record":{"source":{"id":"2507.00116","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-30T18:00:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2fd4d2a3f54812cb9f042dad717eb486415a51ad57185e586b8ebcba9c6796f8","abstract_canon_sha256":"e1d4609bc9703addc842edfaa131b533c21eded11d3a7e96e46228509c3aac7f"},"schema_version":"1.0"},"canonical_sha256":"b116a9ce74d55538232a54ee46b08f5d412ca7375cf99a30d8717b5fef08fca7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:37:24.888766Z","signature_b64":"WFu9+RB/LMqcQjeQNa+V/SQpNTu6BT3inx7araLVurRwrMILsNeZ+Ju7PJ/6bSUS5ZnIXStl2rngqQRYW6gCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b116a9ce74d55538232a54ee46b08f5d412ca7375cf99a30d8717b5fef08fca7","last_reissued_at":"2026-07-05T11:37:24.888245Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:37:24.888245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.00116","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":"2026-07-05T11:37:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KncS4ML+XNP1Ct752kPOkxEvvhcdUttXVs+RekPagLZCU77febsz+nph5XJJCvpKQXmGymUjuM78hgbmA6aVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:15:49.031308Z"},"content_sha256":"9749dcc1221ba1d1aaed64892d4a90f62fe8688738d7159dfb35f500015216cb","schema_version":"1.0","event_id":"sha256:9749dcc1221ba1d1aaed64892d4a90f62fe8688738d7159dfb35f500015216cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WELKTTTU2VKTQIZKKTXENMEPLV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum K-theory levels in physics and math","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"E. Sharpe, H. Zhang, I. Huq-Kuruvilla, L. Mihalcea","submitted_at":"2025-06-30T18:00:00Z","abstract_excerpt":"The purpose of this paper is to describe the basics of a dictionary between Chern-Simons levels in three-dimensional gauged linear sigma models (GLSMs) and the (coincidentally-named) Ruan-Zhang levels for twisted quantum K-theory in mathematics. Each defines a twisting of quantum K-theory, and our proposed dictionary identifies these two twistings, in the cases of projective spaces, Grassmannians, and flag manifolds. We verify the dictionary by realizing the Coulomb branch equations as symbols of certain differential operators annihilating a twisted version of the I function associated to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00116","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/2507.00116/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":"2026-07-05T11:37:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KrQsolmHa9DXg5A6utgM1OnFfdGE33XZQr4B+pl3hD7tLeT2L6cJWcsc/dPUku6957xS2kxpXJ65xwN8E1yCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:15:49.031922Z"},"content_sha256":"378ed086d4612ae1692b725c85acfd7e86cb1454669a63796d68faebe87d1e9e","schema_version":"1.0","event_id":"sha256:378ed086d4612ae1692b725c85acfd7e86cb1454669a63796d68faebe87d1e9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WELKTTTU2VKTQIZKKTXENMEPLV/bundle.json","state_url":"https://pith.science/pith/WELKTTTU2VKTQIZKKTXENMEPLV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WELKTTTU2VKTQIZKKTXENMEPLV/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":"2026-08-08T12:15:49Z","links":{"resolver":"https://pith.science/pith/WELKTTTU2VKTQIZKKTXENMEPLV","bundle":"https://pith.science/pith/WELKTTTU2VKTQIZKKTXENMEPLV/bundle.json","state":"https://pith.science/pith/WELKTTTU2VKTQIZKKTXENMEPLV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WELKTTTU2VKTQIZKKTXENMEPLV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WELKTTTU2VKTQIZKKTXENMEPLV","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":"e1d4609bc9703addc842edfaa131b533c21eded11d3a7e96e46228509c3aac7f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-30T18:00:00Z","title_canon_sha256":"2fd4d2a3f54812cb9f042dad717eb486415a51ad57185e586b8ebcba9c6796f8"},"schema_version":"1.0","source":{"id":"2507.00116","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.00116","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"arxiv_version","alias_value":"2507.00116v2","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00116","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"pith_short_12","alias_value":"WELKTTTU2VKT","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"pith_short_16","alias_value":"WELKTTTU2VKTQIZK","created_at":"2026-07-05T11:37:24Z"},{"alias_kind":"pith_short_8","alias_value":"WELKTTTU","created_at":"2026-07-05T11:37:24Z"}],"graph_snapshots":[{"event_id":"sha256:378ed086d4612ae1692b725c85acfd7e86cb1454669a63796d68faebe87d1e9e","target":"graph","created_at":"2026-07-05T11:37:24Z","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/2507.00116/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this paper is to describe the basics of a dictionary between Chern-Simons levels in three-dimensional gauged linear sigma models (GLSMs) and the (coincidentally-named) Ruan-Zhang levels for twisted quantum K-theory in mathematics. Each defines a twisting of quantum K-theory, and our proposed dictionary identifies these two twistings, in the cases of projective spaces, Grassmannians, and flag manifolds. We verify the dictionary by realizing the Coulomb branch equations as symbols of certain differential operators annihilating a twisted version of the I function associated to the ","authors_text":"E. Sharpe, H. Zhang, I. Huq-Kuruvilla, L. Mihalcea","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-30T18:00:00Z","title":"Quantum K-theory levels in physics and math"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00116","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":"sha256:9749dcc1221ba1d1aaed64892d4a90f62fe8688738d7159dfb35f500015216cb","target":"record","created_at":"2026-07-05T11:37:24Z","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":"e1d4609bc9703addc842edfaa131b533c21eded11d3a7e96e46228509c3aac7f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-06-30T18:00:00Z","title_canon_sha256":"2fd4d2a3f54812cb9f042dad717eb486415a51ad57185e586b8ebcba9c6796f8"},"schema_version":"1.0","source":{"id":"2507.00116","kind":"arxiv","version":2}},"canonical_sha256":"b116a9ce74d55538232a54ee46b08f5d412ca7375cf99a30d8717b5fef08fca7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b116a9ce74d55538232a54ee46b08f5d412ca7375cf99a30d8717b5fef08fca7","first_computed_at":"2026-07-05T11:37:24.888245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:37:24.888245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFu9+RB/LMqcQjeQNa+V/SQpNTu6BT3inx7araLVurRwrMILsNeZ+Ju7PJ/6bSUS5ZnIXStl2rngqQRYW6gCAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:37:24.888766Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.00116","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9749dcc1221ba1d1aaed64892d4a90f62fe8688738d7159dfb35f500015216cb","sha256:378ed086d4612ae1692b725c85acfd7e86cb1454669a63796d68faebe87d1e9e"],"state_sha256":"1d4714db6d57a18320c595d26b90b259654209eb2ce228dee235c4ab325054c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyMhfSn8tw4jvYANANLgsMHhxiP5ziJCZqjh/IUBxKCh0mzhGadHVcNBPWhqHdT8pTIMJ8iSmI5bgi867PxVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T12:15:49.036913Z","bundle_sha256":"3030565ccd45d8860558ea1922d776795cccd7d50c040c7a584a6345d8f5d83f"}}