{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:4Y4NJ4SXJBN3SROWR6LXZ2NSXG","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":"936d6672e1c5610730a5fbe64a1a8f3370f7827b9f7e5ab8f920cfcab5db3218","cross_cats_sorted":["math-ph","math.AG","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-23T19:34:58Z","title_canon_sha256":"d683c6ecee8993e7e6aa83dcc2a64a1261116f463a750ba7bd24ce4b9f6e2a3d"},"schema_version":"1.0","source":{"id":"2211.13269","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.13269","created_at":"2026-07-05T08:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"2211.13269v2","created_at":"2026-07-05T08:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.13269","created_at":"2026-07-05T08:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"4Y4NJ4SXJBN3","created_at":"2026-07-05T08:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"4Y4NJ4SXJBN3SROW","created_at":"2026-07-05T08:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"4Y4NJ4SX","created_at":"2026-07-05T08:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:092339cc956e36f8e6998f8d007c0d15811083e54c1fba5404b5ffadffee0c13","target":"graph","created_at":"2026-07-05T08:30:01Z","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/2211.13269/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider generalizations of equivariant volumes of abelian GIT quotients obtained as partition functions of 1d, 2d, and 3d supersymmetric GLSM on $S^1$, $D^2$ and $D^2 \\times S^1$, respectively. We define these objects and study their dependence on equivariant parameters for non-compact toric K\\\"ahler quotients. We generalize the finite-difference equations (shift equations) obeyed by equivariant volumes to these partition functions. The partition functions are annihilated by differential/difference operators that represent equivariant quantum cohomology/K-theory relations of the target and","authors_text":"Luca Cassia, Maxim Zabzine, Nicolo Piazzalunga","cross_cats":["math-ph","math.AG","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-23T19:34:58Z","title":"From equivariant volumes to equivariant periods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.13269","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":"sha256:37f91a68d0c5cb98c4baa5e4f7a9356aface5c8743c3d8226f1540c6423efbd8","target":"record","created_at":"2026-07-05T08:30:01Z","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":"936d6672e1c5610730a5fbe64a1a8f3370f7827b9f7e5ab8f920cfcab5db3218","cross_cats_sorted":["math-ph","math.AG","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-23T19:34:58Z","title_canon_sha256":"d683c6ecee8993e7e6aa83dcc2a64a1261116f463a750ba7bd24ce4b9f6e2a3d"},"schema_version":"1.0","source":{"id":"2211.13269","kind":"arxiv","version":2}},"canonical_sha256":"e638d4f257485bb945d68f977ce9b2b98a3b4a6899271641bdd687d052a1b357","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e638d4f257485bb945d68f977ce9b2b98a3b4a6899271641bdd687d052a1b357","first_computed_at":"2026-07-05T08:30:01.775103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:30:01.775103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YkV3VLqEx7CpjIhGiO2D5FkkrnuEyBQlrxrh491/m62KJp8ZFCh9H/kACk/cH3qmP9uqXyMeCawk/GVU0chHCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:30:01.775644Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.13269","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37f91a68d0c5cb98c4baa5e4f7a9356aface5c8743c3d8226f1540c6423efbd8","sha256:092339cc956e36f8e6998f8d007c0d15811083e54c1fba5404b5ffadffee0c13"],"state_sha256":"d94bb5a8687405a881c90d413c32299dff73306da099341db934396ae8ea2784"}