{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2F7DGIGAMKGXX4M55T6KTTENIV","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":"01351593f0b459079d756371a2233f2e07699614be1da3093c59880a64074ce8","cross_cats_sorted":["math.AT","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-04-30T20:39:34Z","title_canon_sha256":"a0c9b2383c11743067f424dd97ccdb7e0bb965a3e6df1c76244cc6217fcfadfa"},"schema_version":"1.0","source":{"id":"2505.00172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00172","created_at":"2026-07-05T10:56:43Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00172v1","created_at":"2026-07-05T10:56:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00172","created_at":"2026-07-05T10:56:43Z"},{"alias_kind":"pith_short_12","alias_value":"2F7DGIGAMKGX","created_at":"2026-07-05T10:56:43Z"},{"alias_kind":"pith_short_16","alias_value":"2F7DGIGAMKGXX4M5","created_at":"2026-07-05T10:56:43Z"},{"alias_kind":"pith_short_8","alias_value":"2F7DGIGA","created_at":"2026-07-05T10:56:43Z"}],"graph_snapshots":[{"event_id":"sha256:1b2b276a8b43c688f0f1afe8fce78eaca89b49f6ba8ceb31995e9e690398be23","target":"graph","created_at":"2026-07-05T10:56:43Z","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/2505.00172/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper establishes a unifying framework for various forms of twisted Hochschild homology by comparing two definitions of elliptic Hochschild homology: one introduced by Moulinos--Robalo--To\\\"en and the other by Sibilla--Tomasini. Central to our approach is a new Fourier--Mukai duality for formal groups. We prove that when $\\widehat{E}$ is the formal group associated to an elliptic curve $E$, the resulting $\\widehat{E}$-Hochschild homology coincides with the mapping stack construction of Sibilla--Tomasini. This identification also recovers ordinary and Hodge Hochschild homology as degenerat","authors_text":"Nicol\\`o Sibilla, Paolo Tomasini, Sarah Scherotzke","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-04-30T20:39:34Z","title":"Fourier--Mukai equivalences for formal groups and elliptic Hochschild homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00172","kind":"arxiv","version":1},"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":"sha256:82b16180ca6dd9efce2020298a58a7f2b9a659743cc92a6a60792746cc192c7a","target":"record","created_at":"2026-07-05T10:56:43Z","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":"01351593f0b459079d756371a2233f2e07699614be1da3093c59880a64074ce8","cross_cats_sorted":["math.AT","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-04-30T20:39:34Z","title_canon_sha256":"a0c9b2383c11743067f424dd97ccdb7e0bb965a3e6df1c76244cc6217fcfadfa"},"schema_version":"1.0","source":{"id":"2505.00172","kind":"arxiv","version":1}},"canonical_sha256":"d17e3320c0628d7bf19decfca9cc8d456d2af15ecfaf0b5ad97b97e93c6cd694","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d17e3320c0628d7bf19decfca9cc8d456d2af15ecfaf0b5ad97b97e93c6cd694","first_computed_at":"2026-07-05T10:56:43.426228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:56:43.426228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggyYE657DZn8g3OUe4rqwqAUvYCo1V2eMq0EwM9PXwaCN5sq0kIsVAndg+WVx6dVJ5/kTleEJBmKSjv0tqVDAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:56:43.426678Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.00172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82b16180ca6dd9efce2020298a58a7f2b9a659743cc92a6a60792746cc192c7a","sha256:1b2b276a8b43c688f0f1afe8fce78eaca89b49f6ba8ceb31995e9e690398be23"],"state_sha256":"afa906f4e60bb9495dced316ef365d7c3032d410cfdf5f2a18af7e6d7d5066bc"}