{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TI2ARWI7KFBP2TWZWISIHMQTWX","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":"0284dd5f6a68f9c7d6dbc6822bf583779f70c1ec81fbebc3c6ea00545a655d3b","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-09-05T13:45:17Z","title_canon_sha256":"bf502e3e19740d7daeb5d6e0a4f657ee8f5619fbdd2105a631038d01b93c947d"},"schema_version":"1.0","source":{"id":"2409.03532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.03532","created_at":"2026-07-05T09:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"2409.03532v1","created_at":"2026-07-05T09:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.03532","created_at":"2026-07-05T09:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"TI2ARWI7KFBP","created_at":"2026-07-05T09:03:32Z"},{"alias_kind":"pith_short_16","alias_value":"TI2ARWI7KFBP2TWZ","created_at":"2026-07-05T09:03:32Z"},{"alias_kind":"pith_short_8","alias_value":"TI2ARWI7","created_at":"2026-07-05T09:03:32Z"}],"graph_snapshots":[{"event_id":"sha256:7cf413b57b23227e92a8e3f33d65b42cc3b037cdf774aac399b7fbcbed3207d7","target":"graph","created_at":"2026-07-05T09:03:32Z","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/2409.03532/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use shifted symplectic geometry to construct the Moore-Tachikawa topological quantum field theories (TQFTs) in a category of Hamiltonian schemes. Our new and overarching insight is an algebraic explanation for the existence of these TQFTs, i.e. that their structure comes naturally from three ingredients: Morita equivalence, as well as multiplication and identity bisections in abelian symplectic groupoids. Using this insight, we generalize the Moore-Tachikawa TQFTs in two directions.\n  The first generalization concerns a 1-shifted version of the Weinstein symplectic category $\\mathbf{WS}_1$.","authors_text":"Maxence Mayrand, Peter Crooks","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-09-05T13:45:17Z","title":"The Moore-Tachikawa conjecture via shifted symplectic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.03532","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":"sha256:620ddc6daedfc9caee0b357e7f7a6c78e36153ee185a64a93e197c085bb10287","target":"record","created_at":"2026-07-05T09:03:32Z","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":"0284dd5f6a68f9c7d6dbc6822bf583779f70c1ec81fbebc3c6ea00545a655d3b","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-09-05T13:45:17Z","title_canon_sha256":"bf502e3e19740d7daeb5d6e0a4f657ee8f5619fbdd2105a631038d01b93c947d"},"schema_version":"1.0","source":{"id":"2409.03532","kind":"arxiv","version":1}},"canonical_sha256":"9a3408d91f5142fd4ed9b22483b213b5d123ede024a6911ad1fa718598f1abe3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a3408d91f5142fd4ed9b22483b213b5d123ede024a6911ad1fa718598f1abe3","first_computed_at":"2026-07-05T09:03:32.836572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:03:32.836572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"du/YxcgIsH6Y/nr0ue/12ZIm2zNV5zfebUe5Eh5cbQ5T1K1OhBy23yVFHOacGKDte4EhGa9P98Y2FbeWG5pgBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:03:32.837019Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.03532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:620ddc6daedfc9caee0b357e7f7a6c78e36153ee185a64a93e197c085bb10287","sha256:7cf413b57b23227e92a8e3f33d65b42cc3b037cdf774aac399b7fbcbed3207d7"],"state_sha256":"f5388a0933d5350418d753c4f46943d873a6c6f8be12e09ef42e7bb61e4541c2"}