{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WEDEHY4Q2O4IBPLMPSFIXONANG","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":"34684a1dcf20aa90fae6ceaeee05ca196c38d3c915a9caee91cdd0fed722966d","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-25T13:42:13Z","title_canon_sha256":"20cf2b7bdb2f03411de0d1e8c0eae99342f7ac3b7f628c844bea984cec11411f"},"schema_version":"1.0","source":{"id":"1212.6049","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6049","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6049v3","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6049","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"WEDEHY4Q2O4I","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WEDEHY4Q2O4IBPLM","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WEDEHY4Q","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:7150c5899d97b58d00e4ee861f8fb6b293b5d214f33153adc0e3670499a25dba","target":"graph","created_at":"2026-05-18T03:12:33Z","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":"We review the formalism of free fermions used for construction of tau-functions of classical integrable hierarchies and give a detailed derivation of group-like properties of the normally ordered exponents, transformations between different normal orderings, the bilinear relations, the generalized Wick theorem and the bosonization rules. We also consider various examples of tau-functions and give their fermionic realization.","authors_text":"Alexander Alexandrov, Anton Zabrodin","cross_cats":["hep-th","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-25T13:42:13Z","title":"Free fermions and tau-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6049","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":"sha256:09f1651b2a0486a78b60e8e7ae7acc6fa5eb06d54013a12aadf07d3aada28a1a","target":"record","created_at":"2026-05-18T03:12:33Z","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":"34684a1dcf20aa90fae6ceaeee05ca196c38d3c915a9caee91cdd0fed722966d","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-25T13:42:13Z","title_canon_sha256":"20cf2b7bdb2f03411de0d1e8c0eae99342f7ac3b7f628c844bea984cec11411f"},"schema_version":"1.0","source":{"id":"1212.6049","kind":"arxiv","version":3}},"canonical_sha256":"b10643e390d3b880bd6c7c8a8bb9a069831798970f4882244f51e95dea6a3505","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b10643e390d3b880bd6c7c8a8bb9a069831798970f4882244f51e95dea6a3505","first_computed_at":"2026-05-18T03:12:33.138915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:33.138915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l+94sehv2ow47QFBy6cx4GzcEGELwESZASId5c9gtXqrhds1o3FKUG1ojHKb3Xw1khMEGZFDrh8qWmr+1YpyCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:33.139672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6049","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09f1651b2a0486a78b60e8e7ae7acc6fa5eb06d54013a12aadf07d3aada28a1a","sha256:7150c5899d97b58d00e4ee861f8fb6b293b5d214f33153adc0e3670499a25dba"],"state_sha256":"395f4ad6e638050679854653293e3804f1f1b897e1f3ea5b7192ee85027e4b50"}