{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4DUILRA7BHDJIJLPOVMSSJBNOW","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":"c4a8a4a5c7d3dfedbf7fed80998889cee356cc1d3b7381b59ac03a9fc9feecf7","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-07T10:17:40Z","title_canon_sha256":"635d10bf05d2347fbb64a0068fe7fcdb1c9b21648ede714092664eddbd64aa70"},"schema_version":"1.0","source":{"id":"1207.1784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1784","created_at":"2026-05-18T01:56:27Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1784v2","created_at":"2026-05-18T01:56:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1784","created_at":"2026-05-18T01:56:27Z"},{"alias_kind":"pith_short_12","alias_value":"4DUILRA7BHDJ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4DUILRA7BHDJIJLP","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4DUILRA7","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:d2577348fa1affa3afa923826c7df90f075addda7f75a0ef86f70be51001443a","target":"graph","created_at":"2026-05-18T01:56:27Z","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":"Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables \"above\" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $ \\chi^{(n)}$, corresponding to the decomposition of the ","authors_text":"J-M. Maillard, S. Boukraa, S. Hassani","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-07T10:17:40Z","title":"Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1784","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":"sha256:3831e73602bcd1d5c071c94f45e81389a73a11e264cab9c8dc1cbdfe2f96d7b6","target":"record","created_at":"2026-05-18T01:56:27Z","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":"c4a8a4a5c7d3dfedbf7fed80998889cee356cc1d3b7381b59ac03a9fc9feecf7","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-07T10:17:40Z","title_canon_sha256":"635d10bf05d2347fbb64a0068fe7fcdb1c9b21648ede714092664eddbd64aa70"},"schema_version":"1.0","source":{"id":"1207.1784","kind":"arxiv","version":2}},"canonical_sha256":"e0e885c41f09c694256f755929242d75a9535fa954706b0d5e56583308496574","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0e885c41f09c694256f755929242d75a9535fa954706b0d5e56583308496574","first_computed_at":"2026-05-18T01:56:27.045718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:27.045718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vkXcH5qGG9WkOyIK95LGv54PCiDWhFXie+8A//L9/jSehF1nYmHZRuO3bYffITwQvZmsFeJZ6+3+SiGLdL0ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:27.046301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3831e73602bcd1d5c071c94f45e81389a73a11e264cab9c8dc1cbdfe2f96d7b6","sha256:d2577348fa1affa3afa923826c7df90f075addda7f75a0ef86f70be51001443a"],"state_sha256":"8653fc3faf986870e14ed117d9e24f18fdd1b5df4f3e7708eeca1dd591746ad0"}