{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:4AZYHUEPAAVQDW3TL672BHCQIA","short_pith_number":"pith:4AZYHUEP","schema_version":"1.0","canonical_sha256":"e03383d08f002b01db735fbfa09c504027689e2bb041e678a6a2913fcd9f59c9","source":{"kind":"arxiv","id":"1002.2480","version":2},"attestation_state":"computed","paper":{"title":"Form factor expansions in the 2D Ising model and Painlev\\'e VI","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Anthony J. Guttmann, Vladimir V. Mangazeev","submitted_at":"2010-02-12T06:56:53Z","abstract_excerpt":"We derive a Toda-type recurrence relation, in both high and low temperature regimes, for the $\\lambda$ - extended diagonal correlation functions $C(N,N;\\lambda)$ of the two-dimensional Ising model, using an earlier connection between diagonal form factor expansions and tau-functions within Painlev\\'e VI (PVI) theory, originally discovered by Jimbo and Miwa. This greatly simplifies the calculation of the diagonal correlation functions, particularly their $\\lambda$-extended counterparts. We also conjecture a closed form expression for the simplest off-diagonal case $C^{\\pm}(0,1;\\lambda)$ where a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1002.2480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-12T06:56:53Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"f1172ef77d14291224a8bef4279c05464a217d38ae8e8a7d45ed8c1aeea69de2","abstract_canon_sha256":"4c5cb3a21556faf28603a79151ac97974e49e4ed1f3873c917f63eba211db028"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:10.086290Z","signature_b64":"kO9pOxlvxsNwvly40JG8BCn90iEVA6aTJs6jlgugGFWm4BJ0grkhoiLx4sheOL5xs9reioqT9akX48QV324MCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e03383d08f002b01db735fbfa09c504027689e2bb041e678a6a2913fcd9f59c9","last_reissued_at":"2026-05-18T00:43:10.085579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:10.085579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Form factor expansions in the 2D Ising model and Painlev\\'e VI","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Anthony J. Guttmann, Vladimir V. Mangazeev","submitted_at":"2010-02-12T06:56:53Z","abstract_excerpt":"We derive a Toda-type recurrence relation, in both high and low temperature regimes, for the $\\lambda$ - extended diagonal correlation functions $C(N,N;\\lambda)$ of the two-dimensional Ising model, using an earlier connection between diagonal form factor expansions and tau-functions within Painlev\\'e VI (PVI) theory, originally discovered by Jimbo and Miwa. This greatly simplifies the calculation of the diagonal correlation functions, particularly their $\\lambda$-extended counterparts. We also conjecture a closed form expression for the simplest off-diagonal case $C^{\\pm}(0,1;\\lambda)$ where a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2480","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1002.2480","created_at":"2026-05-18T00:43:10.085710+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.2480v2","created_at":"2026-05-18T00:43:10.085710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2480","created_at":"2026-05-18T00:43:10.085710+00:00"},{"alias_kind":"pith_short_12","alias_value":"4AZYHUEPAAVQ","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"4AZYHUEPAAVQDW3T","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"4AZYHUEP","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA","json":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA.json","graph_json":"https://pith.science/api/pith-number/4AZYHUEPAAVQDW3TL672BHCQIA/graph.json","events_json":"https://pith.science/api/pith-number/4AZYHUEPAAVQDW3TL672BHCQIA/events.json","paper":"https://pith.science/paper/4AZYHUEP"},"agent_actions":{"view_html":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA","download_json":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA.json","view_paper":"https://pith.science/paper/4AZYHUEP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.2480&json=true","fetch_graph":"https://pith.science/api/pith-number/4AZYHUEPAAVQDW3TL672BHCQIA/graph.json","fetch_events":"https://pith.science/api/pith-number/4AZYHUEPAAVQDW3TL672BHCQIA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA/action/storage_attestation","attest_author":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA/action/author_attestation","sign_citation":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA/action/citation_signature","submit_replication":"https://pith.science/pith/4AZYHUEPAAVQDW3TL672BHCQIA/action/replication_record"}},"created_at":"2026-05-18T00:43:10.085710+00:00","updated_at":"2026-05-18T00:43:10.085710+00:00"}