{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:Q2ZUDHARLDINLIJC2GXNRC26SS","short_pith_number":"pith:Q2ZUDHAR","canonical_record":{"source":{"id":"cond-mat/0605568","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-05-23T12:06:36Z","cross_cats_sorted":[],"title_canon_sha256":"bcccee3efa8f3e1ca8a6cd0b6f847e6ba636cd193ec9b67380ef54e3376d22c6","abstract_canon_sha256":"d72725d70d1136b4151083bdb338ac6ba646b0d2b31275acdbb8034fc22e1e0a"},"schema_version":"1.0"},"canonical_sha256":"86b3419c1158d0d5a122d1aed88b5e94917587f5bf65d6a6ec6d3c799a908ade","source":{"kind":"arxiv","id":"cond-mat/0605568","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0605568","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0605568v1","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0605568","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"Q2ZUDHARLDIN","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"pith_short_16","alias_value":"Q2ZUDHARLDINLIJC","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"pith_short_8","alias_value":"Q2ZUDHAR","created_at":"2026-07-04T14:54:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:Q2ZUDHARLDINLIJC2GXNRC26SS","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0605568","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-05-23T12:06:36Z","cross_cats_sorted":[],"title_canon_sha256":"bcccee3efa8f3e1ca8a6cd0b6f847e6ba636cd193ec9b67380ef54e3376d22c6","abstract_canon_sha256":"d72725d70d1136b4151083bdb338ac6ba646b0d2b31275acdbb8034fc22e1e0a"},"schema_version":"1.0"},"canonical_sha256":"86b3419c1158d0d5a122d1aed88b5e94917587f5bf65d6a6ec6d3c799a908ade","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:54:25.025720Z","signature_b64":"tqbi7pM1AejpdzIwbz0eRlfPlfU53SoYzvoCjbco4cp8U5xQqZDslUkc5j5tuUMDxZqr/4621E8hbCCIu7NIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86b3419c1158d0d5a122d1aed88b5e94917587f5bf65d6a6ec6d3c799a908ade","last_reissued_at":"2026-07-04T14:54:25.025310Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:54:25.025310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0605568","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:54:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1RQBOfKAen9vVLAnEqrM0Js+XrKZfdtmwTxg15QaeB5TmzvRjEMlPZGZ7i70elXJImKlFCKh5N+SqCEdgHYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:30:58.269733Z"},"content_sha256":"ecff4edc495aaac4e9530611c2dbe6cfd8a153d3920a0365c4f00c67612cd4e4","schema_version":"1.0","event_id":"sha256:ecff4edc495aaac4e9530611c2dbe6cfd8a153d3920a0365c4f00c67612cd4e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:Q2ZUDHARLDINLIJC2GXNRC26SS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recursion relations for the partition function of the two-dimensional Ising model","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Michael Kastner","submitted_at":"2006-05-23T12:06:36Z","abstract_excerpt":"The partition function of the two-dimensional Ising model on a square lattice with nearest-neighbour interactions and periodic boundary conditions is investigated. Kaufman [Phys. Rev. 76, 1232--1243 (1949)] gave a solution for this function consisting of four summands. The summands are rewritten as functions of a low-temperature expansion variable, resulting in polynomials with integer coefficients. Considering these polynomials for system sizes $2^m\\times 2^n$ ($m,n\\in\\N$), a variety of recursion relations in $m,n$ are found. The recursions reveal a rich structure of the partition function an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0605568","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/0605568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:54:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UX+l0dpZFoQU636DTFgJYGGmWu0BoKHEkN/YhOr3zhutxh0QrWPEE1FCVjmn8HtwMlP5PP3GXsUKT3e8aJMeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:30:58.270112Z"},"content_sha256":"27cc68acdde9f11c979f4940dc8be6340db5ef82a1a93c160151ad392dae1b87","schema_version":"1.0","event_id":"sha256:27cc68acdde9f11c979f4940dc8be6340db5ef82a1a93c160151ad392dae1b87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2ZUDHARLDINLIJC2GXNRC26SS/bundle.json","state_url":"https://pith.science/pith/Q2ZUDHARLDINLIJC2GXNRC26SS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2ZUDHARLDINLIJC2GXNRC26SS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-04T18:30:58Z","links":{"resolver":"https://pith.science/pith/Q2ZUDHARLDINLIJC2GXNRC26SS","bundle":"https://pith.science/pith/Q2ZUDHARLDINLIJC2GXNRC26SS/bundle.json","state":"https://pith.science/pith/Q2ZUDHARLDINLIJC2GXNRC26SS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2ZUDHARLDINLIJC2GXNRC26SS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:Q2ZUDHARLDINLIJC2GXNRC26SS","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":"d72725d70d1136b4151083bdb338ac6ba646b0d2b31275acdbb8034fc22e1e0a","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-05-23T12:06:36Z","title_canon_sha256":"bcccee3efa8f3e1ca8a6cd0b6f847e6ba636cd193ec9b67380ef54e3376d22c6"},"schema_version":"1.0","source":{"id":"cond-mat/0605568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0605568","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0605568v1","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0605568","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"Q2ZUDHARLDIN","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"pith_short_16","alias_value":"Q2ZUDHARLDINLIJC","created_at":"2026-07-04T14:54:25Z"},{"alias_kind":"pith_short_8","alias_value":"Q2ZUDHAR","created_at":"2026-07-04T14:54:25Z"}],"graph_snapshots":[{"event_id":"sha256:27cc68acdde9f11c979f4940dc8be6340db5ef82a1a93c160151ad392dae1b87","target":"graph","created_at":"2026-07-04T14:54:25Z","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/cond-mat/0605568/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The partition function of the two-dimensional Ising model on a square lattice with nearest-neighbour interactions and periodic boundary conditions is investigated. Kaufman [Phys. Rev. 76, 1232--1243 (1949)] gave a solution for this function consisting of four summands. The summands are rewritten as functions of a low-temperature expansion variable, resulting in polynomials with integer coefficients. Considering these polynomials for system sizes $2^m\\times 2^n$ ($m,n\\in\\N$), a variety of recursion relations in $m,n$ are found. The recursions reveal a rich structure of the partition function an","authors_text":"Michael Kastner","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-05-23T12:06:36Z","title":"Recursion relations for the partition function of the two-dimensional Ising model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0605568","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:ecff4edc495aaac4e9530611c2dbe6cfd8a153d3920a0365c4f00c67612cd4e4","target":"record","created_at":"2026-07-04T14:54:25Z","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":"d72725d70d1136b4151083bdb338ac6ba646b0d2b31275acdbb8034fc22e1e0a","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-05-23T12:06:36Z","title_canon_sha256":"bcccee3efa8f3e1ca8a6cd0b6f847e6ba636cd193ec9b67380ef54e3376d22c6"},"schema_version":"1.0","source":{"id":"cond-mat/0605568","kind":"arxiv","version":1}},"canonical_sha256":"86b3419c1158d0d5a122d1aed88b5e94917587f5bf65d6a6ec6d3c799a908ade","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86b3419c1158d0d5a122d1aed88b5e94917587f5bf65d6a6ec6d3c799a908ade","first_computed_at":"2026-07-04T14:54:25.025310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:54:25.025310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tqbi7pM1AejpdzIwbz0eRlfPlfU53SoYzvoCjbco4cp8U5xQqZDslUkc5j5tuUMDxZqr/4621E8hbCCIu7NIAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:54:25.025720Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0605568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecff4edc495aaac4e9530611c2dbe6cfd8a153d3920a0365c4f00c67612cd4e4","sha256:27cc68acdde9f11c979f4940dc8be6340db5ef82a1a93c160151ad392dae1b87"],"state_sha256":"de8d108d062a74bf0f116d8d8acecc1501e93ee552f2748999fe460f7ad56c78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1xCuXot4F7i1WvoJnyO0I4w3PTF9tzJWkm+kOSJEZKQwdP0x0DXf8ubqC6cSpMYzULlj9YcvYDFz4J5azlHaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T18:30:58.272139Z","bundle_sha256":"e30fd4e5c29c7b660c707ed990f1a544001ef04ed68b3ac098346570ee937194"}}