{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3FKQDB6NG2BD5MZ4OLJYVNCNSH","short_pith_number":"pith:3FKQDB6N","canonical_record":{"source":{"id":"1403.3966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-16T22:05:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"28887115a14e44d8ad66edce965283ae6c22c89cc1123ba770ba445bc462ad67","abstract_canon_sha256":"1eabb1533b2274640ece3ef552b5226f1b29da7e6cb1a33b194f6c95114d1b5f"},"schema_version":"1.0"},"canonical_sha256":"d9550187cd36823eb33c72d38ab44d91fa2fb3756946c032271f641b8b599300","source":{"kind":"arxiv","id":"1403.3966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3966","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3966v1","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3966","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"3FKQDB6NG2BD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3FKQDB6NG2BD5MZ4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3FKQDB6N","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3FKQDB6NG2BD5MZ4OLJYVNCNSH","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-16T22:05:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"28887115a14e44d8ad66edce965283ae6c22c89cc1123ba770ba445bc462ad67","abstract_canon_sha256":"1eabb1533b2274640ece3ef552b5226f1b29da7e6cb1a33b194f6c95114d1b5f"},"schema_version":"1.0"},"canonical_sha256":"d9550187cd36823eb33c72d38ab44d91fa2fb3756946c032271f641b8b599300","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:48.477604Z","signature_b64":"2hb81Ks77bmK/7iK4arV2gGIjgfSSoR7aRFbGm6tvj2eLwL8RXe1LJlC4YjqzLsgqgEEJzbFPoNVY2+ONof7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9550187cd36823eb33c72d38ab44d91fa2fb3756946c032271f641b8b599300","last_reissued_at":"2026-05-18T02:45:48.477138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:48.477138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3966","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":"2026-05-18T02:45:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jc0Yooj7HcL6avfAI15biAOf1DaAhMj8cyAFM6iaBd2cuDzACGNbEzRnWuFTzMO1EzTjdoXWqoTsEBfqTXRmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:35:02.749738Z"},"content_sha256":"fecf79609a1c02d9a6cf2220c6856367b7635bb2f4592a763aa628a3e62d34db","schema_version":"1.0","event_id":"sha256:fecf79609a1c02d9a6cf2220c6856367b7635bb2f4592a763aa628a3e62d34db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3FKQDB6NG2BD5MZ4OLJYVNCNSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Singularities in the Susceptibility Expansion for the Two-Dimensional Ising Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Craig A. Tracy, Harold Widom","submitted_at":"2014-03-16T22:05:24Z","abstract_excerpt":"For temperatures below the critical temperature, the magnetic susceptibility for the two-dimensional isotropic Ising model can be expressed in terms of an infinite series of multiple integrals. With respect to a parameter related to temperature and the interaction constant, the integrals may be extended to functions analytic outside the unit circle. In a groundbreaking paper, B. G. Nickel identified a class of singularities of these integrals on the unit circle. In this note we show that there are no other singularities on the unit circle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3966","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":""},"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":"2026-05-18T02:45:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"emEi+KxXpDiNJpdlulAtiUIUT4crlTkq2IbyCnDqRcyUovWJbpvIVGLUd1io4a+CWFwmbIpxkL8NgJBypC8PBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:35:02.750088Z"},"content_sha256":"d3fb3fd5a762812995364269dd3966df02f3e9b78d673ad51a9df7d67314a62d","schema_version":"1.0","event_id":"sha256:d3fb3fd5a762812995364269dd3966df02f3e9b78d673ad51a9df7d67314a62d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FKQDB6NG2BD5MZ4OLJYVNCNSH/bundle.json","state_url":"https://pith.science/pith/3FKQDB6NG2BD5MZ4OLJYVNCNSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FKQDB6NG2BD5MZ4OLJYVNCNSH/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":"2026-06-04T23:35:02Z","links":{"resolver":"https://pith.science/pith/3FKQDB6NG2BD5MZ4OLJYVNCNSH","bundle":"https://pith.science/pith/3FKQDB6NG2BD5MZ4OLJYVNCNSH/bundle.json","state":"https://pith.science/pith/3FKQDB6NG2BD5MZ4OLJYVNCNSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FKQDB6NG2BD5MZ4OLJYVNCNSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3FKQDB6NG2BD5MZ4OLJYVNCNSH","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":"1eabb1533b2274640ece3ef552b5226f1b29da7e6cb1a33b194f6c95114d1b5f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-16T22:05:24Z","title_canon_sha256":"28887115a14e44d8ad66edce965283ae6c22c89cc1123ba770ba445bc462ad67"},"schema_version":"1.0","source":{"id":"1403.3966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3966","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3966v1","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3966","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"3FKQDB6NG2BD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3FKQDB6NG2BD5MZ4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3FKQDB6N","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:d3fb3fd5a762812995364269dd3966df02f3e9b78d673ad51a9df7d67314a62d","target":"graph","created_at":"2026-05-18T02:45:48Z","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":"For temperatures below the critical temperature, the magnetic susceptibility for the two-dimensional isotropic Ising model can be expressed in terms of an infinite series of multiple integrals. With respect to a parameter related to temperature and the interaction constant, the integrals may be extended to functions analytic outside the unit circle. In a groundbreaking paper, B. G. Nickel identified a class of singularities of these integrals on the unit circle. In this note we show that there are no other singularities on the unit circle.","authors_text":"Craig A. Tracy, Harold Widom","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-16T22:05:24Z","title":"On the Singularities in the Susceptibility Expansion for the Two-Dimensional Ising Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3966","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:fecf79609a1c02d9a6cf2220c6856367b7635bb2f4592a763aa628a3e62d34db","target":"record","created_at":"2026-05-18T02:45:48Z","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":"1eabb1533b2274640ece3ef552b5226f1b29da7e6cb1a33b194f6c95114d1b5f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-16T22:05:24Z","title_canon_sha256":"28887115a14e44d8ad66edce965283ae6c22c89cc1123ba770ba445bc462ad67"},"schema_version":"1.0","source":{"id":"1403.3966","kind":"arxiv","version":1}},"canonical_sha256":"d9550187cd36823eb33c72d38ab44d91fa2fb3756946c032271f641b8b599300","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9550187cd36823eb33c72d38ab44d91fa2fb3756946c032271f641b8b599300","first_computed_at":"2026-05-18T02:45:48.477138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:48.477138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2hb81Ks77bmK/7iK4arV2gGIjgfSSoR7aRFbGm6tvj2eLwL8RXe1LJlC4YjqzLsgqgEEJzbFPoNVY2+ONof7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:48.477604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fecf79609a1c02d9a6cf2220c6856367b7635bb2f4592a763aa628a3e62d34db","sha256:d3fb3fd5a762812995364269dd3966df02f3e9b78d673ad51a9df7d67314a62d"],"state_sha256":"7c8ec443edb4ab8df1d5564637410b4d2b1ba5c129961f2c4085c4de0a961cab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZWznM9UOJOCZR9p7qGrtda6QT8I9QjfS2yLdILHKpdnzdfUA17oXgSAip8FfXKbZjF/gfB6wx/21hidV6/kQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:35:02.752147Z","bundle_sha256":"1873c63bc4b24159e06b31574bea820df59dca64b8984a890dd10d2875b20d9e"}}