{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:X7SE4777GNG3EVG222MU5UEQJE","short_pith_number":"pith:X7SE4777","canonical_record":{"source":{"id":"0901.1931","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-01-14T05:55:43Z","cross_cats_sorted":[],"title_canon_sha256":"451f59748062a86d616784424d84692624d7667bc83932d46a8515904d470b41","abstract_canon_sha256":"50783230181e4036e52b30377517ec5e7f66131ff3d153406ff32dbb8a9c57f5"},"schema_version":"1.0"},"canonical_sha256":"bfe44e7fff334db254dad6994ed090490aa5c87fabdd1effbc52268510b5d4f9","source":{"kind":"arxiv","id":"0901.1931","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1931","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1931v3","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1931","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"X7SE4777GNG3","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"X7SE4777GNG3EVG2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"X7SE4777","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:X7SE4777GNG3EVG222MU5UEQJE","target":"record","payload":{"canonical_record":{"source":{"id":"0901.1931","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-01-14T05:55:43Z","cross_cats_sorted":[],"title_canon_sha256":"451f59748062a86d616784424d84692624d7667bc83932d46a8515904d470b41","abstract_canon_sha256":"50783230181e4036e52b30377517ec5e7f66131ff3d153406ff32dbb8a9c57f5"},"schema_version":"1.0"},"canonical_sha256":"bfe44e7fff334db254dad6994ed090490aa5c87fabdd1effbc52268510b5d4f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:02.408894Z","signature_b64":"VBqdE2acEPGoSc4V8u3589B4Tzr0WWFHviH86QNPDm3Cd5YBuvZHNHgAaEQrokeOaYLAjP2BbINd6cWhD3UABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfe44e7fff334db254dad6994ed090490aa5c87fabdd1effbc52268510b5d4f9","last_reissued_at":"2026-05-18T02:15:02.408359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:02.408359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.1931","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:15:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpjGLmv6MBIG16y/hqj/5gO93GXb9YTyu+6h32XRrEAME9OfGANto9aajDTcdILHPUFwl909BVKkw/bFlxg+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:07:00.025243Z"},"content_sha256":"239aad0404aee795bebdef2654ec250a17afb775d0e0ab4c16078f67a69d6e94","schema_version":"1.0","event_id":"sha256:239aad0404aee795bebdef2654ec250a17afb775d0e0ab4c16078f67a69d6e94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:X7SE4777GNG3EVG222MU5UEQJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Helen Au-Yang, Jacques H.H. Perk","submitted_at":"2009-01-14T05:55:43Z","abstract_excerpt":"In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-depe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1931","kind":"arxiv","version":3},"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":"2026-05-18T02:15:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0kFo+wMC4YWOINhDZYdRhRQztaFGDaL1ydHx+/FvGBjHCo9OdQcPQFOPFBPHf67qKsXV1yFwden6r/gP2PbfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:07:00.025614Z"},"content_sha256":"8b2c5ee1ef8274771211e7f337a54b4c9bf3bf12d99e9cb5547e20bce6efb217","schema_version":"1.0","event_id":"sha256:8b2c5ee1ef8274771211e7f337a54b4c9bf3bf12d99e9cb5547e20bce6efb217"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7SE4777GNG3EVG222MU5UEQJE/bundle.json","state_url":"https://pith.science/pith/X7SE4777GNG3EVG222MU5UEQJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7SE4777GNG3EVG222MU5UEQJE/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":"2026-06-01T12:07:00Z","links":{"resolver":"https://pith.science/pith/X7SE4777GNG3EVG222MU5UEQJE","bundle":"https://pith.science/pith/X7SE4777GNG3EVG222MU5UEQJE/bundle.json","state":"https://pith.science/pith/X7SE4777GNG3EVG222MU5UEQJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7SE4777GNG3EVG222MU5UEQJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:X7SE4777GNG3EVG222MU5UEQJE","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":"50783230181e4036e52b30377517ec5e7f66131ff3d153406ff32dbb8a9c57f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-01-14T05:55:43Z","title_canon_sha256":"451f59748062a86d616784424d84692624d7667bc83932d46a8515904d470b41"},"schema_version":"1.0","source":{"id":"0901.1931","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1931","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1931v3","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1931","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"X7SE4777GNG3","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"X7SE4777GNG3EVG2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"X7SE4777","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:8b2c5ee1ef8274771211e7f337a54b4c9bf3bf12d99e9cb5547e20bce6efb217","target":"graph","created_at":"2026-05-18T02:15:02Z","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":"In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-depe","authors_text":"Helen Au-Yang, Jacques H.H. Perk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-01-14T05:55:43Z","title":"New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1931","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":"sha256:239aad0404aee795bebdef2654ec250a17afb775d0e0ab4c16078f67a69d6e94","target":"record","created_at":"2026-05-18T02:15:02Z","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":"50783230181e4036e52b30377517ec5e7f66131ff3d153406ff32dbb8a9c57f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-01-14T05:55:43Z","title_canon_sha256":"451f59748062a86d616784424d84692624d7667bc83932d46a8515904d470b41"},"schema_version":"1.0","source":{"id":"0901.1931","kind":"arxiv","version":3}},"canonical_sha256":"bfe44e7fff334db254dad6994ed090490aa5c87fabdd1effbc52268510b5d4f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfe44e7fff334db254dad6994ed090490aa5c87fabdd1effbc52268510b5d4f9","first_computed_at":"2026-05-18T02:15:02.408359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:02.408359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VBqdE2acEPGoSc4V8u3589B4Tzr0WWFHviH86QNPDm3Cd5YBuvZHNHgAaEQrokeOaYLAjP2BbINd6cWhD3UABw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:02.408894Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1931","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:239aad0404aee795bebdef2654ec250a17afb775d0e0ab4c16078f67a69d6e94","sha256:8b2c5ee1ef8274771211e7f337a54b4c9bf3bf12d99e9cb5547e20bce6efb217"],"state_sha256":"ce8c232e7664164d52e91b8e1c864c5512bb96cf788a2d60bdc73c8500bd6f0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ho0PZCARs6SA19HZZ9WQVg9JR2RGOPiKDEG8mq1tAFJJYV0VEXXmhSdtMMT8eYqw/YPkMzkSmucgft/+VL20Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:07:00.027643Z","bundle_sha256":"7bc0e329d325370da1dfb9d25a99d138e4311014f1869dc24c020fa585b71144"}}