{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GFG7TZIFYT6JWTTOS7PDMZYENK","short_pith_number":"pith:GFG7TZIF","canonical_record":{"source":{"id":"1306.3510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T20:39:37Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"e5f77c5a3bb03d78ec78312eb357dcc8429aa266523c98f2588cfbd460e74479","abstract_canon_sha256":"f09076e17815c43c355cc29abfe8e9eca0631f48fab34447b48f7378eacb4053"},"schema_version":"1.0"},"canonical_sha256":"314df9e505c4fc9b4e6e97de3667046abc6333b4168244a27faa1478695b2365","source":{"kind":"arxiv","id":"1306.3510","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3510","created_at":"2026-05-18T02:47:05Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3510v2","created_at":"2026-05-18T02:47:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3510","created_at":"2026-05-18T02:47:05Z"},{"alias_kind":"pith_short_12","alias_value":"GFG7TZIFYT6J","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GFG7TZIFYT6JWTTO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GFG7TZIF","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GFG7TZIFYT6JWTTOS7PDMZYENK","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T20:39:37Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"e5f77c5a3bb03d78ec78312eb357dcc8429aa266523c98f2588cfbd460e74479","abstract_canon_sha256":"f09076e17815c43c355cc29abfe8e9eca0631f48fab34447b48f7378eacb4053"},"schema_version":"1.0"},"canonical_sha256":"314df9e505c4fc9b4e6e97de3667046abc6333b4168244a27faa1478695b2365","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:05.792243Z","signature_b64":"1fp4psbaKRYrb81ReAsy/cxin24W0VuazEanMT5cPg5IR753R6hNqe24iMjCU+s72tkfd/+LLQYC/WMpExZKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"314df9e505c4fc9b4e6e97de3667046abc6333b4168244a27faa1478695b2365","last_reissued_at":"2026-05-18T02:47:05.791728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:05.791728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3510","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KyMZfs3f6sW8UX1JnJKi9wl1kr9mS15TTleKLl/iEVNs7+MOjTfW4/b1bMtbbr9tAc9FDF0eTkg1wJq0AU2rCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:45:02.059592Z"},"content_sha256":"34930d1c4e76862710f8c62906f0b00184a03f57c0d3e637197460d3ff4c36ca","schema_version":"1.0","event_id":"sha256:34930d1c4e76862710f8c62906f0b00184a03f57c0d3e637197460d3ff4c36ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GFG7TZIFYT6JWTTOS7PDMZYENK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calculation of the constant factor in the six-vertex model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Pavel Bleher, Thomas Bothner","submitted_at":"2013-06-14T20:39:37Z","abstract_excerpt":"In the present paper we calculate explicitly the constant factor $C$ in the large $N$ asymptotics of the partition function $Z_N$ of the six-vertex model with domain wall boundary conditions on the critical line between the disordered and ferroelectric phases. On the critical line the weights $a,b,c$ of the model are parameterized by a parameter $\\al>1$, as $a=\\frac{\\al-1}{2}$, $b=\\frac{\\al+1}{2}$, $c=1$. The asymptotics of $Z_N$ on the critical line was obtained earlier in the paper \\cite{BL2} of Bleher and Liechty: $Z_N=CF^{N^2}G^{\\sqrt{N}}N^{1/4}\\big(1+O(N^{-1/2})\\big)$, where $F$ and $G$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3510","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oXWVPDNHLYk/cu+6rcVcSZij3xSFBJQUyuDcFnb0OO0Bk44zXzLzLspGUe58tDrKaf5LGi+OQhQpyjUfdXnuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:45:02.059934Z"},"content_sha256":"5c469096166ff35df857cb68606c5d138900084bad276f1a2eae19357086d6ad","schema_version":"1.0","event_id":"sha256:5c469096166ff35df857cb68606c5d138900084bad276f1a2eae19357086d6ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFG7TZIFYT6JWTTOS7PDMZYENK/bundle.json","state_url":"https://pith.science/pith/GFG7TZIFYT6JWTTOS7PDMZYENK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFG7TZIFYT6JWTTOS7PDMZYENK/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":"2026-06-25T22:45:02Z","links":{"resolver":"https://pith.science/pith/GFG7TZIFYT6JWTTOS7PDMZYENK","bundle":"https://pith.science/pith/GFG7TZIFYT6JWTTOS7PDMZYENK/bundle.json","state":"https://pith.science/pith/GFG7TZIFYT6JWTTOS7PDMZYENK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFG7TZIFYT6JWTTOS7PDMZYENK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GFG7TZIFYT6JWTTOS7PDMZYENK","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":"f09076e17815c43c355cc29abfe8e9eca0631f48fab34447b48f7378eacb4053","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T20:39:37Z","title_canon_sha256":"e5f77c5a3bb03d78ec78312eb357dcc8429aa266523c98f2588cfbd460e74479"},"schema_version":"1.0","source":{"id":"1306.3510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3510","created_at":"2026-05-18T02:47:05Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3510v2","created_at":"2026-05-18T02:47:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3510","created_at":"2026-05-18T02:47:05Z"},{"alias_kind":"pith_short_12","alias_value":"GFG7TZIFYT6J","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GFG7TZIFYT6JWTTO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GFG7TZIF","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:5c469096166ff35df857cb68606c5d138900084bad276f1a2eae19357086d6ad","target":"graph","created_at":"2026-05-18T02:47:05Z","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 the present paper we calculate explicitly the constant factor $C$ in the large $N$ asymptotics of the partition function $Z_N$ of the six-vertex model with domain wall boundary conditions on the critical line between the disordered and ferroelectric phases. On the critical line the weights $a,b,c$ of the model are parameterized by a parameter $\\al>1$, as $a=\\frac{\\al-1}{2}$, $b=\\frac{\\al+1}{2}$, $c=1$. The asymptotics of $Z_N$ on the critical line was obtained earlier in the paper \\cite{BL2} of Bleher and Liechty: $Z_N=CF^{N^2}G^{\\sqrt{N}}N^{1/4}\\big(1+O(N^{-1/2})\\big)$, where $F$ and $G$ a","authors_text":"Pavel Bleher, Thomas Bothner","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T20:39:37Z","title":"Calculation of the constant factor in the six-vertex model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3510","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":"sha256:34930d1c4e76862710f8c62906f0b00184a03f57c0d3e637197460d3ff4c36ca","target":"record","created_at":"2026-05-18T02:47:05Z","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":"f09076e17815c43c355cc29abfe8e9eca0631f48fab34447b48f7378eacb4053","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T20:39:37Z","title_canon_sha256":"e5f77c5a3bb03d78ec78312eb357dcc8429aa266523c98f2588cfbd460e74479"},"schema_version":"1.0","source":{"id":"1306.3510","kind":"arxiv","version":2}},"canonical_sha256":"314df9e505c4fc9b4e6e97de3667046abc6333b4168244a27faa1478695b2365","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"314df9e505c4fc9b4e6e97de3667046abc6333b4168244a27faa1478695b2365","first_computed_at":"2026-05-18T02:47:05.791728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:05.791728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1fp4psbaKRYrb81ReAsy/cxin24W0VuazEanMT5cPg5IR753R6hNqe24iMjCU+s72tkfd/+LLQYC/WMpExZKCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:05.792243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34930d1c4e76862710f8c62906f0b00184a03f57c0d3e637197460d3ff4c36ca","sha256:5c469096166ff35df857cb68606c5d138900084bad276f1a2eae19357086d6ad"],"state_sha256":"5d051eeda8e8c1738f43678c77f0f1c3f11d40f47e109124aea78d0456ddf738"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zCJUTH7uSYeTzX2hijdJxujn+udkBdL/BGBvEifRs11b6gQEjfBRHLDFaduUWz4zpZqNA64fvdrC2nCxBSKtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:45:02.061832Z","bundle_sha256":"16b8d3801ba3787fca0bb48d5bc0ce43721c1a0b43ef556e5595ddc51fdfc2f8"}}