{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WWZBTBUDTONJHT4625EQWYXO5L","short_pith_number":"pith:WWZBTBUD","schema_version":"1.0","canonical_sha256":"b5b21986839b9a93cf9ed7490b62eeeace2217d310603bb77d3672ad4a470206","source":{"kind":"arxiv","id":"1606.01616","version":4},"attestation_state":"computed","paper":{"title":"Surface and corner free energies of the self-dual Potts model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"R. J. Baxter","submitted_at":"2016-06-06T05:35:27Z","abstract_excerpt":"We consider the bulk, vertical surface, horizontal surface and corner free energies $f_b, f_s, f'_s, f_c$ of the anisotropic self-dual $Q$-state Potts model for $Q > 4$. $f_b$ was calculated in 1973[1]. For $Q<4$, $f_s, f'_s$ were calculated in 1989[2]. Here we extend this last calculation to $Q>4$ and find agreement with the conjectures made in 2012 by Vernier and Jacobsen (VJ)[3] for the isotropic case. All these four free energies satisfy inversion and rotation relations. Together with some plausible analyticity assumptions, these provide a less rigorous, but much simpler, way of determinin"},"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":"1606.01616","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-06T05:35:27Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"13595623d3f91f16f7ccebb0e2d0a2c48a2756fdcbd04602d06103b3962e1f9b","abstract_canon_sha256":"241c79aa86d9d8433e495ea61705e1c37a5b82c2d48735cb524ba6f797786913"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:04.034039Z","signature_b64":"eVu46P0LGy+0MdSj5Dm4xk3ZYWsf+C2inAP6ptrNlQ9VpCgu0MDWj/E/jWwSNAHbEv0emLGVWDnNzLyjn7aEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5b21986839b9a93cf9ed7490b62eeeace2217d310603bb77d3672ad4a470206","last_reissued_at":"2026-05-18T00:52:04.033537Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:04.033537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Surface and corner free energies of the self-dual Potts model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"R. J. Baxter","submitted_at":"2016-06-06T05:35:27Z","abstract_excerpt":"We consider the bulk, vertical surface, horizontal surface and corner free energies $f_b, f_s, f'_s, f_c$ of the anisotropic self-dual $Q$-state Potts model for $Q > 4$. $f_b$ was calculated in 1973[1]. For $Q<4$, $f_s, f'_s$ were calculated in 1989[2]. Here we extend this last calculation to $Q>4$ and find agreement with the conjectures made in 2012 by Vernier and Jacobsen (VJ)[3] for the isotropic case. All these four free energies satisfy inversion and rotation relations. Together with some plausible analyticity assumptions, these provide a less rigorous, but much simpler, way of determinin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01616","kind":"arxiv","version":4},"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":"1606.01616","created_at":"2026-05-18T00:52:04.033600+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01616v4","created_at":"2026-05-18T00:52:04.033600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01616","created_at":"2026-05-18T00:52:04.033600+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWZBTBUDTONJ","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWZBTBUDTONJHT46","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWZBTBUD","created_at":"2026-05-18T12:30:51.357362+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/WWZBTBUDTONJHT4625EQWYXO5L","json":"https://pith.science/pith/WWZBTBUDTONJHT4625EQWYXO5L.json","graph_json":"https://pith.science/api/pith-number/WWZBTBUDTONJHT4625EQWYXO5L/graph.json","events_json":"https://pith.science/api/pith-number/WWZBTBUDTONJHT4625EQWYXO5L/events.json","paper":"https://pith.science/paper/WWZBTBUD"},"agent_actions":{"view_html":"https://pith.science/pith/WWZBTBUDTONJHT4625EQWYXO5L","download_json":"https://pith.science/pith/WWZBTBUDTONJHT4625EQWYXO5L.json","view_paper":"https://pith.science/paper/WWZBTBUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01616&json=true","fetch_graph":"https://pith.science/api/pith-number/WWZBTBUDTONJHT4625EQWYXO5L/graph.json","fetch_events":"https://pith.science/api/pith-number/WWZBTBUDTONJHT4625EQWYXO5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWZBTBUDTONJHT4625EQWYXO5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWZBTBUDTONJHT4625EQWYXO5L/action/storage_attestation","attest_author":"https://pith.science/pith/WWZBTBUDTONJHT4625EQWYXO5L/action/author_attestation","sign_citation":"https://pith.science/pith/WWZBTBUDTONJHT4625EQWYXO5L/action/citation_signature","submit_replication":"https://pith.science/pith/WWZBTBUDTONJHT4625EQWYXO5L/action/replication_record"}},"created_at":"2026-05-18T00:52:04.033600+00:00","updated_at":"2026-05-18T00:52:04.033600+00:00"}