{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:H2PFRK4XTGGWJ3NFBEJ6GUPUMR","short_pith_number":"pith:H2PFRK4X","schema_version":"1.0","canonical_sha256":"3e9e58ab97998d64eda50913e351f4647362ae0cc552782e2162191e76ff8a63","source":{"kind":"arxiv","id":"0807.4970","version":4},"attestation_state":"computed","paper":{"title":"Integrable structure of melting crystal model with external potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Kanehisa Takasaki, Toshio Nakatsu","submitted_at":"2008-07-31T01:50:11Z","abstract_excerpt":"This is a review of the authors' recent results on an integrable structure of the melting crystal model with external potentials. The partition function of this model is a sum over all plane partitions (3D Young diagrams). By the method of transfer matrices, this sum turns into a sum over ordinary partitions (Young diagrams), which may be thought of as a model of q -deformed random partitions. This model can be further translated to the language of a complex fermion system. A fermionic realization of the quantum torus Lie algebra is shown to underlie therein. With the aid of hidden symmetry of"},"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":"0807.4970","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-07-31T01:50:11Z","cross_cats_sorted":["hep-th","math.MP","math.QA","nlin.SI"],"title_canon_sha256":"2636fe8810cb3a8b831be8077ad6dffcff39b753ba120092810efda09f231ff6","abstract_canon_sha256":"1318027b201fec73bd08db4a1b4e8ac9e04d839daf78fa02cdf051fe53b90472"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:27.699070Z","signature_b64":"mZnLt2TRrOFoR6I6g8ab4imLQqEoexJd3QkOw65QcmiiY/OeL5AE7iw+BaFPCmsx+zxbuUP9kTUM/u2JuuieAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e9e58ab97998d64eda50913e351f4647362ae0cc552782e2162191e76ff8a63","last_reissued_at":"2026-05-18T04:14:27.698582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:27.698582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrable structure of melting crystal model with external potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Kanehisa Takasaki, Toshio Nakatsu","submitted_at":"2008-07-31T01:50:11Z","abstract_excerpt":"This is a review of the authors' recent results on an integrable structure of the melting crystal model with external potentials. The partition function of this model is a sum over all plane partitions (3D Young diagrams). By the method of transfer matrices, this sum turns into a sum over ordinary partitions (Young diagrams), which may be thought of as a model of q -deformed random partitions. This model can be further translated to the language of a complex fermion system. A fermionic realization of the quantum torus Lie algebra is shown to underlie therein. With the aid of hidden symmetry of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4970","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":"0807.4970","created_at":"2026-05-18T04:14:27.698674+00:00"},{"alias_kind":"arxiv_version","alias_value":"0807.4970v4","created_at":"2026-05-18T04:14:27.698674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4970","created_at":"2026-05-18T04:14:27.698674+00:00"},{"alias_kind":"pith_short_12","alias_value":"H2PFRK4XTGGW","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"H2PFRK4XTGGWJ3NF","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"H2PFRK4X","created_at":"2026-05-18T12:25:57.157939+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/H2PFRK4XTGGWJ3NFBEJ6GUPUMR","json":"https://pith.science/pith/H2PFRK4XTGGWJ3NFBEJ6GUPUMR.json","graph_json":"https://pith.science/api/pith-number/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/graph.json","events_json":"https://pith.science/api/pith-number/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/events.json","paper":"https://pith.science/paper/H2PFRK4X"},"agent_actions":{"view_html":"https://pith.science/pith/H2PFRK4XTGGWJ3NFBEJ6GUPUMR","download_json":"https://pith.science/pith/H2PFRK4XTGGWJ3NFBEJ6GUPUMR.json","view_paper":"https://pith.science/paper/H2PFRK4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0807.4970&json=true","fetch_graph":"https://pith.science/api/pith-number/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/graph.json","fetch_events":"https://pith.science/api/pith-number/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/action/storage_attestation","attest_author":"https://pith.science/pith/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/action/author_attestation","sign_citation":"https://pith.science/pith/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/action/citation_signature","submit_replication":"https://pith.science/pith/H2PFRK4XTGGWJ3NFBEJ6GUPUMR/action/replication_record"}},"created_at":"2026-05-18T04:14:27.698674+00:00","updated_at":"2026-05-18T04:14:27.698674+00:00"}