{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:JZPNRUOZ3QWSJJFLBTF6ZZI4OB","short_pith_number":"pith:JZPNRUOZ","canonical_record":{"source":{"id":"hep-th/0309208","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-09-22T17:14:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"724559d491b7e277047ce40c7a48a7e6ec488df7f91e7508c6f5314a4c3a51ce","abstract_canon_sha256":"0b77b500ccc95a9279b914a9d5b5a775bc688201407de78cd102d5cee8c1b44b"},"schema_version":"1.0"},"canonical_sha256":"4e5ed8d1d9dc2d24a4ab0ccbece51c7049d55128c4c94c522d5ab4c7e5542e46","source":{"kind":"arxiv","id":"hep-th/0309208","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0309208","created_at":"2026-05-18T01:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0309208v2","created_at":"2026-05-18T01:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0309208","created_at":"2026-05-18T01:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"JZPNRUOZ3QWS","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"JZPNRUOZ3QWSJJFL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"JZPNRUOZ","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:JZPNRUOZ3QWSJJFLBTF6ZZI4OB","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0309208","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-09-22T17:14:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"724559d491b7e277047ce40c7a48a7e6ec488df7f91e7508c6f5314a4c3a51ce","abstract_canon_sha256":"0b77b500ccc95a9279b914a9d5b5a775bc688201407de78cd102d5cee8c1b44b"},"schema_version":"1.0"},"canonical_sha256":"4e5ed8d1d9dc2d24a4ab0ccbece51c7049d55128c4c94c522d5ab4c7e5542e46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:59.049673Z","signature_b64":"urPXdC/DCyWJpxTXZkbwXPfKqoCnYBKBYM3RqdH8TNo1V1fcMv9d8o6fvyxrm16NXmxBE+8l3v5ffDLaNpgGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e5ed8d1d9dc2d24a4ab0ccbece51c7049d55128c4c94c522d5ab4c7e5542e46","last_reissued_at":"2026-05-18T01:05:59.049239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:59.049239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0309208","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":"2026-05-18T01:05:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Oqa2FyKaqxLULs4qg8qs64TLBaAye5VVawMYnEK5ji3Xqde2J8s0MjOmusRockWxvm4qWDnZuYh+J8LnDJeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:05:36.911438Z"},"content_sha256":"5a9786eb2c61db721226623e1f470132f80324159be1eacb9f1fb1e13aca1450","schema_version":"1.0","event_id":"sha256:5a9786eb2c61db721226623e1f470132f80324159be1eacb9f1fb1e13aca1450"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:JZPNRUOZ3QWSJJFLBTF6ZZI4OB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Calabi-Yau and Classical Crystals","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Andrei Okounkov, Cumrun Vafa, Nikolai Reshetikhin","submitted_at":"2003-09-22T17:14:32Z","abstract_excerpt":"We propose a new duality involving topological strings in the limit of large string coupling constant.\n  The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is inverse of the string coupling constant. The crystal is a discretization of the toric base of the Calabi-Yau with lattice length $g_s$. As a strong evidence for this duality we recover the topological vertex in terms of the statistical mechanical probability distribution for crystal melting.\n We also propose a more general duality involving the dimer problem on periodic la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0309208","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":"2026-05-18T01:05:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c33wF2woHnlffsH4HV3txGjYPQtHO/hKNt1BzGxsIC41Do8FLFHSJVgjlbmBuYB7+zlRQAcfurJWxpYh5bsuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:05:36.911786Z"},"content_sha256":"7fc31bae4d4fe194315fc6a5f197bc8ac6f08cf3cd0c981a210fd660ec99668b","schema_version":"1.0","event_id":"sha256:7fc31bae4d4fe194315fc6a5f197bc8ac6f08cf3cd0c981a210fd660ec99668b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZPNRUOZ3QWSJJFLBTF6ZZI4OB/bundle.json","state_url":"https://pith.science/pith/JZPNRUOZ3QWSJJFLBTF6ZZI4OB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZPNRUOZ3QWSJJFLBTF6ZZI4OB/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":"2026-06-02T03:05:36Z","links":{"resolver":"https://pith.science/pith/JZPNRUOZ3QWSJJFLBTF6ZZI4OB","bundle":"https://pith.science/pith/JZPNRUOZ3QWSJJFLBTF6ZZI4OB/bundle.json","state":"https://pith.science/pith/JZPNRUOZ3QWSJJFLBTF6ZZI4OB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZPNRUOZ3QWSJJFLBTF6ZZI4OB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:JZPNRUOZ3QWSJJFLBTF6ZZI4OB","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":"0b77b500ccc95a9279b914a9d5b5a775bc688201407de78cd102d5cee8c1b44b","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2003-09-22T17:14:32Z","title_canon_sha256":"724559d491b7e277047ce40c7a48a7e6ec488df7f91e7508c6f5314a4c3a51ce"},"schema_version":"1.0","source":{"id":"hep-th/0309208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0309208","created_at":"2026-05-18T01:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0309208v2","created_at":"2026-05-18T01:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0309208","created_at":"2026-05-18T01:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"JZPNRUOZ3QWS","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"JZPNRUOZ3QWSJJFL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"JZPNRUOZ","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:7fc31bae4d4fe194315fc6a5f197bc8ac6f08cf3cd0c981a210fd660ec99668b","target":"graph","created_at":"2026-05-18T01:05:59Z","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":"We propose a new duality involving topological strings in the limit of large string coupling constant.\n  The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is inverse of the string coupling constant. The crystal is a discretization of the toric base of the Calabi-Yau with lattice length $g_s$. As a strong evidence for this duality we recover the topological vertex in terms of the statistical mechanical probability distribution for crystal melting.\n We also propose a more general duality involving the dimer problem on periodic la","authors_text":"Andrei Okounkov, Cumrun Vafa, Nikolai Reshetikhin","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-09-22T17:14:32Z","title":"Quantum Calabi-Yau and Classical Crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0309208","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":"sha256:5a9786eb2c61db721226623e1f470132f80324159be1eacb9f1fb1e13aca1450","target":"record","created_at":"2026-05-18T01:05:59Z","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":"0b77b500ccc95a9279b914a9d5b5a775bc688201407de78cd102d5cee8c1b44b","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2003-09-22T17:14:32Z","title_canon_sha256":"724559d491b7e277047ce40c7a48a7e6ec488df7f91e7508c6f5314a4c3a51ce"},"schema_version":"1.0","source":{"id":"hep-th/0309208","kind":"arxiv","version":2}},"canonical_sha256":"4e5ed8d1d9dc2d24a4ab0ccbece51c7049d55128c4c94c522d5ab4c7e5542e46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e5ed8d1d9dc2d24a4ab0ccbece51c7049d55128c4c94c522d5ab4c7e5542e46","first_computed_at":"2026-05-18T01:05:59.049239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:59.049239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"urPXdC/DCyWJpxTXZkbwXPfKqoCnYBKBYM3RqdH8TNo1V1fcMv9d8o6fvyxrm16NXmxBE+8l3v5ffDLaNpgGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:59.049673Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0309208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a9786eb2c61db721226623e1f470132f80324159be1eacb9f1fb1e13aca1450","sha256:7fc31bae4d4fe194315fc6a5f197bc8ac6f08cf3cd0c981a210fd660ec99668b"],"state_sha256":"36d29230bcc5aa6d4fd59493c60ec1d1eedf4005bab6e7c304879f2697a141a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2NEnUbGAL0YM6GekCrNQP7ks+fP0V0jktovAXg/I0ulQkIQolX2SiBLu4oJWBvtJTck/272rFVJeXClhtRwFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:05:36.913698Z","bundle_sha256":"82324d20133adbaa5f186a48e75bc9c6568fd665423075139f270f9cc584388c"}}