{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SUPDP72W4SZCIH2HVHRSGIDBYQ","short_pith_number":"pith:SUPDP72W","canonical_record":{"source":{"id":"1701.01561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-06T08:05:40Z","cross_cats_sorted":[],"title_canon_sha256":"32e18d9c2d332e66c19605edc23dcd7510c4b2ac8b587e5c6e816f53e8953805","abstract_canon_sha256":"e54142d365c0d05ce7f46080cb975bcc3d695277e6d810dce9570b30b932e699"},"schema_version":"1.0"},"canonical_sha256":"951e37ff56e4b2241f47a9e3232061c41703ae179398393861e49fa77a3ea31f","source":{"kind":"arxiv","id":"1701.01561","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01561","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01561v2","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01561","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"pith_short_12","alias_value":"SUPDP72W4SZC","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SUPDP72W4SZCIH2H","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SUPDP72W","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SUPDP72W4SZCIH2HVHRSGIDBYQ","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-06T08:05:40Z","cross_cats_sorted":[],"title_canon_sha256":"32e18d9c2d332e66c19605edc23dcd7510c4b2ac8b587e5c6e816f53e8953805","abstract_canon_sha256":"e54142d365c0d05ce7f46080cb975bcc3d695277e6d810dce9570b30b932e699"},"schema_version":"1.0"},"canonical_sha256":"951e37ff56e4b2241f47a9e3232061c41703ae179398393861e49fa77a3ea31f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:38.141051Z","signature_b64":"jHxNmki4kG4SWVdVHK64Librrm1ZDnGDx/zhuwPP+4SWFG5wXU2UHGllrrzIiAt1HeQoSTwot8QS4rJujx6sCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"951e37ff56e4b2241f47a9e3232061c41703ae179398393861e49fa77a3ea31f","last_reissued_at":"2026-05-18T00:46:38.140378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:38.140378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01561","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":"2026-05-18T00:46:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dif3OTVqAPgzMP99cSvy+mFoq4Uv+U15x0fap3kFSKlVGrMltRyvNt9FdqWpn2aITuGUKLEBFRYdkqWSf9UkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T05:21:08.894713Z"},"content_sha256":"db2b443e51c7fcc87cb1e89349cfacb0382a723a66b41f0ec2e1b1beba8e572f","schema_version":"1.0","event_id":"sha256:db2b443e51c7fcc87cb1e89349cfacb0382a723a66b41f0ec2e1b1beba8e572f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SUPDP72W4SZCIH2HVHRSGIDBYQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calabi-Yau geometry and electrons on 2d lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Yasuyuki Hatsuda, Yuji Sugimoto, Zhaojie Xu","submitted_at":"2017-01-06T08:05:40Z","abstract_excerpt":"The B-model approach of topological string theory leads to difference equations by quantizing algebraic mirror curves. It is known that these quantum mechanical systems are solved by the refined topological strings. Recently, it was pointed out that the quantum eigenvalue problem for a particular Calabi--Yau manifold, known as local $\\mathbb{F}_0$, is closely related to the Hofstadter problem for electrons on a two-dimensional square lattice. In this paper, we generalize this idea to a more complicated Calabi--Yau manifold. We find that the local $\\mathcal{B}_3$ geometry, which is a three-poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01561","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":"2026-05-18T00:46:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQKQ9BE8/LdfGFqQc3k1WVSdV3cMKNdavPybd/FOGUjHDevaqhPd4EXEK5CekRrZIok6KEhxDj+LhOmJ5H26Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T05:21:08.895375Z"},"content_sha256":"9ab996c23ee9a51f4dca6cada3c52e4f9433eaebfad8562a7d65d65c0983f2bb","schema_version":"1.0","event_id":"sha256:9ab996c23ee9a51f4dca6cada3c52e4f9433eaebfad8562a7d65d65c0983f2bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUPDP72W4SZCIH2HVHRSGIDBYQ/bundle.json","state_url":"https://pith.science/pith/SUPDP72W4SZCIH2HVHRSGIDBYQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUPDP72W4SZCIH2HVHRSGIDBYQ/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":"2026-05-23T05:21:08Z","links":{"resolver":"https://pith.science/pith/SUPDP72W4SZCIH2HVHRSGIDBYQ","bundle":"https://pith.science/pith/SUPDP72W4SZCIH2HVHRSGIDBYQ/bundle.json","state":"https://pith.science/pith/SUPDP72W4SZCIH2HVHRSGIDBYQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUPDP72W4SZCIH2HVHRSGIDBYQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SUPDP72W4SZCIH2HVHRSGIDBYQ","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":"e54142d365c0d05ce7f46080cb975bcc3d695277e6d810dce9570b30b932e699","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-06T08:05:40Z","title_canon_sha256":"32e18d9c2d332e66c19605edc23dcd7510c4b2ac8b587e5c6e816f53e8953805"},"schema_version":"1.0","source":{"id":"1701.01561","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01561","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01561v2","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01561","created_at":"2026-05-18T00:46:38Z"},{"alias_kind":"pith_short_12","alias_value":"SUPDP72W4SZC","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SUPDP72W4SZCIH2H","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SUPDP72W","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:9ab996c23ee9a51f4dca6cada3c52e4f9433eaebfad8562a7d65d65c0983f2bb","target":"graph","created_at":"2026-05-18T00:46:38Z","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":"The B-model approach of topological string theory leads to difference equations by quantizing algebraic mirror curves. It is known that these quantum mechanical systems are solved by the refined topological strings. Recently, it was pointed out that the quantum eigenvalue problem for a particular Calabi--Yau manifold, known as local $\\mathbb{F}_0$, is closely related to the Hofstadter problem for electrons on a two-dimensional square lattice. In this paper, we generalize this idea to a more complicated Calabi--Yau manifold. We find that the local $\\mathcal{B}_3$ geometry, which is a three-poin","authors_text":"Yasuyuki Hatsuda, Yuji Sugimoto, Zhaojie Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-06T08:05:40Z","title":"Calabi-Yau geometry and electrons on 2d lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01561","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:db2b443e51c7fcc87cb1e89349cfacb0382a723a66b41f0ec2e1b1beba8e572f","target":"record","created_at":"2026-05-18T00:46:38Z","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":"e54142d365c0d05ce7f46080cb975bcc3d695277e6d810dce9570b30b932e699","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-06T08:05:40Z","title_canon_sha256":"32e18d9c2d332e66c19605edc23dcd7510c4b2ac8b587e5c6e816f53e8953805"},"schema_version":"1.0","source":{"id":"1701.01561","kind":"arxiv","version":2}},"canonical_sha256":"951e37ff56e4b2241f47a9e3232061c41703ae179398393861e49fa77a3ea31f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"951e37ff56e4b2241f47a9e3232061c41703ae179398393861e49fa77a3ea31f","first_computed_at":"2026-05-18T00:46:38.140378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:38.140378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jHxNmki4kG4SWVdVHK64Librrm1ZDnGDx/zhuwPP+4SWFG5wXU2UHGllrrzIiAt1HeQoSTwot8QS4rJujx6sCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:38.141051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01561","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db2b443e51c7fcc87cb1e89349cfacb0382a723a66b41f0ec2e1b1beba8e572f","sha256:9ab996c23ee9a51f4dca6cada3c52e4f9433eaebfad8562a7d65d65c0983f2bb"],"state_sha256":"6c9ec91b3c3fda0f63993fd45fcde20ef80828ee32d68e8f4c0bd41e51e7eaa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JcKISq/ASBS+D60RqYXuFxo07s+6GcDqk8dGLlT+6RtjHLHszsCTk3mbTcBnEzktqK/+8mYcjGAxsEHc4HLKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T05:21:08.898867Z","bundle_sha256":"cec280a4bec79d0981f2ae998486b8454597d1b71dd3699a8177ffda7f121196"}}