{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AHEEFT5JQUFKQKF76AGULSQGJB","short_pith_number":"pith:AHEEFT5J","schema_version":"1.0","canonical_sha256":"01c842cfa9850aa828bff00d45ca064870a18ca1379c59bf002011cfb9cb9de8","source":{"kind":"arxiv","id":"1606.05297","version":2},"attestation_state":"computed","paper":{"title":"Exact eigenfunctions and the open topological string","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.SP"],"primary_cat":"hep-th","authors_text":"Marcos Marino, Szabolcs Zakany","submitted_at":"2016-06-16T18:03:33Z","abstract_excerpt":"Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the underlying threefold, but much less is known about their eigenfunctions. In this paper we first develop methods in spectral theory to compute these eigenfunctions. We also provide a matrix integral representation which allows to study them in a 't Hooft limit, where they are described by standard topological open string amplitudes. Based on these results, we propose a conjecture for the exact eigenfunctions"},"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":"1606.05297","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-16T18:03:33Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.SP"],"title_canon_sha256":"da38b6eb97dad5cdbc799ca690762a1beeb7d904749ae6f9a5ff559d37b84cc4","abstract_canon_sha256":"301d0a3f64ea421fc4537d85b3a7d4425d465b87ca4845304b0d59cc1f64ae35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:02.722790Z","signature_b64":"YrZlVbfipzYgCBd1xchUJys5dXh6Jghy8TERXDvKbndSMYkpgnTZHjO6Z2w6gkRqtClq8A3doMKpEhSWQbGQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01c842cfa9850aa828bff00d45ca064870a18ca1379c59bf002011cfb9cb9de8","last_reissued_at":"2026-05-18T00:39:02.722109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:02.722109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact eigenfunctions and the open topological string","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.SP"],"primary_cat":"hep-th","authors_text":"Marcos Marino, Szabolcs Zakany","submitted_at":"2016-06-16T18:03:33Z","abstract_excerpt":"Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the underlying threefold, but much less is known about their eigenfunctions. In this paper we first develop methods in spectral theory to compute these eigenfunctions. We also provide a matrix integral representation which allows to study them in a 't Hooft limit, where they are described by standard topological open string amplitudes. Based on these results, we propose a conjecture for the exact eigenfunctions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05297","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.05297","created_at":"2026-05-18T00:39:02.722210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.05297v2","created_at":"2026-05-18T00:39:02.722210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05297","created_at":"2026-05-18T00:39:02.722210+00:00"},{"alias_kind":"pith_short_12","alias_value":"AHEEFT5JQUFK","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AHEEFT5JQUFKQKF7","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AHEEFT5J","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2301.05214","citing_title":"All the D-Branes of Resurgence","ref_index":79,"is_internal_anchor":true},{"citing_arxiv_id":"2605.20338","citing_title":"Higher-Rank Connections and Deformed Schr\\\"odinger Operators","ref_index":24,"is_internal_anchor":true},{"citing_arxiv_id":"2602.20576","citing_title":"Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics","ref_index":54,"is_internal_anchor":true},{"citing_arxiv_id":"2603.19159","citing_title":"$S^3$ partition functions and Equivariant CY$_4 $/CY$_3$ correspondence from Quantum curves","ref_index":92,"is_internal_anchor":true},{"citing_arxiv_id":"2604.19885","citing_title":"On non-relativistic integrable models and 4d SCFTs","ref_index":86,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB","json":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB.json","graph_json":"https://pith.science/api/pith-number/AHEEFT5JQUFKQKF76AGULSQGJB/graph.json","events_json":"https://pith.science/api/pith-number/AHEEFT5JQUFKQKF76AGULSQGJB/events.json","paper":"https://pith.science/paper/AHEEFT5J"},"agent_actions":{"view_html":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB","download_json":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB.json","view_paper":"https://pith.science/paper/AHEEFT5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.05297&json=true","fetch_graph":"https://pith.science/api/pith-number/AHEEFT5JQUFKQKF76AGULSQGJB/graph.json","fetch_events":"https://pith.science/api/pith-number/AHEEFT5JQUFKQKF76AGULSQGJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB/action/storage_attestation","attest_author":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB/action/author_attestation","sign_citation":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB/action/citation_signature","submit_replication":"https://pith.science/pith/AHEEFT5JQUFKQKF76AGULSQGJB/action/replication_record"}},"created_at":"2026-05-18T00:39:02.722210+00:00","updated_at":"2026-05-18T00:39:02.722210+00:00"}