{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:T5R65XIFS3HQP3AZLX4V4SNFZF","short_pith_number":"pith:T5R65XIF","canonical_record":{"source":{"id":"2312.12629","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T22:18:04Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"3bb28a69c2ad897764ce2c4ee0f888cba5809383aabdc885a98cc927887dd4fc","abstract_canon_sha256":"32d3e23a69fb4e6ac2776162d5708009e0d88c015b5ddaf26908ed72d6e7ee9a"},"schema_version":"1.0"},"canonical_sha256":"9f63eedd0596cf07ec195df95e49a5c954f25512d9271d70175d3d35679b9743","source":{"kind":"arxiv","id":"2312.12629","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.12629","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"2312.12629v1","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.12629","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"T5R65XIFS3HQ","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"T5R65XIFS3HQP3AZ","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"T5R65XIF","created_at":"2026-07-05T07:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:T5R65XIFS3HQP3AZLX4V4SNFZF","target":"record","payload":{"canonical_record":{"source":{"id":"2312.12629","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T22:18:04Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"3bb28a69c2ad897764ce2c4ee0f888cba5809383aabdc885a98cc927887dd4fc","abstract_canon_sha256":"32d3e23a69fb4e6ac2776162d5708009e0d88c015b5ddaf26908ed72d6e7ee9a"},"schema_version":"1.0"},"canonical_sha256":"9f63eedd0596cf07ec195df95e49a5c954f25512d9271d70175d3d35679b9743","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:26:24.088199Z","signature_b64":"AyOjEFoxw/XMmMwh/8ZLaIwnh5F12s/ceOecd864FyIOA3dLOpkU+oeKRSYC4H7aBYxcqyhydeAOg0I7lDakBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f63eedd0596cf07ec195df95e49a5c954f25512d9271d70175d3d35679b9743","last_reissued_at":"2026-07-05T07:26:24.087713Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:26:24.087713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.12629","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:26:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KTR85S/8ia1j0ZeREsAyGV4qw8E5gu7LMEz6anXUHztvIzsUBqbXYmhfohoSQTURLiQGE0ImjdvijMpu9o/BDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:24:22.314541Z"},"content_sha256":"7b3e1db869105932b88a5a0567a118b606c1a9a31c054fe5eb4546daab592696","schema_version":"1.0","event_id":"sha256:7b3e1db869105932b88a5a0567a118b606c1a9a31c054fe5eb4546daab592696"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:T5R65XIFS3HQP3AZLX4V4SNFZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum geometry and mock modularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Albrecht Klemm, Boris Pioline, Sergei Alexandrov, Soheyla Feyzbakhsh","submitted_at":"2023-12-19T22:18:04Z","abstract_excerpt":"In previous work, we used new mathematical relations between Gopakumar-Vafa (GV) invariants and rank 0 Donaldson-Thomas (DT) invariants to determine the first few terms in the generating series of Abelian D4-D2-D0 indices for a class of compact one-parameter Calabi-Yau threefolds. This allowed us to obtain striking checks of S-duality, namely the prediction that these series should be vector-valued weakly holomorphic modular forms under $SL(2,\\mathbb{Z})$. In this work, we extend this analysis to the case of D4-D2-D0 indices with two units of D4-brane charge, where S-duality instead predicts t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12629","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.12629/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:26:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NWMyyRtqtm/9OAk5RbkxCWlDwfwOJHduBMFNLXz7RnrICVXRv+vziLc7+EEQVIm6ZWB9RZ+T+Cz1i2M/3c4ADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:24:22.315355Z"},"content_sha256":"21b188e7f0a68cf3e1bc81850125f78d2a495c5e8c433cf90abbf23311496596","schema_version":"1.0","event_id":"sha256:21b188e7f0a68cf3e1bc81850125f78d2a495c5e8c433cf90abbf23311496596"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T5R65XIFS3HQP3AZLX4V4SNFZF/bundle.json","state_url":"https://pith.science/pith/T5R65XIFS3HQP3AZLX4V4SNFZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T5R65XIFS3HQP3AZLX4V4SNFZF/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":"2026-08-04T20:24:22Z","links":{"resolver":"https://pith.science/pith/T5R65XIFS3HQP3AZLX4V4SNFZF","bundle":"https://pith.science/pith/T5R65XIFS3HQP3AZLX4V4SNFZF/bundle.json","state":"https://pith.science/pith/T5R65XIFS3HQP3AZLX4V4SNFZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T5R65XIFS3HQP3AZLX4V4SNFZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:T5R65XIFS3HQP3AZLX4V4SNFZF","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":"32d3e23a69fb4e6ac2776162d5708009e0d88c015b5ddaf26908ed72d6e7ee9a","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T22:18:04Z","title_canon_sha256":"3bb28a69c2ad897764ce2c4ee0f888cba5809383aabdc885a98cc927887dd4fc"},"schema_version":"1.0","source":{"id":"2312.12629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.12629","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"2312.12629v1","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.12629","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"T5R65XIFS3HQ","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"T5R65XIFS3HQP3AZ","created_at":"2026-07-05T07:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"T5R65XIF","created_at":"2026-07-05T07:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:21b188e7f0a68cf3e1bc81850125f78d2a495c5e8c433cf90abbf23311496596","target":"graph","created_at":"2026-07-05T07:26:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2312.12629/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In previous work, we used new mathematical relations between Gopakumar-Vafa (GV) invariants and rank 0 Donaldson-Thomas (DT) invariants to determine the first few terms in the generating series of Abelian D4-D2-D0 indices for a class of compact one-parameter Calabi-Yau threefolds. This allowed us to obtain striking checks of S-duality, namely the prediction that these series should be vector-valued weakly holomorphic modular forms under $SL(2,\\mathbb{Z})$. In this work, we extend this analysis to the case of D4-D2-D0 indices with two units of D4-brane charge, where S-duality instead predicts t","authors_text":"Albrecht Klemm, Boris Pioline, Sergei Alexandrov, Soheyla Feyzbakhsh","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T22:18:04Z","title":"Quantum geometry and mock modularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12629","kind":"arxiv","version":1},"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":"sha256:7b3e1db869105932b88a5a0567a118b606c1a9a31c054fe5eb4546daab592696","target":"record","created_at":"2026-07-05T07:26:24Z","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":"32d3e23a69fb4e6ac2776162d5708009e0d88c015b5ddaf26908ed72d6e7ee9a","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T22:18:04Z","title_canon_sha256":"3bb28a69c2ad897764ce2c4ee0f888cba5809383aabdc885a98cc927887dd4fc"},"schema_version":"1.0","source":{"id":"2312.12629","kind":"arxiv","version":1}},"canonical_sha256":"9f63eedd0596cf07ec195df95e49a5c954f25512d9271d70175d3d35679b9743","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f63eedd0596cf07ec195df95e49a5c954f25512d9271d70175d3d35679b9743","first_computed_at":"2026-07-05T07:26:24.087713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:26:24.087713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AyOjEFoxw/XMmMwh/8ZLaIwnh5F12s/ceOecd864FyIOA3dLOpkU+oeKRSYC4H7aBYxcqyhydeAOg0I7lDakBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:26:24.088199Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.12629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b3e1db869105932b88a5a0567a118b606c1a9a31c054fe5eb4546daab592696","sha256:21b188e7f0a68cf3e1bc81850125f78d2a495c5e8c433cf90abbf23311496596"],"state_sha256":"0ba62d417d53867d24b0b2ac02967c5c8b14938fd4343ce7928fad78f4fda20e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hsDn9ymxj6FUmBvOgRORuQ0ENTNxgXx4X/cWkLeZw2NPtmTOkKiP/dzEd7ylk0YaS02PVBYmUMNW+cWcJ/7eBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T20:24:22.326099Z","bundle_sha256":"26a00caa4a3210068ff5d2bf1bd06b4e72ac7c93a3ef385d9b93cc2e9b73ce2c"}}