{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:63RALXFZEGG2ZHECTVNO46NO7T","short_pith_number":"pith:63RALXFZ","canonical_record":{"source":{"id":"1608.08588","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-30T18:24:41Z","cross_cats_sorted":["math.DG","math.SG"],"title_canon_sha256":"c35d294d5e254f03101f3144ca9d1e3314fda1274c6fdf6cc358c35e1325fa61","abstract_canon_sha256":"2ca14892f96b58e2936a01e6ac9f8100fd985858adc5c06a9159f3b27d5644c8"},"schema_version":"1.0"},"canonical_sha256":"f6e205dcb9218dac9c829d5aee79aefcea166e0e5eab4d98c9bddc5f69ee6bd4","source":{"kind":"arxiv","id":"1608.08588","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08588","created_at":"2026-05-18T00:26:16Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08588v5","created_at":"2026-05-18T00:26:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08588","created_at":"2026-05-18T00:26:16Z"},{"alias_kind":"pith_short_12","alias_value":"63RALXFZEGG2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"63RALXFZEGG2ZHEC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"63RALXFZ","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:63RALXFZEGG2ZHECTVNO46NO7T","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08588","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-30T18:24:41Z","cross_cats_sorted":["math.DG","math.SG"],"title_canon_sha256":"c35d294d5e254f03101f3144ca9d1e3314fda1274c6fdf6cc358c35e1325fa61","abstract_canon_sha256":"2ca14892f96b58e2936a01e6ac9f8100fd985858adc5c06a9159f3b27d5644c8"},"schema_version":"1.0"},"canonical_sha256":"f6e205dcb9218dac9c829d5aee79aefcea166e0e5eab4d98c9bddc5f69ee6bd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:16.663060Z","signature_b64":"FLX6KhaGs10BEufp54ELkZgjbclLNUFf6Ch3jaf3WotP8NnmYcmATPls/ujwT6nqkzc53wbZNDjBkVkt3d1BCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e205dcb9218dac9c829d5aee79aefcea166e0e5eab4d98c9bddc5f69ee6bd4","last_reissued_at":"2026-05-18T00:26:16.662447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:16.662447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08588","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/U+boU2uOw/iSoPAIUjHVnlKOBJ/QuGmVC7Aw6Q2ggA3gm7UfzZvj+kjf5WwrtvEJdIU1nEKlCJPqcYPx8nfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:50:00.585248Z"},"content_sha256":"730ff1b26c6c2cf3c9ac495bfa3f7fe6f7954ab423d95837371d37cea1d60bb3","schema_version":"1.0","event_id":"sha256:730ff1b26c6c2cf3c9ac495bfa3f7fe6f7954ab423d95837371d37cea1d60bb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:63RALXFZEGG2ZHECTVNO46NO7T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Indefinite theta functions arising in Gromov-Witten Theory of elliptic orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.NT","authors_text":"Jonas Kaszian, Kathrin Bringmann, Larry Rolen","submitted_at":"2016-08-30T18:24:41Z","abstract_excerpt":"In this paper, we consider natural geometric objects coming from Lagrangian Floer theory and mirror symmetry. Lau and Zhou showed that some of the explicit Gromov-Witten potentials computed by Cho, Hong, Kim, and Lau are essentially classical modular forms. Recent work by Zwegers and two of the authors determined modularity properties of several simpler pieces of the last, and most mysterious, function by developing several identities between functions with properties generalizing those of the mock modular forms in Zwegers' thesis. Here, we complete the analysis of all pieces of Cho, Hong, Kim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08588","kind":"arxiv","version":5},"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":"2026-05-18T00:26:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uCnNGMOhT4pEabM2XzbsYrSNju1rEnbTzjhGCykadG8Hl4EXleR9jif9K9RYHE6gGWatgNkIlt5h1BvFdiQoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:50:00.585613Z"},"content_sha256":"aa5c4c01defe3b72aaa5f905adf7221d0aa56408fcd08b029a51ea030264fef3","schema_version":"1.0","event_id":"sha256:aa5c4c01defe3b72aaa5f905adf7221d0aa56408fcd08b029a51ea030264fef3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63RALXFZEGG2ZHECTVNO46NO7T/bundle.json","state_url":"https://pith.science/pith/63RALXFZEGG2ZHECTVNO46NO7T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63RALXFZEGG2ZHECTVNO46NO7T/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":"2026-06-03T06:50:00Z","links":{"resolver":"https://pith.science/pith/63RALXFZEGG2ZHECTVNO46NO7T","bundle":"https://pith.science/pith/63RALXFZEGG2ZHECTVNO46NO7T/bundle.json","state":"https://pith.science/pith/63RALXFZEGG2ZHECTVNO46NO7T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63RALXFZEGG2ZHECTVNO46NO7T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:63RALXFZEGG2ZHECTVNO46NO7T","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":"2ca14892f96b58e2936a01e6ac9f8100fd985858adc5c06a9159f3b27d5644c8","cross_cats_sorted":["math.DG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-30T18:24:41Z","title_canon_sha256":"c35d294d5e254f03101f3144ca9d1e3314fda1274c6fdf6cc358c35e1325fa61"},"schema_version":"1.0","source":{"id":"1608.08588","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08588","created_at":"2026-05-18T00:26:16Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08588v5","created_at":"2026-05-18T00:26:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08588","created_at":"2026-05-18T00:26:16Z"},{"alias_kind":"pith_short_12","alias_value":"63RALXFZEGG2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"63RALXFZEGG2ZHEC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"63RALXFZ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:aa5c4c01defe3b72aaa5f905adf7221d0aa56408fcd08b029a51ea030264fef3","target":"graph","created_at":"2026-05-18T00:26:16Z","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":"In this paper, we consider natural geometric objects coming from Lagrangian Floer theory and mirror symmetry. Lau and Zhou showed that some of the explicit Gromov-Witten potentials computed by Cho, Hong, Kim, and Lau are essentially classical modular forms. Recent work by Zwegers and two of the authors determined modularity properties of several simpler pieces of the last, and most mysterious, function by developing several identities between functions with properties generalizing those of the mock modular forms in Zwegers' thesis. Here, we complete the analysis of all pieces of Cho, Hong, Kim","authors_text":"Jonas Kaszian, Kathrin Bringmann, Larry Rolen","cross_cats":["math.DG","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-30T18:24:41Z","title":"Indefinite theta functions arising in Gromov-Witten Theory of elliptic orbifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08588","kind":"arxiv","version":5},"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":"sha256:730ff1b26c6c2cf3c9ac495bfa3f7fe6f7954ab423d95837371d37cea1d60bb3","target":"record","created_at":"2026-05-18T00:26:16Z","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":"2ca14892f96b58e2936a01e6ac9f8100fd985858adc5c06a9159f3b27d5644c8","cross_cats_sorted":["math.DG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-30T18:24:41Z","title_canon_sha256":"c35d294d5e254f03101f3144ca9d1e3314fda1274c6fdf6cc358c35e1325fa61"},"schema_version":"1.0","source":{"id":"1608.08588","kind":"arxiv","version":5}},"canonical_sha256":"f6e205dcb9218dac9c829d5aee79aefcea166e0e5eab4d98c9bddc5f69ee6bd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e205dcb9218dac9c829d5aee79aefcea166e0e5eab4d98c9bddc5f69ee6bd4","first_computed_at":"2026-05-18T00:26:16.662447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:16.662447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FLX6KhaGs10BEufp54ELkZgjbclLNUFf6Ch3jaf3WotP8NnmYcmATPls/ujwT6nqkzc53wbZNDjBkVkt3d1BCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:16.663060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08588","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:730ff1b26c6c2cf3c9ac495bfa3f7fe6f7954ab423d95837371d37cea1d60bb3","sha256:aa5c4c01defe3b72aaa5f905adf7221d0aa56408fcd08b029a51ea030264fef3"],"state_sha256":"1bd35184a1159a0605af5750b45903ce0d96f83c472446324ff9e73bbf40c681"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkU2ScVn42Hv7zwv/E9ci8xpUec+r6eBm9uMcXe0CXH8yse5Tesg7k/eIM/cZju6jATJyqWbbcNHeuFbWEkyBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:50:00.587603Z","bundle_sha256":"c7786bc52ad3c52b3fe24787c1d65f5ea2f3bc245be2da9d9577c0a7ea694b8d"}}