{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OSI5NVT7OVVEHMH2GSGEFHHTMT","short_pith_number":"pith:OSI5NVT7","canonical_record":{"source":{"id":"2405.09993","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-05-16T11:26:20Z","cross_cats_sorted":["cs.LG","cs.NE","math-ph","math.GT","math.MP"],"title_canon_sha256":"7a5d7f3c2e475ec0903eb4de8b0754f1c49845cfefcb62a1bd80a781c9dc09ed","abstract_canon_sha256":"83ea107a6cf74a4e8d14dd8518623240cc523eb7505637fbb5ddd03b75913a35"},"schema_version":"1.0"},"canonical_sha256":"7491d6d67f756a43b0fa348c429cf364d95383724afbfd46fb4e5be38c00a7f4","source":{"kind":"arxiv","id":"2405.09993","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.09993","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"arxiv_version","alias_value":"2405.09993v1","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.09993","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"pith_short_12","alias_value":"OSI5NVT7OVVE","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"pith_short_16","alias_value":"OSI5NVT7OVVEHMH2","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"pith_short_8","alias_value":"OSI5NVT7","created_at":"2026-07-05T08:58:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OSI5NVT7OVVEHMH2GSGEFHHTMT","target":"record","payload":{"canonical_record":{"source":{"id":"2405.09993","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-05-16T11:26:20Z","cross_cats_sorted":["cs.LG","cs.NE","math-ph","math.GT","math.MP"],"title_canon_sha256":"7a5d7f3c2e475ec0903eb4de8b0754f1c49845cfefcb62a1bd80a781c9dc09ed","abstract_canon_sha256":"83ea107a6cf74a4e8d14dd8518623240cc523eb7505637fbb5ddd03b75913a35"},"schema_version":"1.0"},"canonical_sha256":"7491d6d67f756a43b0fa348c429cf364d95383724afbfd46fb4e5be38c00a7f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:58:44.297665Z","signature_b64":"T2dZtqW0pWk035SKSOsj0wnfz1ZQYb16kxx1+Rdi3UxTEeXTpLWMLAeeXIlyOGpNRRhRNhmDEbvO6Q0kjEcfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7491d6d67f756a43b0fa348c429cf364d95383724afbfd46fb4e5be38c00a7f4","last_reissued_at":"2026-07-05T08:58:44.297187Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:58:44.297187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.09993","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":"2026-07-05T08:58:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0FP18+8Cne+MsmCwtReMpVCjg5BGb+BfWrvgaaJt1OSigr6zOAqBtbzfAQ2NTQfk4MIu5MnX4yguGcTcrKIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:52:16.503894Z"},"content_sha256":"0485819db8e8e96b7874785d8ea0d7b716b8a5386ac8e7ed8456ec2061594bcd","schema_version":"1.0","event_id":"sha256:0485819db8e8e96b7874785d8ea0d7b716b8a5386ac8e7ed8456ec2061594bcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OSI5NVT7OVVEHMH2GSGEFHHTMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning BPS Spectra and the Gap Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NE","math-ph","math.GT","math.MP"],"primary_cat":"hep-th","authors_text":"Rak-Kyeong Seong, Sergei Gukov","submitted_at":"2024-05-16T11:26:20Z","abstract_excerpt":"We explore statistical properties of BPS q-series for 3d N=2 strongly coupled supersymmetric theories that correspond to a particular family of 3-manifolds Y. We discover that gaps between exponents in the q-series are statistically more significant at the beginning of the q-series compared to gaps that appear in higher powers of q. Our observations are obtained by calculating saliencies of q-series features used as input data for principal component analysis, which is a standard example of an explainable machine learning technique that allows for a direct calculation and a better analysis of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.09993","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/2405.09993/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":"2026-07-05T08:58:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gu9JXo/dSQV7OSk6tIlh+BLPBz4spDkARNocCHfaGF+1RZFVgInV4fLn3vbC8emn52274kOKNzDehavWrL7HAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:52:16.504274Z"},"content_sha256":"bb2769482d2cd17399f4428d52024e3eb3a5cf690ca7f96cc695520942cae029","schema_version":"1.0","event_id":"sha256:bb2769482d2cd17399f4428d52024e3eb3a5cf690ca7f96cc695520942cae029"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSI5NVT7OVVEHMH2GSGEFHHTMT/bundle.json","state_url":"https://pith.science/pith/OSI5NVT7OVVEHMH2GSGEFHHTMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSI5NVT7OVVEHMH2GSGEFHHTMT/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":"2026-08-05T22:52:16Z","links":{"resolver":"https://pith.science/pith/OSI5NVT7OVVEHMH2GSGEFHHTMT","bundle":"https://pith.science/pith/OSI5NVT7OVVEHMH2GSGEFHHTMT/bundle.json","state":"https://pith.science/pith/OSI5NVT7OVVEHMH2GSGEFHHTMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSI5NVT7OVVEHMH2GSGEFHHTMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OSI5NVT7OVVEHMH2GSGEFHHTMT","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":"83ea107a6cf74a4e8d14dd8518623240cc523eb7505637fbb5ddd03b75913a35","cross_cats_sorted":["cs.LG","cs.NE","math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-05-16T11:26:20Z","title_canon_sha256":"7a5d7f3c2e475ec0903eb4de8b0754f1c49845cfefcb62a1bd80a781c9dc09ed"},"schema_version":"1.0","source":{"id":"2405.09993","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.09993","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"arxiv_version","alias_value":"2405.09993v1","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.09993","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"pith_short_12","alias_value":"OSI5NVT7OVVE","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"pith_short_16","alias_value":"OSI5NVT7OVVEHMH2","created_at":"2026-07-05T08:58:44Z"},{"alias_kind":"pith_short_8","alias_value":"OSI5NVT7","created_at":"2026-07-05T08:58:44Z"}],"graph_snapshots":[{"event_id":"sha256:bb2769482d2cd17399f4428d52024e3eb3a5cf690ca7f96cc695520942cae029","target":"graph","created_at":"2026-07-05T08:58:44Z","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/2405.09993/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore statistical properties of BPS q-series for 3d N=2 strongly coupled supersymmetric theories that correspond to a particular family of 3-manifolds Y. We discover that gaps between exponents in the q-series are statistically more significant at the beginning of the q-series compared to gaps that appear in higher powers of q. Our observations are obtained by calculating saliencies of q-series features used as input data for principal component analysis, which is a standard example of an explainable machine learning technique that allows for a direct calculation and a better analysis of ","authors_text":"Rak-Kyeong Seong, Sergei Gukov","cross_cats":["cs.LG","cs.NE","math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-05-16T11:26:20Z","title":"Learning BPS Spectra and the Gap Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.09993","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":"sha256:0485819db8e8e96b7874785d8ea0d7b716b8a5386ac8e7ed8456ec2061594bcd","target":"record","created_at":"2026-07-05T08:58:44Z","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":"83ea107a6cf74a4e8d14dd8518623240cc523eb7505637fbb5ddd03b75913a35","cross_cats_sorted":["cs.LG","cs.NE","math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-05-16T11:26:20Z","title_canon_sha256":"7a5d7f3c2e475ec0903eb4de8b0754f1c49845cfefcb62a1bd80a781c9dc09ed"},"schema_version":"1.0","source":{"id":"2405.09993","kind":"arxiv","version":1}},"canonical_sha256":"7491d6d67f756a43b0fa348c429cf364d95383724afbfd46fb4e5be38c00a7f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7491d6d67f756a43b0fa348c429cf364d95383724afbfd46fb4e5be38c00a7f4","first_computed_at":"2026-07-05T08:58:44.297187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:58:44.297187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T2dZtqW0pWk035SKSOsj0wnfz1ZQYb16kxx1+Rdi3UxTEeXTpLWMLAeeXIlyOGpNRRhRNhmDEbvO6Q0kjEcfCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:58:44.297665Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.09993","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0485819db8e8e96b7874785d8ea0d7b716b8a5386ac8e7ed8456ec2061594bcd","sha256:bb2769482d2cd17399f4428d52024e3eb3a5cf690ca7f96cc695520942cae029"],"state_sha256":"0d805e4267e196deba1191f565329c1ed179915845c8ab1173aef53125f08ff3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sCOtvrCa+lE1X5TRktlGtDA/iaotSJ/yxoYFLEvdgrNn/JgJPzg+peIjYjbBqS2mcjkUxFF4TWiQWvEJABfWDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T22:52:16.506682Z","bundle_sha256":"f2df7d27ab635ecb6a00d7e9a4e21fab0e873043a78ebcbe019c87ce903bef16"}}