{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GZAN5SWCXCJKHPWWUD4XS4OPGG","short_pith_number":"pith:GZAN5SWC","canonical_record":{"source":{"id":"2502.08620","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-02-12T18:15:35Z","cross_cats_sorted":["cs.LG","math.CO","math.NT","math.RT"],"title_canon_sha256":"ba372d43e723a519d4e0131310c429cd430bd36d53a5ad38cb88a705bac15305","abstract_canon_sha256":"5e6c26f0492d3d30b071ad20c385a18bfe9859c4051fe4428157ef30fb66497d"},"schema_version":"1.0"},"canonical_sha256":"3640decac2b892a3bed6a0f97971cf31b8d9cae76552817e66568275effe0e54","source":{"kind":"arxiv","id":"2502.08620","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08620","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08620v1","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08620","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"pith_short_12","alias_value":"GZAN5SWCXCJK","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"pith_short_16","alias_value":"GZAN5SWCXCJKHPWW","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"pith_short_8","alias_value":"GZAN5SWC","created_at":"2026-07-05T10:13:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GZAN5SWCXCJKHPWWUD4XS4OPGG","target":"record","payload":{"canonical_record":{"source":{"id":"2502.08620","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-02-12T18:15:35Z","cross_cats_sorted":["cs.LG","math.CO","math.NT","math.RT"],"title_canon_sha256":"ba372d43e723a519d4e0131310c429cd430bd36d53a5ad38cb88a705bac15305","abstract_canon_sha256":"5e6c26f0492d3d30b071ad20c385a18bfe9859c4051fe4428157ef30fb66497d"},"schema_version":"1.0"},"canonical_sha256":"3640decac2b892a3bed6a0f97971cf31b8d9cae76552817e66568275effe0e54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:48.666947Z","signature_b64":"EooQjiL+Z+xWvOW04DZGArT9mSty8HELGq4fKuoL6N1o7UzvMvges/h6A/mkPcpBs/LgasGMgnbrfUqFmSgQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3640decac2b892a3bed6a0f97971cf31b8d9cae76552817e66568275effe0e54","last_reissued_at":"2026-07-05T10:13:48.666334Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:48.666334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.08620","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":"2026-07-05T10:13:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOJSLQ73bME++r4w6k6xUcJS/0AQBLrA9io3KjWlk5vvKnvqUt+pMBqvLn521aXPyZy3knNNCdpPorA2xeQxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:46:15.035614Z"},"content_sha256":"1c3f68454c5196adcd11678aad1ecbc308ee0c0e8b75aceb68ddf2ece259e5b5","schema_version":"1.0","event_id":"sha256:1c3f68454c5196adcd11678aad1ecbc308ee0c0e8b75aceb68ddf2ece259e5b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GZAN5SWCXCJKHPWWUD4XS4OPGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mathematical Data Science","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.CO","math.NT","math.RT"],"primary_cat":"math.HO","authors_text":"Kyu-Hwan Lee, Michael R. Douglas","submitted_at":"2025-02-12T18:15:35Z","abstract_excerpt":"Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call \"mathematical data science\". In this paradigm, one studies mathematical objects collectively rather than individually, by creating datasets and doing machine learning experiments and interpretations. After an overview, we present two case studies: murmurations in number theory and loadings of partitions related to Kronecker coefficients in representation theory and combinatorics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08620","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/2502.08620/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":"2026-07-05T10:13:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWynoNHaO6bYN4l5aZteX3X7I/sCfqcb65Hzg7KEnlqS9n6sSlowu4Ig9q6BduS2C9pex+v8OBqLaJKWounrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:46:15.036315Z"},"content_sha256":"03747ed0ed43e60dc101aea8619c0af8076553cf9c646eefb84452c7c337e54e","schema_version":"1.0","event_id":"sha256:03747ed0ed43e60dc101aea8619c0af8076553cf9c646eefb84452c7c337e54e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZAN5SWCXCJKHPWWUD4XS4OPGG/bundle.json","state_url":"https://pith.science/pith/GZAN5SWCXCJKHPWWUD4XS4OPGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZAN5SWCXCJKHPWWUD4XS4OPGG/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":"2026-08-09T07:46:15Z","links":{"resolver":"https://pith.science/pith/GZAN5SWCXCJKHPWWUD4XS4OPGG","bundle":"https://pith.science/pith/GZAN5SWCXCJKHPWWUD4XS4OPGG/bundle.json","state":"https://pith.science/pith/GZAN5SWCXCJKHPWWUD4XS4OPGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZAN5SWCXCJKHPWWUD4XS4OPGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GZAN5SWCXCJKHPWWUD4XS4OPGG","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":"5e6c26f0492d3d30b071ad20c385a18bfe9859c4051fe4428157ef30fb66497d","cross_cats_sorted":["cs.LG","math.CO","math.NT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-02-12T18:15:35Z","title_canon_sha256":"ba372d43e723a519d4e0131310c429cd430bd36d53a5ad38cb88a705bac15305"},"schema_version":"1.0","source":{"id":"2502.08620","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08620","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08620v1","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08620","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"pith_short_12","alias_value":"GZAN5SWCXCJK","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"pith_short_16","alias_value":"GZAN5SWCXCJKHPWW","created_at":"2026-07-05T10:13:48Z"},{"alias_kind":"pith_short_8","alias_value":"GZAN5SWC","created_at":"2026-07-05T10:13:48Z"}],"graph_snapshots":[{"event_id":"sha256:03747ed0ed43e60dc101aea8619c0af8076553cf9c646eefb84452c7c337e54e","target":"graph","created_at":"2026-07-05T10:13:48Z","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/2502.08620/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call \"mathematical data science\". In this paradigm, one studies mathematical objects collectively rather than individually, by creating datasets and doing machine learning experiments and interpretations. After an overview, we present two case studies: murmurations in number theory and loadings of partitions related to Kronecker coefficients in representation theory and combinatorics.","authors_text":"Kyu-Hwan Lee, Michael R. Douglas","cross_cats":["cs.LG","math.CO","math.NT","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-02-12T18:15:35Z","title":"Mathematical Data Science"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08620","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":"sha256:1c3f68454c5196adcd11678aad1ecbc308ee0c0e8b75aceb68ddf2ece259e5b5","target":"record","created_at":"2026-07-05T10:13:48Z","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":"5e6c26f0492d3d30b071ad20c385a18bfe9859c4051fe4428157ef30fb66497d","cross_cats_sorted":["cs.LG","math.CO","math.NT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-02-12T18:15:35Z","title_canon_sha256":"ba372d43e723a519d4e0131310c429cd430bd36d53a5ad38cb88a705bac15305"},"schema_version":"1.0","source":{"id":"2502.08620","kind":"arxiv","version":1}},"canonical_sha256":"3640decac2b892a3bed6a0f97971cf31b8d9cae76552817e66568275effe0e54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3640decac2b892a3bed6a0f97971cf31b8d9cae76552817e66568275effe0e54","first_computed_at":"2026-07-05T10:13:48.666334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:48.666334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EooQjiL+Z+xWvOW04DZGArT9mSty8HELGq4fKuoL6N1o7UzvMvges/h6A/mkPcpBs/LgasGMgnbrfUqFmSgQCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:48.666947Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.08620","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c3f68454c5196adcd11678aad1ecbc308ee0c0e8b75aceb68ddf2ece259e5b5","sha256:03747ed0ed43e60dc101aea8619c0af8076553cf9c646eefb84452c7c337e54e"],"state_sha256":"35c24dec60947ca5440154db61a835fc55cba1dd2de9f04caca4a49e3129babb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4dFdArcJv5+MhzkkyuTExFOD0E1JQF2ohzC5itkKGZaSr39q1IsOz8QOijyDilFbKUgvuRzyKzhm/3+xdJKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:46:15.041619Z","bundle_sha256":"b42e7e1b3a4f707ea8351f738439939262794c08a8f761fe682d3bba2e769a00"}}