{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ASJKNAH2SVNX5Y7FGQZD5KOXJE","short_pith_number":"pith:ASJKNAH2","canonical_record":{"source":{"id":"1304.0203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-31T13:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"205a03e9a453f0b47ae68982c54febf9ffe2c50a2f2b80ac96efccd9c445e505","abstract_canon_sha256":"9cf50519c108adbc499c1f6e366dfe18f29e87264d69f9733460319ce87e8e7f"},"schema_version":"1.0"},"canonical_sha256":"0492a680fa955b7ee3e534323ea9d749140068c792f9a6e0bda5da3ba8d6c4e2","source":{"kind":"arxiv","id":"1304.0203","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0203","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0203v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0203","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"ASJKNAH2SVNX","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ASJKNAH2SVNX5Y7F","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ASJKNAH2","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ASJKNAH2SVNX5Y7FGQZD5KOXJE","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-31T13:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"205a03e9a453f0b47ae68982c54febf9ffe2c50a2f2b80ac96efccd9c445e505","abstract_canon_sha256":"9cf50519c108adbc499c1f6e366dfe18f29e87264d69f9733460319ce87e8e7f"},"schema_version":"1.0"},"canonical_sha256":"0492a680fa955b7ee3e534323ea9d749140068c792f9a6e0bda5da3ba8d6c4e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:25.701078Z","signature_b64":"aUhQ7zqwm+22ZVFUk2xmph3gzMSvobOH2KNTis1j9V1vY63/wOsxVFUOPVHT5Fy6mIQHr2pJeWYgDrdfnCV0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0492a680fa955b7ee3e534323ea9d749140068c792f9a6e0bda5da3ba8d6c4e2","last_reissued_at":"2026-05-18T03:29:25.700465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:25.700465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0203","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":"2026-05-18T03:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8IE04UB6ppdIBHHYvVdG+b5H0xAuSWwWUPFdiv0SU0I8YdXltjQb2LNtWEmlNNuThOjw8GSgiBZCc1SPNgViDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T11:52:18.049126Z"},"content_sha256":"a04c1c9df9ed460c44b00780cdc893167e8dff7b537bb16b07fad0d66e97e8a1","schema_version":"1.0","event_id":"sha256:a04c1c9df9ed460c44b00780cdc893167e8dff7b537bb16b07fad0d66e97e8a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ASJKNAH2SVNX5Y7FGQZD5KOXJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic Properties of Picard-Fuchs Equations and Holonomic Recurrences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander W. Walker, Zane Kun Li","submitted_at":"2013-03-31T13:36:23Z","abstract_excerpt":"The coefficient series of the holomorphic Picard-Fuchs differential equation associated with the periods of elliptic curves often have surprising number-theoretic properties. These have been widely studied in the case of the torsion-free, genus zero congruence subgroups of index 6 and 12 (e.g. the Beauville families). Here, we consider arithmetic properties of the Picard-Fuchs solutions associated to general elliptic families, with a particular focus on the index 24 congruence subgroups. We prove that elliptic families with rational parameters admit linear reparametrizations such that their as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0203","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":""},"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":"2026-05-18T03:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D44ZHmpxrQ84aapHsIHuq9mqIwXYIaxnzcRHpK2ldWvQxJXI+dHERU4a473dLOmitQku223+P6af8S4biMAmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T11:52:18.049494Z"},"content_sha256":"e049f07f00437627ad1bf88951e637dfc73c9bc3ff7193388cb6cc7cdf7934a3","schema_version":"1.0","event_id":"sha256:e049f07f00437627ad1bf88951e637dfc73c9bc3ff7193388cb6cc7cdf7934a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASJKNAH2SVNX5Y7FGQZD5KOXJE/bundle.json","state_url":"https://pith.science/pith/ASJKNAH2SVNX5Y7FGQZD5KOXJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASJKNAH2SVNX5Y7FGQZD5KOXJE/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":"2026-06-28T11:52:18Z","links":{"resolver":"https://pith.science/pith/ASJKNAH2SVNX5Y7FGQZD5KOXJE","bundle":"https://pith.science/pith/ASJKNAH2SVNX5Y7FGQZD5KOXJE/bundle.json","state":"https://pith.science/pith/ASJKNAH2SVNX5Y7FGQZD5KOXJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASJKNAH2SVNX5Y7FGQZD5KOXJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ASJKNAH2SVNX5Y7FGQZD5KOXJE","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":"9cf50519c108adbc499c1f6e366dfe18f29e87264d69f9733460319ce87e8e7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-31T13:36:23Z","title_canon_sha256":"205a03e9a453f0b47ae68982c54febf9ffe2c50a2f2b80ac96efccd9c445e505"},"schema_version":"1.0","source":{"id":"1304.0203","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0203","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0203v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0203","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"ASJKNAH2SVNX","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ASJKNAH2SVNX5Y7F","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ASJKNAH2","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:e049f07f00437627ad1bf88951e637dfc73c9bc3ff7193388cb6cc7cdf7934a3","target":"graph","created_at":"2026-05-18T03:29:25Z","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":"The coefficient series of the holomorphic Picard-Fuchs differential equation associated with the periods of elliptic curves often have surprising number-theoretic properties. These have been widely studied in the case of the torsion-free, genus zero congruence subgroups of index 6 and 12 (e.g. the Beauville families). Here, we consider arithmetic properties of the Picard-Fuchs solutions associated to general elliptic families, with a particular focus on the index 24 congruence subgroups. We prove that elliptic families with rational parameters admit linear reparametrizations such that their as","authors_text":"Alexander W. Walker, Zane Kun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-31T13:36:23Z","title":"Arithmetic Properties of Picard-Fuchs Equations and Holonomic Recurrences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0203","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:a04c1c9df9ed460c44b00780cdc893167e8dff7b537bb16b07fad0d66e97e8a1","target":"record","created_at":"2026-05-18T03:29:25Z","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":"9cf50519c108adbc499c1f6e366dfe18f29e87264d69f9733460319ce87e8e7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-31T13:36:23Z","title_canon_sha256":"205a03e9a453f0b47ae68982c54febf9ffe2c50a2f2b80ac96efccd9c445e505"},"schema_version":"1.0","source":{"id":"1304.0203","kind":"arxiv","version":1}},"canonical_sha256":"0492a680fa955b7ee3e534323ea9d749140068c792f9a6e0bda5da3ba8d6c4e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0492a680fa955b7ee3e534323ea9d749140068c792f9a6e0bda5da3ba8d6c4e2","first_computed_at":"2026-05-18T03:29:25.700465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:25.700465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aUhQ7zqwm+22ZVFUk2xmph3gzMSvobOH2KNTis1j9V1vY63/wOsxVFUOPVHT5Fy6mIQHr2pJeWYgDrdfnCV0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:25.701078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0203","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a04c1c9df9ed460c44b00780cdc893167e8dff7b537bb16b07fad0d66e97e8a1","sha256:e049f07f00437627ad1bf88951e637dfc73c9bc3ff7193388cb6cc7cdf7934a3"],"state_sha256":"3f0d061162eac65f3c525a9355d95fb763f0b6b406d7b09f669835476d928ea3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gSj7i8exKgiOhZwYe6vb5j8Up8xDhRfVBK2dDBCHaIzSfXfymrE/GJ84znTdvgT2qInE2hvioAM1WkMfQayABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T11:52:18.051357Z","bundle_sha256":"2249bdc87b1d667087eb4e99d8006b31b71f48039c44cbc4e9b46bcba50b5f60"}}