{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XK2O2V2IXZ5HHR3LHKTSIAF5IJ","short_pith_number":"pith:XK2O2V2I","canonical_record":{"source":{"id":"1001.5312","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-01-29T02:18:40Z","cross_cats_sorted":[],"title_canon_sha256":"7cd9e3ae84097cbbf6be2ab267cb5f1bda54779047f725975446149ea160e986","abstract_canon_sha256":"8620e2b728460e73c1eea7e0be4aad8d2fea45eb953cf70c59a9861fa1f0cbc4"},"schema_version":"1.0"},"canonical_sha256":"bab4ed5748be7a73c76b3aa72400bd427e7747e033935021dbe6ad6dba2733d4","source":{"kind":"arxiv","id":"1001.5312","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5312","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5312v5","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5312","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"pith_short_12","alias_value":"XK2O2V2IXZ5H","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XK2O2V2IXZ5HHR3L","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XK2O2V2I","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XK2O2V2IXZ5HHR3LHKTSIAF5IJ","target":"record","payload":{"canonical_record":{"source":{"id":"1001.5312","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-01-29T02:18:40Z","cross_cats_sorted":[],"title_canon_sha256":"7cd9e3ae84097cbbf6be2ab267cb5f1bda54779047f725975446149ea160e986","abstract_canon_sha256":"8620e2b728460e73c1eea7e0be4aad8d2fea45eb953cf70c59a9861fa1f0cbc4"},"schema_version":"1.0"},"canonical_sha256":"bab4ed5748be7a73c76b3aa72400bd427e7747e033935021dbe6ad6dba2733d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:10.537920Z","signature_b64":"+VRdW24CxOMJ0eh2xaIShlRowXeM8keHygLKrySMQhV9l6BozgRe5KoieyT2JCYf3xuoMVmbMAjtRy4EujTvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bab4ed5748be7a73c76b3aa72400bd427e7747e033935021dbe6ad6dba2733d4","last_reissued_at":"2026-05-18T01:18:10.537360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:10.537360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.5312","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":"2026-05-18T01:18:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GiUxm1nH+BLFVJoAbHGIAii775PNy0gO0LVeNojPvQXKat/Ksv9uJA/uJHBYhAIKp1MmO+ODPlsgXqisFWXjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:31:00.139965Z"},"content_sha256":"bd5ba9bc21d5a991fbcb902559cb303ee534a50ce9853bb86d17f6876abb9930","schema_version":"1.0","event_id":"sha256:bd5ba9bc21d5a991fbcb902559cb303ee534a50ce9853bb86d17f6876abb9930"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XK2O2V2IXZ5HHR3LHKTSIAF5IJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Period differential equations for families of K3 surfaces derived from some 3 dimensional reflexive polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Atsuhira Nagano","submitted_at":"2010-01-29T02:18:40Z","abstract_excerpt":"We study period maps for families of $K3$ surfaces those are given by anti canonical divisors of toric varieties coming from reflexive polytopes $P_2, P_4, P_5$ and $P_r$. We obtain systems of period differential equations for these families. Moreover, in the case $P_4$, we determine the projective monodromy group of the period map. This group is explicitly related with the Hilbert modular group for $\\mathbb{Q}(\\sqrt{5})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5312","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":"2026-05-18T01:18:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xM43/ml30bkVKXXX+Gsuzcg4J6Yjt7a102211lF216yK/D4EcCW+K5ydYXJZHt6tja0CdvRf0lHr+kAdLP21BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:31:00.140349Z"},"content_sha256":"ea2ff9fc2af7afc7946939536ed6f14717f1295aaba69bc859d313fd0efb8b9b","schema_version":"1.0","event_id":"sha256:ea2ff9fc2af7afc7946939536ed6f14717f1295aaba69bc859d313fd0efb8b9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XK2O2V2IXZ5HHR3LHKTSIAF5IJ/bundle.json","state_url":"https://pith.science/pith/XK2O2V2IXZ5HHR3LHKTSIAF5IJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XK2O2V2IXZ5HHR3LHKTSIAF5IJ/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":"2026-06-03T10:31:00Z","links":{"resolver":"https://pith.science/pith/XK2O2V2IXZ5HHR3LHKTSIAF5IJ","bundle":"https://pith.science/pith/XK2O2V2IXZ5HHR3LHKTSIAF5IJ/bundle.json","state":"https://pith.science/pith/XK2O2V2IXZ5HHR3LHKTSIAF5IJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XK2O2V2IXZ5HHR3LHKTSIAF5IJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XK2O2V2IXZ5HHR3LHKTSIAF5IJ","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":"8620e2b728460e73c1eea7e0be4aad8d2fea45eb953cf70c59a9861fa1f0cbc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-01-29T02:18:40Z","title_canon_sha256":"7cd9e3ae84097cbbf6be2ab267cb5f1bda54779047f725975446149ea160e986"},"schema_version":"1.0","source":{"id":"1001.5312","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5312","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5312v5","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5312","created_at":"2026-05-18T01:18:10Z"},{"alias_kind":"pith_short_12","alias_value":"XK2O2V2IXZ5H","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XK2O2V2IXZ5HHR3L","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XK2O2V2I","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:ea2ff9fc2af7afc7946939536ed6f14717f1295aaba69bc859d313fd0efb8b9b","target":"graph","created_at":"2026-05-18T01:18:10Z","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":"We study period maps for families of $K3$ surfaces those are given by anti canonical divisors of toric varieties coming from reflexive polytopes $P_2, P_4, P_5$ and $P_r$. We obtain systems of period differential equations for these families. Moreover, in the case $P_4$, we determine the projective monodromy group of the period map. This group is explicitly related with the Hilbert modular group for $\\mathbb{Q}(\\sqrt{5})$.","authors_text":"Atsuhira Nagano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-01-29T02:18:40Z","title":"Period differential equations for families of K3 surfaces derived from some 3 dimensional reflexive polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5312","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:bd5ba9bc21d5a991fbcb902559cb303ee534a50ce9853bb86d17f6876abb9930","target":"record","created_at":"2026-05-18T01:18:10Z","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":"8620e2b728460e73c1eea7e0be4aad8d2fea45eb953cf70c59a9861fa1f0cbc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-01-29T02:18:40Z","title_canon_sha256":"7cd9e3ae84097cbbf6be2ab267cb5f1bda54779047f725975446149ea160e986"},"schema_version":"1.0","source":{"id":"1001.5312","kind":"arxiv","version":5}},"canonical_sha256":"bab4ed5748be7a73c76b3aa72400bd427e7747e033935021dbe6ad6dba2733d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bab4ed5748be7a73c76b3aa72400bd427e7747e033935021dbe6ad6dba2733d4","first_computed_at":"2026-05-18T01:18:10.537360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:10.537360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+VRdW24CxOMJ0eh2xaIShlRowXeM8keHygLKrySMQhV9l6BozgRe5KoieyT2JCYf3xuoMVmbMAjtRy4EujTvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:10.537920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.5312","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd5ba9bc21d5a991fbcb902559cb303ee534a50ce9853bb86d17f6876abb9930","sha256:ea2ff9fc2af7afc7946939536ed6f14717f1295aaba69bc859d313fd0efb8b9b"],"state_sha256":"f4030d264c80c2233f2ca9a14622e20bb2a183614e26da20e1c59b02c6e32ea9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2qsrEEx8xRaCEgiQSTJdADQe/eqfBCuG0uNRwohThTjwmDlxcqiejxlJ+Nm4Oov4/1dsCuorXruc5tTqHg4Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:31:00.142645Z","bundle_sha256":"97b9f51534cc88a86dfade5774dfef3f206a50d027d6980d372d76a5dbf9da74"}}