{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:66H5AXXHQFBGW5EGC3B32FNLCQ","short_pith_number":"pith:66H5AXXH","canonical_record":{"source":{"id":"1609.04154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T07:29:39Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"98bf2f7ec340af286fec3a63fd34c016be8a54f4e4a018d409bad11ca9fe49db","abstract_canon_sha256":"6d559779f2d8b5a5c3633e42a789ae23d6f2a39e221f8e8d637c9cf2123b606c"},"schema_version":"1.0"},"canonical_sha256":"f78fd05ee781426b748616c3bd15ab1439a7da16f305089b6e8fb22aa9c45daa","source":{"kind":"arxiv","id":"1609.04154","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04154","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04154v1","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04154","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"66H5AXXHQFBG","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"66H5AXXHQFBGW5EG","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"66H5AXXH","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:66H5AXXHQFBGW5EGC3B32FNLCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T07:29:39Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"98bf2f7ec340af286fec3a63fd34c016be8a54f4e4a018d409bad11ca9fe49db","abstract_canon_sha256":"6d559779f2d8b5a5c3633e42a789ae23d6f2a39e221f8e8d637c9cf2123b606c"},"schema_version":"1.0"},"canonical_sha256":"f78fd05ee781426b748616c3bd15ab1439a7da16f305089b6e8fb22aa9c45daa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:38.826503Z","signature_b64":"PMaKszNXkEqyPnskSZYZgyip0/D/54HJsjwlU0a12caqGFU0/UD/1tO9fM2ODeCCgfHWzUc7oH50vZC2ztpBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f78fd05ee781426b748616c3bd15ab1439a7da16f305089b6e8fb22aa9c45daa","last_reissued_at":"2026-05-18T01:04:38.825862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:38.825862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04154","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":"2026-05-18T01:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6AInebXTLdo2QQM70Ejw4431bUlqCNdqdtMv+GDTH84Iaf1U7XYYHvibYob5sSNgZzTdJtZ3hju23ZnUo2t+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:46:42.232132Z"},"content_sha256":"15fc6bbc00c39da4f18f0f0900ee4f8c2a10d44b6c37abff0c6be8d3e9c22bdb","schema_version":"1.0","event_id":"sha256:15fc6bbc00c39da4f18f0f0900ee4f8c2a10d44b6c37abff0c6be8d3e9c22bdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:66H5AXXHQFBGW5EGC3B32FNLCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphisms of certain Niemeier lattices and Elliptic Fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Marie Jos\\'e Bertin, Odile Lecacheux","submitted_at":"2016-09-14T07:29:39Z","abstract_excerpt":"Nishiyama introduced a lattice theoretic classification of the elliptic fibrations on a $K3$ surface. In a previous paper we used his method to exhibit $52$ elliptic fibrations, up to isomorphisms, of the singular $K3$ surface of discriminant $-12$. We prove here that the list is complete with a $53$th fibration, thanks to a remark of Elkies and Sch\\\"{u}tt. We characterize the fibration both theoretically and with a Weierstrass model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04154","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":"2026-05-18T01:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzvNhlmf+ywtzloQ/s/IRLk39memAzv01cYbGZuJ8NAP2zkGYKJ6vsDY/FC8VgkxQoKoLgCbZNfeVJRdLEM3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:46:42.232479Z"},"content_sha256":"44f6378fdbb90590af8214753e5b838aba118205ff70cefcf0788f01bbb57c2a","schema_version":"1.0","event_id":"sha256:44f6378fdbb90590af8214753e5b838aba118205ff70cefcf0788f01bbb57c2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66H5AXXHQFBGW5EGC3B32FNLCQ/bundle.json","state_url":"https://pith.science/pith/66H5AXXHQFBGW5EGC3B32FNLCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66H5AXXHQFBGW5EGC3B32FNLCQ/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":"2026-06-03T01:46:42Z","links":{"resolver":"https://pith.science/pith/66H5AXXHQFBGW5EGC3B32FNLCQ","bundle":"https://pith.science/pith/66H5AXXHQFBGW5EGC3B32FNLCQ/bundle.json","state":"https://pith.science/pith/66H5AXXHQFBGW5EGC3B32FNLCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66H5AXXHQFBGW5EGC3B32FNLCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:66H5AXXHQFBGW5EGC3B32FNLCQ","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":"6d559779f2d8b5a5c3633e42a789ae23d6f2a39e221f8e8d637c9cf2123b606c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T07:29:39Z","title_canon_sha256":"98bf2f7ec340af286fec3a63fd34c016be8a54f4e4a018d409bad11ca9fe49db"},"schema_version":"1.0","source":{"id":"1609.04154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04154","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04154v1","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04154","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"66H5AXXHQFBG","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"66H5AXXHQFBGW5EG","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"66H5AXXH","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:44f6378fdbb90590af8214753e5b838aba118205ff70cefcf0788f01bbb57c2a","target":"graph","created_at":"2026-05-18T01:04:38Z","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":"Nishiyama introduced a lattice theoretic classification of the elliptic fibrations on a $K3$ surface. In a previous paper we used his method to exhibit $52$ elliptic fibrations, up to isomorphisms, of the singular $K3$ surface of discriminant $-12$. We prove here that the list is complete with a $53$th fibration, thanks to a remark of Elkies and Sch\\\"{u}tt. We characterize the fibration both theoretically and with a Weierstrass model.","authors_text":"Marie Jos\\'e Bertin, Odile Lecacheux","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T07:29:39Z","title":"Automorphisms of certain Niemeier lattices and Elliptic Fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04154","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":"sha256:15fc6bbc00c39da4f18f0f0900ee4f8c2a10d44b6c37abff0c6be8d3e9c22bdb","target":"record","created_at":"2026-05-18T01:04:38Z","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":"6d559779f2d8b5a5c3633e42a789ae23d6f2a39e221f8e8d637c9cf2123b606c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T07:29:39Z","title_canon_sha256":"98bf2f7ec340af286fec3a63fd34c016be8a54f4e4a018d409bad11ca9fe49db"},"schema_version":"1.0","source":{"id":"1609.04154","kind":"arxiv","version":1}},"canonical_sha256":"f78fd05ee781426b748616c3bd15ab1439a7da16f305089b6e8fb22aa9c45daa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f78fd05ee781426b748616c3bd15ab1439a7da16f305089b6e8fb22aa9c45daa","first_computed_at":"2026-05-18T01:04:38.825862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:38.825862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PMaKszNXkEqyPnskSZYZgyip0/D/54HJsjwlU0a12caqGFU0/UD/1tO9fM2ODeCCgfHWzUc7oH50vZC2ztpBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:38.826503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15fc6bbc00c39da4f18f0f0900ee4f8c2a10d44b6c37abff0c6be8d3e9c22bdb","sha256:44f6378fdbb90590af8214753e5b838aba118205ff70cefcf0788f01bbb57c2a"],"state_sha256":"4fd97a462f0398c214f0fceeca0659422e864a6cbeaa6b29399c8463f63be59b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WHAymoJKjHqjjntQoO5O92TH/5SyiDKsfhyVMrYRca17XAqjAr7eMoxcIWINCQql1N8JojPd2lQK6Aw/EgFvCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:46:42.234544Z","bundle_sha256":"91926330f0a0e08c58e6c9720017740138097268430d9336b5765a6aba91d71f"}}