{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FZ7PF65TWVJUIEZPQL4C3GS6PB","short_pith_number":"pith:FZ7PF65T","canonical_record":{"source":{"id":"1312.4421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-16T16:38:04Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"f0f4afa4abdcba62932e423ea3d491bded43d33d0a74722c55108d0d609d72bb","abstract_canon_sha256":"f30955c04b66d75e7f73e9cca26070b47d33435a3dbc043bf725019bc56fe38a"},"schema_version":"1.0"},"canonical_sha256":"2e7ef2fbb3b55344132f82f82d9a5e7864c9a718639c3675278d57493b704b21","source":{"kind":"arxiv","id":"1312.4421","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4421","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4421v1","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4421","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"FZ7PF65TWVJU","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FZ7PF65TWVJUIEZP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FZ7PF65T","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FZ7PF65TWVJUIEZPQL4C3GS6PB","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-16T16:38:04Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"f0f4afa4abdcba62932e423ea3d491bded43d33d0a74722c55108d0d609d72bb","abstract_canon_sha256":"f30955c04b66d75e7f73e9cca26070b47d33435a3dbc043bf725019bc56fe38a"},"schema_version":"1.0"},"canonical_sha256":"2e7ef2fbb3b55344132f82f82d9a5e7864c9a718639c3675278d57493b704b21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:34.485694Z","signature_b64":"fN3k4WcnTRYYfttV8roSo5JXOXYWdnguKox7aJeFxiW+7w1+udeoDC4YpiGD5ABvtIR0RrW1tyJ7HXYpZXxKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e7ef2fbb3b55344132f82f82d9a5e7864c9a718639c3675278d57493b704b21","last_reissued_at":"2026-05-18T03:04:34.484855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:34.484855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4421","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":"2026-05-18T03:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFCsyp+/1zco0DYv46J9plDiBzncS1yloBR9vZRTLlRDzj599zAKYy5e9beXQA3hiM0wFJI2gU7I0UteJ7aCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:21:52.325649Z"},"content_sha256":"636be567878d2369ead9092fd7b5906cc1e56303e4cfb2732a4a55a66d8de3b3","schema_version":"1.0","event_id":"sha256:636be567878d2369ead9092fd7b5906cc1e56303e4cfb2732a4a55a66d8de3b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FZ7PF65TWVJUIEZPQL4C3GS6PB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Classification of Elliptic Fibrations modulo Isomorphism on K3 Surfaces with large Picard Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Andreas P. Braun, Taizan Watari, Yusuke Kimura","submitted_at":"2013-12-16T16:38:04Z","abstract_excerpt":"Motivated by a problem originating in string theory, we study elliptic fibrations on K3 surfaces with large Picard number modulo isomorphism. We give methods to determine upper bounds for the number of inequivalent K3 surfaces sharing the same frame lattice. For any given Neron--Severi lattice $S_X$, such a bound on the `multiplicity' can be derived by investigating the quotient of the isometry group of $S_X$ by the automorphism group. The resulting bounds are strongest for large Picard numbers and multiplicities of unity do indeed occur for a number of K3 surfaces with Picard number 20. Under"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4421","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":"2026-05-18T03:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3/SsWgVK5S3Wd6v+qKL9zPhnRpWlN9604MRbun7NpyKo4IpcR/5B51dF1noTPjMeog2Yp6Zvu5ilWqqi4cF9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:21:52.326044Z"},"content_sha256":"c721c98295374fc34438f471944d2d667045ccd09499aca6835d29f8c6b54c8c","schema_version":"1.0","event_id":"sha256:c721c98295374fc34438f471944d2d667045ccd09499aca6835d29f8c6b54c8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZ7PF65TWVJUIEZPQL4C3GS6PB/bundle.json","state_url":"https://pith.science/pith/FZ7PF65TWVJUIEZPQL4C3GS6PB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZ7PF65TWVJUIEZPQL4C3GS6PB/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":"2026-05-31T23:21:52Z","links":{"resolver":"https://pith.science/pith/FZ7PF65TWVJUIEZPQL4C3GS6PB","bundle":"https://pith.science/pith/FZ7PF65TWVJUIEZPQL4C3GS6PB/bundle.json","state":"https://pith.science/pith/FZ7PF65TWVJUIEZPQL4C3GS6PB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZ7PF65TWVJUIEZPQL4C3GS6PB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FZ7PF65TWVJUIEZPQL4C3GS6PB","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":"f30955c04b66d75e7f73e9cca26070b47d33435a3dbc043bf725019bc56fe38a","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-16T16:38:04Z","title_canon_sha256":"f0f4afa4abdcba62932e423ea3d491bded43d33d0a74722c55108d0d609d72bb"},"schema_version":"1.0","source":{"id":"1312.4421","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4421","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4421v1","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4421","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"FZ7PF65TWVJU","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FZ7PF65TWVJUIEZP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FZ7PF65T","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:c721c98295374fc34438f471944d2d667045ccd09499aca6835d29f8c6b54c8c","target":"graph","created_at":"2026-05-18T03:04:34Z","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":"Motivated by a problem originating in string theory, we study elliptic fibrations on K3 surfaces with large Picard number modulo isomorphism. We give methods to determine upper bounds for the number of inequivalent K3 surfaces sharing the same frame lattice. For any given Neron--Severi lattice $S_X$, such a bound on the `multiplicity' can be derived by investigating the quotient of the isometry group of $S_X$ by the automorphism group. The resulting bounds are strongest for large Picard numbers and multiplicities of unity do indeed occur for a number of K3 surfaces with Picard number 20. Under","authors_text":"Andreas P. Braun, Taizan Watari, Yusuke Kimura","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-16T16:38:04Z","title":"On the Classification of Elliptic Fibrations modulo Isomorphism on K3 Surfaces with large Picard Number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4421","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":"sha256:636be567878d2369ead9092fd7b5906cc1e56303e4cfb2732a4a55a66d8de3b3","target":"record","created_at":"2026-05-18T03:04:34Z","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":"f30955c04b66d75e7f73e9cca26070b47d33435a3dbc043bf725019bc56fe38a","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-16T16:38:04Z","title_canon_sha256":"f0f4afa4abdcba62932e423ea3d491bded43d33d0a74722c55108d0d609d72bb"},"schema_version":"1.0","source":{"id":"1312.4421","kind":"arxiv","version":1}},"canonical_sha256":"2e7ef2fbb3b55344132f82f82d9a5e7864c9a718639c3675278d57493b704b21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e7ef2fbb3b55344132f82f82d9a5e7864c9a718639c3675278d57493b704b21","first_computed_at":"2026-05-18T03:04:34.484855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:34.484855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fN3k4WcnTRYYfttV8roSo5JXOXYWdnguKox7aJeFxiW+7w1+udeoDC4YpiGD5ABvtIR0RrW1tyJ7HXYpZXxKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:34.485694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4421","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:636be567878d2369ead9092fd7b5906cc1e56303e4cfb2732a4a55a66d8de3b3","sha256:c721c98295374fc34438f471944d2d667045ccd09499aca6835d29f8c6b54c8c"],"state_sha256":"48398514970add79f3e34002962c69c77429d4774747778c7e92f185f4faabd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A85ZIH0CA3GJAQNlrVk2CrP/QFnPj0wpRgiptNm3VKdHMSCY2m8lFSk6H6PH2rmPvP1NHehvPB8pIYcEvQz9DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:21:52.328761Z","bundle_sha256":"1882767bf1af35c0beacfcb2a6406c939bff57d4cfc307a60187556331acedbb"}}