{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7SANUYZHXIBPDT34B5O7ZGYEXJ","short_pith_number":"pith:7SANUYZH","canonical_record":{"source":{"id":"1808.08001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-24T04:22:15Z","cross_cats_sorted":[],"title_canon_sha256":"900b08d9a782c5bbd848d50b6df34f84dd059b93946abd65512930692ce72749","abstract_canon_sha256":"abe2386edc661148557059a978ea618ed4969088ab4232d51ace8ba2e7c4981c"},"schema_version":"1.0"},"canonical_sha256":"fc80da6327ba02f1cf7c0f5dfc9b04ba65bcdbee401ec40e0191d12372ed8eb0","source":{"kind":"arxiv","id":"1808.08001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08001","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08001v2","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08001","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"pith_short_12","alias_value":"7SANUYZHXIBP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7SANUYZHXIBPDT34","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7SANUYZH","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7SANUYZHXIBPDT34B5O7ZGYEXJ","target":"record","payload":{"canonical_record":{"source":{"id":"1808.08001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-24T04:22:15Z","cross_cats_sorted":[],"title_canon_sha256":"900b08d9a782c5bbd848d50b6df34f84dd059b93946abd65512930692ce72749","abstract_canon_sha256":"abe2386edc661148557059a978ea618ed4969088ab4232d51ace8ba2e7c4981c"},"schema_version":"1.0"},"canonical_sha256":"fc80da6327ba02f1cf7c0f5dfc9b04ba65bcdbee401ec40e0191d12372ed8eb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:30.487778Z","signature_b64":"zZDY1RCwF/x4Yk1LfGYyYRQDHCYP8UzqyZagk57urmHh2N5iMYe5Vl53v3jmEM96Bl+EJXmHYZcCV7rkD4SnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc80da6327ba02f1cf7c0f5dfc9b04ba65bcdbee401ec40e0191d12372ed8eb0","last_reissued_at":"2026-05-17T23:47:30.487325Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:30.487325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.08001","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nT6hyba91W2taPP5rONRl0tQHyQONYDIKblZTrqL4DBnemhRhWnBtI5me//8mtvNVpVKNRZisvw87NVL6KtwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:21:57.794630Z"},"content_sha256":"29446e717058f0e41f808fa0f1665a7d08e0e7177c7a1e1a292000359f153d50","schema_version":"1.0","event_id":"sha256:29446e717058f0e41f808fa0f1665a7d08e0e7177c7a1e1a292000359f153d50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7SANUYZHXIBPDT34B5O7ZGYEXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Kurume College), Shun'ya Mizoguchi (KEK, Taro Tani (NIT, Tsukuba), Tsukuba & Sokendai","submitted_at":"2018-08-24T04:22:15Z","abstract_excerpt":"The Mordell-Weil lattices (MW lattices) associated to rational elliptic surfaces are classified into 74 types. Among them, there are cases in which the MW lattice is none of the weight lattices of simple Lie algebras or direct sums thereof. We study how such \"non-Cartan MW lattices\" are realized in the six-dimensional heterotic/F-theory compactifications. In this paper, we focus on non-Cartan MW lattices that are torsion free and whose associated singularity lattices are sublattices of $A_7$. For the heterotic string compactification, a non-Cartan MW lattice yields an instanton gauge group $H$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08001","kind":"arxiv","version":2},"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":"2026-05-17T23:47:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LduUA+0EKRNLWq4McQlVwYjzXM1REId5QiQIF/HPo5XAA6Q/dAQ9o2smLwicidDWh3QBnbufQcoWzgehYa2YAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:21:57.794983Z"},"content_sha256":"c26de4c273955691af5ffd249b411a6d4ab3a35bbe7c543ac1bd58928224baa9","schema_version":"1.0","event_id":"sha256:c26de4c273955691af5ffd249b411a6d4ab3a35bbe7c543ac1bd58928224baa9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SANUYZHXIBPDT34B5O7ZGYEXJ/bundle.json","state_url":"https://pith.science/pith/7SANUYZHXIBPDT34B5O7ZGYEXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SANUYZHXIBPDT34B5O7ZGYEXJ/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":"2026-05-28T06:21:57Z","links":{"resolver":"https://pith.science/pith/7SANUYZHXIBPDT34B5O7ZGYEXJ","bundle":"https://pith.science/pith/7SANUYZHXIBPDT34B5O7ZGYEXJ/bundle.json","state":"https://pith.science/pith/7SANUYZHXIBPDT34B5O7ZGYEXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SANUYZHXIBPDT34B5O7ZGYEXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7SANUYZHXIBPDT34B5O7ZGYEXJ","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":"abe2386edc661148557059a978ea618ed4969088ab4232d51ace8ba2e7c4981c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-24T04:22:15Z","title_canon_sha256":"900b08d9a782c5bbd848d50b6df34f84dd059b93946abd65512930692ce72749"},"schema_version":"1.0","source":{"id":"1808.08001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08001","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08001v2","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08001","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"pith_short_12","alias_value":"7SANUYZHXIBP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7SANUYZHXIBPDT34","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7SANUYZH","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:c26de4c273955691af5ffd249b411a6d4ab3a35bbe7c543ac1bd58928224baa9","target":"graph","created_at":"2026-05-17T23:47:30Z","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 Mordell-Weil lattices (MW lattices) associated to rational elliptic surfaces are classified into 74 types. Among them, there are cases in which the MW lattice is none of the weight lattices of simple Lie algebras or direct sums thereof. We study how such \"non-Cartan MW lattices\" are realized in the six-dimensional heterotic/F-theory compactifications. In this paper, we focus on non-Cartan MW lattices that are torsion free and whose associated singularity lattices are sublattices of $A_7$. For the heterotic string compactification, a non-Cartan MW lattice yields an instanton gauge group $H$","authors_text":"Kurume College), Shun'ya Mizoguchi (KEK, Taro Tani (NIT, Tsukuba), Tsukuba & Sokendai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-24T04:22:15Z","title":"Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08001","kind":"arxiv","version":2},"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":"sha256:29446e717058f0e41f808fa0f1665a7d08e0e7177c7a1e1a292000359f153d50","target":"record","created_at":"2026-05-17T23:47:30Z","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":"abe2386edc661148557059a978ea618ed4969088ab4232d51ace8ba2e7c4981c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-24T04:22:15Z","title_canon_sha256":"900b08d9a782c5bbd848d50b6df34f84dd059b93946abd65512930692ce72749"},"schema_version":"1.0","source":{"id":"1808.08001","kind":"arxiv","version":2}},"canonical_sha256":"fc80da6327ba02f1cf7c0f5dfc9b04ba65bcdbee401ec40e0191d12372ed8eb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc80da6327ba02f1cf7c0f5dfc9b04ba65bcdbee401ec40e0191d12372ed8eb0","first_computed_at":"2026-05-17T23:47:30.487325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:30.487325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zZDY1RCwF/x4Yk1LfGYyYRQDHCYP8UzqyZagk57urmHh2N5iMYe5Vl53v3jmEM96Bl+EJXmHYZcCV7rkD4SnCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:30.487778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29446e717058f0e41f808fa0f1665a7d08e0e7177c7a1e1a292000359f153d50","sha256:c26de4c273955691af5ffd249b411a6d4ab3a35bbe7c543ac1bd58928224baa9"],"state_sha256":"7200396f5e4f604bb61f35fd778728685f71decf5d78053222ac5d44cb2402f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N8oyGsDn8eqDY21xsFINlbavPVjvsvF6zM/EH4c5EH2f507oyAtXdC+vOSh/uOjVUL4uPlMbWePBdJIcLmgqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:21:57.796898Z","bundle_sha256":"227c54bfb368c835d9c6e3cfdba6e86de82577686b041e2d98b70e0eca88f29d"}}