{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OTU3B2WITKDLK2CEZNR32D22GC","short_pith_number":"pith:OTU3B2WI","canonical_record":{"source":{"id":"1511.06912","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-21T17:59:00Z","cross_cats_sorted":[],"title_canon_sha256":"c555cdd04cb33719a0a911a99835bc7a5a80ed1170c2dcc97e3475658497c59a","abstract_canon_sha256":"8ff7309dc812d25c48a2683164d97c9f2be0da46fedf727f4bc77d44ff2482c2"},"schema_version":"1.0"},"canonical_sha256":"74e9b0eac89a86b56844cb63bd0f5a30947cc515f6ef20a61ff119c7546d7571","source":{"kind":"arxiv","id":"1511.06912","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06912","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06912v4","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06912","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"OTU3B2WITKDL","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OTU3B2WITKDLK2CE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OTU3B2WI","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OTU3B2WITKDLK2CEZNR32D22GC","target":"record","payload":{"canonical_record":{"source":{"id":"1511.06912","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-21T17:59:00Z","cross_cats_sorted":[],"title_canon_sha256":"c555cdd04cb33719a0a911a99835bc7a5a80ed1170c2dcc97e3475658497c59a","abstract_canon_sha256":"8ff7309dc812d25c48a2683164d97c9f2be0da46fedf727f4bc77d44ff2482c2"},"schema_version":"1.0"},"canonical_sha256":"74e9b0eac89a86b56844cb63bd0f5a30947cc515f6ef20a61ff119c7546d7571","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:20.273241Z","signature_b64":"ZsYScWz5qfkTb0QhPOZs5O/VIgx8Jnd4PwTqBpg3IWOk4rJqlHPO2VIRHO+OvF1wxNFNvdBKM6pQo7WGAiIZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74e9b0eac89a86b56844cb63bd0f5a30947cc515f6ef20a61ff119c7546d7571","last_reissued_at":"2026-05-18T01:19:20.272782Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:20.272782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.06912","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LzJNsn6ZlzHMo0r/VaUjdu/6xiCbKBnQHcF8HGblWjDm/l9o/hlLOhzVB/H3gAIf/6tyrURRjG7Q2IWinRNCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:24:05.352171Z"},"content_sha256":"f4d6679509cc2f3a6c35ce32ac67791f21635c2aaaaca78a3f25a95fb943423e","schema_version":"1.0","event_id":"sha256:f4d6679509cc2f3a6c35ce32ac67791f21635c2aaaaca78a3f25a95fb943423e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OTU3B2WITKDLK2CEZNR32D22GC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gauge Groups and Matter Fields on Some Models of F-theory without Section","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Yusuke Kimura","submitted_at":"2015-11-21T17:59:00Z","abstract_excerpt":"We investigate F-theory on an elliptic Calabi-Yau 4-fold without a section to the fibration. To construct an elliptic Calabi-Yau 4-fold without a section, we introduce families of elliptic K3 surfaces which do not admit a section. A product K3 $\\times$ K3, with one of the K3's chosen from these families of elliptic K3 surfaces without a section, realises an elliptic Calabi-Yau 4-fold without a section. We then compactify F-theory on such K3 $\\times$ K3's. We determine the gauge groups and matter fields which arise on 7-branes for these models of F-theory compactifications without a section. Si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06912","kind":"arxiv","version":4},"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":"2026-05-18T01:19:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9GElIrzDIX67BWMhAjqEB0G1V/xv79BvjvxJXwP1M3ZoCc+g223rBZJfw8aaZDDK05AHHampeQB/3WFo8sVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:24:05.353021Z"},"content_sha256":"a3e71273bd997e3a74a679acf54a4b8a7b683e972ce0723109e4e8aa0346e3f5","schema_version":"1.0","event_id":"sha256:a3e71273bd997e3a74a679acf54a4b8a7b683e972ce0723109e4e8aa0346e3f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OTU3B2WITKDLK2CEZNR32D22GC/bundle.json","state_url":"https://pith.science/pith/OTU3B2WITKDLK2CEZNR32D22GC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OTU3B2WITKDLK2CEZNR32D22GC/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":"2026-05-31T22:24:05Z","links":{"resolver":"https://pith.science/pith/OTU3B2WITKDLK2CEZNR32D22GC","bundle":"https://pith.science/pith/OTU3B2WITKDLK2CEZNR32D22GC/bundle.json","state":"https://pith.science/pith/OTU3B2WITKDLK2CEZNR32D22GC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OTU3B2WITKDLK2CEZNR32D22GC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OTU3B2WITKDLK2CEZNR32D22GC","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":"8ff7309dc812d25c48a2683164d97c9f2be0da46fedf727f4bc77d44ff2482c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-21T17:59:00Z","title_canon_sha256":"c555cdd04cb33719a0a911a99835bc7a5a80ed1170c2dcc97e3475658497c59a"},"schema_version":"1.0","source":{"id":"1511.06912","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06912","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06912v4","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06912","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"OTU3B2WITKDL","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OTU3B2WITKDLK2CE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OTU3B2WI","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:a3e71273bd997e3a74a679acf54a4b8a7b683e972ce0723109e4e8aa0346e3f5","target":"graph","created_at":"2026-05-18T01:19:20Z","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 investigate F-theory on an elliptic Calabi-Yau 4-fold without a section to the fibration. To construct an elliptic Calabi-Yau 4-fold without a section, we introduce families of elliptic K3 surfaces which do not admit a section. A product K3 $\\times$ K3, with one of the K3's chosen from these families of elliptic K3 surfaces without a section, realises an elliptic Calabi-Yau 4-fold without a section. We then compactify F-theory on such K3 $\\times$ K3's. We determine the gauge groups and matter fields which arise on 7-branes for these models of F-theory compactifications without a section. Si","authors_text":"Yusuke Kimura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-21T17:59:00Z","title":"Gauge Groups and Matter Fields on Some Models of F-theory without Section"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06912","kind":"arxiv","version":4},"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:f4d6679509cc2f3a6c35ce32ac67791f21635c2aaaaca78a3f25a95fb943423e","target":"record","created_at":"2026-05-18T01:19:20Z","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":"8ff7309dc812d25c48a2683164d97c9f2be0da46fedf727f4bc77d44ff2482c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-21T17:59:00Z","title_canon_sha256":"c555cdd04cb33719a0a911a99835bc7a5a80ed1170c2dcc97e3475658497c59a"},"schema_version":"1.0","source":{"id":"1511.06912","kind":"arxiv","version":4}},"canonical_sha256":"74e9b0eac89a86b56844cb63bd0f5a30947cc515f6ef20a61ff119c7546d7571","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74e9b0eac89a86b56844cb63bd0f5a30947cc515f6ef20a61ff119c7546d7571","first_computed_at":"2026-05-18T01:19:20.272782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:20.272782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZsYScWz5qfkTb0QhPOZs5O/VIgx8Jnd4PwTqBpg3IWOk4rJqlHPO2VIRHO+OvF1wxNFNvdBKM6pQo7WGAiIZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:20.273241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06912","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4d6679509cc2f3a6c35ce32ac67791f21635c2aaaaca78a3f25a95fb943423e","sha256:a3e71273bd997e3a74a679acf54a4b8a7b683e972ce0723109e4e8aa0346e3f5"],"state_sha256":"1ae75318a646f584d8059442972024e614343e010f21d9890235d0028d56a30c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a0VWPfwTBXhXWJ9q5GpufXw+uxgz7irLiE3vg2dI1MesNTDD6VuYjtCfiNTRhonJS5X0C3fQIKRk2gSy7WAYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:24:05.357449Z","bundle_sha256":"ea47d12763cc4355db9a125010895b5954840ed7ed73eb92d7d98908c4150969"}}