{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:H5WW7ZOX3VKDZMXOLNH2MC3RMK","short_pith_number":"pith:H5WW7ZOX","canonical_record":{"source":{"id":"2212.11915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T17:55:38Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"804007532c1d0109cc3c6c65569153ea464a6c1bc52848cd782395ceed0b0606","abstract_canon_sha256":"078c36fcc66d482ad6b0666eafe66005d307d19786b1699e4728b11e52c108af"},"schema_version":"1.0"},"canonical_sha256":"3f6d6fe5d7dd543cb2ee5b4fa60b7162b4ae709cdf16e832b2f781ba8538f6a9","source":{"kind":"arxiv","id":"2212.11915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.11915","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"2212.11915v1","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11915","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"H5WW7ZOX3VKD","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"pith_short_16","alias_value":"H5WW7ZOX3VKDZMXO","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"pith_short_8","alias_value":"H5WW7ZOX","created_at":"2026-07-05T05:27:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:H5WW7ZOX3VKDZMXOLNH2MC3RMK","target":"record","payload":{"canonical_record":{"source":{"id":"2212.11915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T17:55:38Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"804007532c1d0109cc3c6c65569153ea464a6c1bc52848cd782395ceed0b0606","abstract_canon_sha256":"078c36fcc66d482ad6b0666eafe66005d307d19786b1699e4728b11e52c108af"},"schema_version":"1.0"},"canonical_sha256":"3f6d6fe5d7dd543cb2ee5b4fa60b7162b4ae709cdf16e832b2f781ba8538f6a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:27:44.681494Z","signature_b64":"RreWRskB9E8Vm8F0eUnB0kot2FamYB0YTLCKO6q9UEMTjE4A72orgLHMZ+WqAa1itjBIkiIP0dXOJwKt5Uz6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f6d6fe5d7dd543cb2ee5b4fa60b7162b4ae709cdf16e832b2f781ba8538f6a9","last_reissued_at":"2026-07-05T05:27:44.681083Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:27:44.681083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.11915","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":"2026-07-05T05:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WBU43PuG0fNEbRKyylIjqwuNovkgr342RcDsi6wlv9d++GeI0HWq6eF7lV7cpcmKWYtCAp0O34LyC+s0Kux7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T00:44:58.179228Z"},"content_sha256":"50f691d3da2cd398a21131ee39e4b41f6409f6397ab8c29d8573e7da71cfef47","schema_version":"1.0","event_id":"sha256:50f691d3da2cd398a21131ee39e4b41f6409f6397ab8c29d8573e7da71cfef47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:H5WW7ZOX3VKDZMXOLNH2MC3RMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Bounds on the 1-Form Gauge Sector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Paul-Konstantin Oehlmann, Seung-Joo Lee","submitted_at":"2022-12-22T17:55:38Z","abstract_excerpt":"We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\\mathbb{Z}_m$ and in particular demands each cyclic factor to obey $m\\leq 6$. Our bounds correspond to the universal geometric constraints on the torsion subgroup of the Mordell-Weil group of elliptic Calabi-Yau three-folds. For any F-theory vacua with at least one tensor multiplet, we derive the constraints from the $\\mathbb{P}^1$ fibration structure of the base two-fold and identify thei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11915","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.11915/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AaFU0mZSZnhOMVm1qeKvuT6n/J8LGtcWADAw3yyNJHxkdpSqGXcgaVA0se+NRQMYMvS5b3Q00qUFLFM9P3JRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T00:44:58.180301Z"},"content_sha256":"30ceedeb605335bbb711629a00689c238ca58c6a72ea43152f0ceb11f0cbb4b1","schema_version":"1.0","event_id":"sha256:30ceedeb605335bbb711629a00689c238ca58c6a72ea43152f0ceb11f0cbb4b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/bundle.json","state_url":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/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":"2026-08-18T00:44:58Z","links":{"resolver":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK","bundle":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/bundle.json","state":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:H5WW7ZOX3VKDZMXOLNH2MC3RMK","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":"078c36fcc66d482ad6b0666eafe66005d307d19786b1699e4728b11e52c108af","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T17:55:38Z","title_canon_sha256":"804007532c1d0109cc3c6c65569153ea464a6c1bc52848cd782395ceed0b0606"},"schema_version":"1.0","source":{"id":"2212.11915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.11915","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"2212.11915v1","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11915","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"H5WW7ZOX3VKD","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"pith_short_16","alias_value":"H5WW7ZOX3VKDZMXO","created_at":"2026-07-05T05:27:44Z"},{"alias_kind":"pith_short_8","alias_value":"H5WW7ZOX","created_at":"2026-07-05T05:27:44Z"}],"graph_snapshots":[{"event_id":"sha256:30ceedeb605335bbb711629a00689c238ca58c6a72ea43152f0ceb11f0cbb4b1","target":"graph","created_at":"2026-07-05T05:27:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.11915/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\\mathbb{Z}_m$ and in particular demands each cyclic factor to obey $m\\leq 6$. Our bounds correspond to the universal geometric constraints on the torsion subgroup of the Mordell-Weil group of elliptic Calabi-Yau three-folds. For any F-theory vacua with at least one tensor multiplet, we derive the constraints from the $\\mathbb{P}^1$ fibration structure of the base two-fold and identify thei","authors_text":"Paul-Konstantin Oehlmann, Seung-Joo Lee","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T17:55:38Z","title":"Geometric Bounds on the 1-Form Gauge Sector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11915","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":"sha256:50f691d3da2cd398a21131ee39e4b41f6409f6397ab8c29d8573e7da71cfef47","target":"record","created_at":"2026-07-05T05:27:44Z","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":"078c36fcc66d482ad6b0666eafe66005d307d19786b1699e4728b11e52c108af","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T17:55:38Z","title_canon_sha256":"804007532c1d0109cc3c6c65569153ea464a6c1bc52848cd782395ceed0b0606"},"schema_version":"1.0","source":{"id":"2212.11915","kind":"arxiv","version":1}},"canonical_sha256":"3f6d6fe5d7dd543cb2ee5b4fa60b7162b4ae709cdf16e832b2f781ba8538f6a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f6d6fe5d7dd543cb2ee5b4fa60b7162b4ae709cdf16e832b2f781ba8538f6a9","first_computed_at":"2026-07-05T05:27:44.681083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:27:44.681083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RreWRskB9E8Vm8F0eUnB0kot2FamYB0YTLCKO6q9UEMTjE4A72orgLHMZ+WqAa1itjBIkiIP0dXOJwKt5Uz6Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:27:44.681494Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.11915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50f691d3da2cd398a21131ee39e4b41f6409f6397ab8c29d8573e7da71cfef47","sha256:30ceedeb605335bbb711629a00689c238ca58c6a72ea43152f0ceb11f0cbb4b1"],"state_sha256":"d3c700f99d32971ff294e1efc49f40ffeb80ef1c8396c6de6f11fd85fcde1e83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4N6L92FNL4fT9esAEDG0MesnVrH4Ll1oogTONfSyQq5wxlqRmGXgU2xY4IpA+L2TJ5R6NXD5lSrCy+NcGpYhDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T00:44:58.186355Z","bundle_sha256":"4768b23f85c438dc3fdf07bff12037ab4f844b2da362761666364ab62ab20055"}}