{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:TCI3FHACUJ332VJCOJJYKJD6M4","short_pith_number":"pith:TCI3FHAC","canonical_record":{"source":{"id":"2109.11534","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-23T17:56:41Z","cross_cats_sorted":[],"title_canon_sha256":"e6a2322a52127c2b161ef6beff63110faa0afa0d76e92ae0e533d0dd7d667840","abstract_canon_sha256":"668e310035ff32065b6eae632ee4520b78d5f11eaa15db493e93d9c62468b51a"},"schema_version":"1.0"},"canonical_sha256":"9891b29c02a277bd5522725385247e672b1ae6b194c60d3852b2b8826caf5218","source":{"kind":"arxiv","id":"2109.11534","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11534","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11534v1","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11534","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_12","alias_value":"TCI3FHACUJ33","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_16","alias_value":"TCI3FHACUJ332VJC","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_8","alias_value":"TCI3FHAC","created_at":"2026-07-05T03:16:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:TCI3FHACUJ332VJCOJJYKJD6M4","target":"record","payload":{"canonical_record":{"source":{"id":"2109.11534","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-23T17:56:41Z","cross_cats_sorted":[],"title_canon_sha256":"e6a2322a52127c2b161ef6beff63110faa0afa0d76e92ae0e533d0dd7d667840","abstract_canon_sha256":"668e310035ff32065b6eae632ee4520b78d5f11eaa15db493e93d9c62468b51a"},"schema_version":"1.0"},"canonical_sha256":"9891b29c02a277bd5522725385247e672b1ae6b194c60d3852b2b8826caf5218","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:16:58.857266Z","signature_b64":"Al+W6B4BKM2sJ4spakdFkzqtqO83ifBGRqX2YNG6lNNQKGO25qplx5QRAVVuWANONfG2rYck/wBR/ixyWQIsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9891b29c02a277bd5522725385247e672b1ae6b194c60d3852b2b8826caf5218","last_reissued_at":"2026-07-05T03:16:58.856845Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:16:58.856845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.11534","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":"2026-07-05T03:16:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43romi3FhjcRhEMe2x56uvQ21uvcDkjaVS6O30xJku5+H7maDT5RMOT1/mhZoNpxJs+aJul4RdhkrWq8NAdTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:01:45.057430Z"},"content_sha256":"c753c9c3ad181b784bff1104cbc63fbe84b27b32fe429520ab95c130bd7603e0","schema_version":"1.0","event_id":"sha256:c753c9c3ad181b784bff1104cbc63fbe84b27b32fe429520ab95c130bd7603e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:TCI3FHACUJ332VJCOJJYKJD6M4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathbb{P}^1$-fibrations in F-theory and String Dualities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"James Gray, Lara B. Anderson, Mohsen Karkheiran, Nikhil Raghuram, Paul-Konstantin Oehlmann","submitted_at":"2021-09-23T17:56:41Z","abstract_excerpt":"In this work we study F-theory compactifications on elliptically fibered Calabi-Yau n-folds which have $\\mathbb{P}^1$-fibered base manifolds. Such geometries, which we study in both 4- and 6-dimensions, are both ubiquitous within the set of Calabi-Yau manifolds and play a crucial role in heterotic/F-theory duality. We discuss the most general formulation of $\\mathbb{P}^1$-bundles of this type, as well as fibrations which degenerate at higher codimension loci. In the course of this study, we find a number of new phenomena. For example, in both 4- and 6-dimensions we find transitions whereby the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11534","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/2109.11534/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":"2026-07-05T03:16:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jX9VAweGuN6YjqOCymggztXLhFXUPsxZ61Jxv3A1NC/WMq6fr0hYqwEBG+mRDIuDvJZFQmKdqcwJHETUVC7nCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:01:45.058307Z"},"content_sha256":"a525d1d1f2d096bfddfffed120af82bf71458e863e9bd739d6ad2e66fe311ac5","schema_version":"1.0","event_id":"sha256:a525d1d1f2d096bfddfffed120af82bf71458e863e9bd739d6ad2e66fe311ac5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCI3FHACUJ332VJCOJJYKJD6M4/bundle.json","state_url":"https://pith.science/pith/TCI3FHACUJ332VJCOJJYKJD6M4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCI3FHACUJ332VJCOJJYKJD6M4/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":"2026-08-06T06:01:45Z","links":{"resolver":"https://pith.science/pith/TCI3FHACUJ332VJCOJJYKJD6M4","bundle":"https://pith.science/pith/TCI3FHACUJ332VJCOJJYKJD6M4/bundle.json","state":"https://pith.science/pith/TCI3FHACUJ332VJCOJJYKJD6M4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCI3FHACUJ332VJCOJJYKJD6M4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TCI3FHACUJ332VJCOJJYKJD6M4","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":"668e310035ff32065b6eae632ee4520b78d5f11eaa15db493e93d9c62468b51a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-23T17:56:41Z","title_canon_sha256":"e6a2322a52127c2b161ef6beff63110faa0afa0d76e92ae0e533d0dd7d667840"},"schema_version":"1.0","source":{"id":"2109.11534","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11534","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11534v1","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11534","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_12","alias_value":"TCI3FHACUJ33","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_16","alias_value":"TCI3FHACUJ332VJC","created_at":"2026-07-05T03:16:58Z"},{"alias_kind":"pith_short_8","alias_value":"TCI3FHAC","created_at":"2026-07-05T03:16:58Z"}],"graph_snapshots":[{"event_id":"sha256:a525d1d1f2d096bfddfffed120af82bf71458e863e9bd739d6ad2e66fe311ac5","target":"graph","created_at":"2026-07-05T03:16:58Z","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/2109.11534/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we study F-theory compactifications on elliptically fibered Calabi-Yau n-folds which have $\\mathbb{P}^1$-fibered base manifolds. Such geometries, which we study in both 4- and 6-dimensions, are both ubiquitous within the set of Calabi-Yau manifolds and play a crucial role in heterotic/F-theory duality. We discuss the most general formulation of $\\mathbb{P}^1$-bundles of this type, as well as fibrations which degenerate at higher codimension loci. In the course of this study, we find a number of new phenomena. For example, in both 4- and 6-dimensions we find transitions whereby the","authors_text":"James Gray, Lara B. Anderson, Mohsen Karkheiran, Nikhil Raghuram, Paul-Konstantin Oehlmann","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-23T17:56:41Z","title":"$\\mathbb{P}^1$-fibrations in F-theory and String Dualities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11534","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:c753c9c3ad181b784bff1104cbc63fbe84b27b32fe429520ab95c130bd7603e0","target":"record","created_at":"2026-07-05T03:16:58Z","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":"668e310035ff32065b6eae632ee4520b78d5f11eaa15db493e93d9c62468b51a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-23T17:56:41Z","title_canon_sha256":"e6a2322a52127c2b161ef6beff63110faa0afa0d76e92ae0e533d0dd7d667840"},"schema_version":"1.0","source":{"id":"2109.11534","kind":"arxiv","version":1}},"canonical_sha256":"9891b29c02a277bd5522725385247e672b1ae6b194c60d3852b2b8826caf5218","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9891b29c02a277bd5522725385247e672b1ae6b194c60d3852b2b8826caf5218","first_computed_at":"2026-07-05T03:16:58.856845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:16:58.856845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Al+W6B4BKM2sJ4spakdFkzqtqO83ifBGRqX2YNG6lNNQKGO25qplx5QRAVVuWANONfG2rYck/wBR/ixyWQIsDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:16:58.857266Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.11534","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c753c9c3ad181b784bff1104cbc63fbe84b27b32fe429520ab95c130bd7603e0","sha256:a525d1d1f2d096bfddfffed120af82bf71458e863e9bd739d6ad2e66fe311ac5"],"state_sha256":"8b6a6abdd12fcdb0acdfd95e8b11df78b6d4dc4f6f1302f69395dca6136a4145"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q6xF1Xl0vvfXRVA9MYHXjRzL4EWrJ/brbpWNSE9SdPBmaDKBewJDbuHg0y74p/Khu3qMuPoPLV4FSQuCoLN6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T06:01:45.064020Z","bundle_sha256":"7057491c9d527a75f8651458be645781d2b3ad81202862c3897d158273a4e8a3"}}