{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PBCL33MAYCJA55GLXW2NBP6EWJ","short_pith_number":"pith:PBCL33MA","canonical_record":{"source":{"id":"1305.0756","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-03T15:49:46Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0298d3230e64664c14652706d833ab65ca3044d16723047e70a9f453cd78ad83","abstract_canon_sha256":"2dd3b391d3ed6dd7439aeb76f5f79b396239cda7a035e3fbc52a294454f99180"},"schema_version":"1.0"},"canonical_sha256":"7844bded80c0920ef4cbbdb4d0bfc4b24a08a72b09595e89ff4f515405b22c7c","source":{"kind":"arxiv","id":"1305.0756","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0756","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0756v3","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0756","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"PBCL33MAYCJA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PBCL33MAYCJA55GL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PBCL33MA","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PBCL33MAYCJA55GLXW2NBP6EWJ","target":"record","payload":{"canonical_record":{"source":{"id":"1305.0756","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-03T15:49:46Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0298d3230e64664c14652706d833ab65ca3044d16723047e70a9f453cd78ad83","abstract_canon_sha256":"2dd3b391d3ed6dd7439aeb76f5f79b396239cda7a035e3fbc52a294454f99180"},"schema_version":"1.0"},"canonical_sha256":"7844bded80c0920ef4cbbdb4d0bfc4b24a08a72b09595e89ff4f515405b22c7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.553306Z","signature_b64":"MLGHsxXRvErtJAQ1YB5hhqG+yvISghQeXU9xh6AweBUgom3FMZ4C4Ertxbpr7enPS+xvHQnywEyZzf9ozi4sCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7844bded80c0920ef4cbbdb4d0bfc4b24a08a72b09595e89ff4f515405b22c7c","last_reissued_at":"2026-05-17T23:53:17.552624Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.552624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.0756","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dC2lzZ4Ty5lvUz2SH88VVNG51l+U2E+AyYgpB6xZ3OZUlnhdKISHhuvC5s28m16Fa1jGN8CHyJl/tTlR1a+7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:00:49.349800Z"},"content_sha256":"aa386a98d6b136803c7e6ecfa2fe4e0f2ad3c09527593b9996accb67fa3b7a0f","schema_version":"1.0","event_id":"sha256:aa386a98d6b136803c7e6ecfa2fe4e0f2ad3c09527593b9996accb67fa3b7a0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PBCL33MAYCJA55GLXW2NBP6EWJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Principes locaux-globaux pour certaines fibrations en torseurs sous un tore","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Arne Smeets","submitted_at":"2013-05-03T15:49:46Z","abstract_excerpt":"Let $k$ be a number field and let $T$ be a $k$-torus. Consider a fibration in torsors under $T$, i.e. a morphism $f: X \\to \\mathbb{P}^1_k$ from a smooth, projective $k$-variety $X$ to $\\mathbb{P}^1_k$ such that the generic fibre $X_\\eta \\to \\eta$ is a smooth compactification of a principal homogeneous space under $T \\times_k \\eta$.\n  We study the Brauer-Manin obstruction to the Hasse principle and weak approximation for $X$, under Schinzel's hypothesis, thereby generalizing recent work of Wei. Our results are unconditional if $k = \\mathbb{Q}$ and the non-split fibres of $f$ are defined over $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0756","kind":"arxiv","version":3},"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":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nGU/6b7/prqKCy3TKtXHJr3afQaBYxAnJQ+ztFdeEv804hEEvQBD/IVZQU0PWDj1RuKKMYbrGAfYAu45bcG0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:00:49.350140Z"},"content_sha256":"b6b643327316d803a0dc8057ea035aee63e69ed53877f5c2fd1398d518229079","schema_version":"1.0","event_id":"sha256:b6b643327316d803a0dc8057ea035aee63e69ed53877f5c2fd1398d518229079"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBCL33MAYCJA55GLXW2NBP6EWJ/bundle.json","state_url":"https://pith.science/pith/PBCL33MAYCJA55GLXW2NBP6EWJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBCL33MAYCJA55GLXW2NBP6EWJ/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":"2026-06-23T00:00:49Z","links":{"resolver":"https://pith.science/pith/PBCL33MAYCJA55GLXW2NBP6EWJ","bundle":"https://pith.science/pith/PBCL33MAYCJA55GLXW2NBP6EWJ/bundle.json","state":"https://pith.science/pith/PBCL33MAYCJA55GLXW2NBP6EWJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBCL33MAYCJA55GLXW2NBP6EWJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PBCL33MAYCJA55GLXW2NBP6EWJ","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":"2dd3b391d3ed6dd7439aeb76f5f79b396239cda7a035e3fbc52a294454f99180","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-03T15:49:46Z","title_canon_sha256":"0298d3230e64664c14652706d833ab65ca3044d16723047e70a9f453cd78ad83"},"schema_version":"1.0","source":{"id":"1305.0756","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0756","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0756v3","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0756","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"PBCL33MAYCJA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PBCL33MAYCJA55GL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PBCL33MA","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:b6b643327316d803a0dc8057ea035aee63e69ed53877f5c2fd1398d518229079","target":"graph","created_at":"2026-05-17T23:53:17Z","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":"Let $k$ be a number field and let $T$ be a $k$-torus. Consider a fibration in torsors under $T$, i.e. a morphism $f: X \\to \\mathbb{P}^1_k$ from a smooth, projective $k$-variety $X$ to $\\mathbb{P}^1_k$ such that the generic fibre $X_\\eta \\to \\eta$ is a smooth compactification of a principal homogeneous space under $T \\times_k \\eta$.\n  We study the Brauer-Manin obstruction to the Hasse principle and weak approximation for $X$, under Schinzel's hypothesis, thereby generalizing recent work of Wei. Our results are unconditional if $k = \\mathbb{Q}$ and the non-split fibres of $f$ are defined over $\\","authors_text":"Arne Smeets","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-03T15:49:46Z","title":"Principes locaux-globaux pour certaines fibrations en torseurs sous un tore"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0756","kind":"arxiv","version":3},"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:aa386a98d6b136803c7e6ecfa2fe4e0f2ad3c09527593b9996accb67fa3b7a0f","target":"record","created_at":"2026-05-17T23:53:17Z","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":"2dd3b391d3ed6dd7439aeb76f5f79b396239cda7a035e3fbc52a294454f99180","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-03T15:49:46Z","title_canon_sha256":"0298d3230e64664c14652706d833ab65ca3044d16723047e70a9f453cd78ad83"},"schema_version":"1.0","source":{"id":"1305.0756","kind":"arxiv","version":3}},"canonical_sha256":"7844bded80c0920ef4cbbdb4d0bfc4b24a08a72b09595e89ff4f515405b22c7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7844bded80c0920ef4cbbdb4d0bfc4b24a08a72b09595e89ff4f515405b22c7c","first_computed_at":"2026-05-17T23:53:17.552624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:17.552624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MLGHsxXRvErtJAQ1YB5hhqG+yvISghQeXU9xh6AweBUgom3FMZ4C4Ertxbpr7enPS+xvHQnywEyZzf9ozi4sCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:17.553306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0756","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa386a98d6b136803c7e6ecfa2fe4e0f2ad3c09527593b9996accb67fa3b7a0f","sha256:b6b643327316d803a0dc8057ea035aee63e69ed53877f5c2fd1398d518229079"],"state_sha256":"fdb83c41d3a73c75ea805b96701839cedfd434625ed16e8f4d6b9979dc62ba03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xqt9NKdCeXIarMPQ9jEl9YyW/tjFzJ3V+EqFMPV0R/pX14vg8lBpoalMrbpMWSxEyHHNiCgDdTBgquPOjRxDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:00:49.352010Z","bundle_sha256":"cb82c14e9095bffbebb9146ed73b1acceaef4282557ecbd18af541af0b487283"}}