{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XBULE7IZRBQ52Z4L2N75AY65KO","short_pith_number":"pith:XBULE7IZ","canonical_record":{"source":{"id":"2505.04760","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-07T19:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"505eb967279d21e34ca7839d0b10dbedb23bd62208da42c41df8e58400343664","abstract_canon_sha256":"a13bd0ba1b8324d0fc47b1fc93857c50b074a4da207ea03ab6188c25dc6a21f5"},"schema_version":"1.0"},"canonical_sha256":"b868b27d198861dd678bd37fd063dd53aba65313087de1aa9f83ca03259c5d17","source":{"kind":"arxiv","id":"2505.04760","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.04760","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2505.04760v2","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04760","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"XBULE7IZRBQ5","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"XBULE7IZRBQ52Z4L","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"XBULE7IZ","created_at":"2026-07-05T11:17:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XBULE7IZRBQ52Z4L2N75AY65KO","target":"record","payload":{"canonical_record":{"source":{"id":"2505.04760","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-07T19:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"505eb967279d21e34ca7839d0b10dbedb23bd62208da42c41df8e58400343664","abstract_canon_sha256":"a13bd0ba1b8324d0fc47b1fc93857c50b074a4da207ea03ab6188c25dc6a21f5"},"schema_version":"1.0"},"canonical_sha256":"b868b27d198861dd678bd37fd063dd53aba65313087de1aa9f83ca03259c5d17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:45.202685Z","signature_b64":"jjhkkyVLe+foL0f54NXOm7cHExXx47T6hUpaGedt8/z8EX9R13tsVWY7dABXAmkpuYokqJP8mjnc/irqR8y6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b868b27d198861dd678bd37fd063dd53aba65313087de1aa9f83ca03259c5d17","last_reissued_at":"2026-07-05T11:17:45.202140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:45.202140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.04760","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":"2026-07-05T11:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VYSD4j7Mufv4fL9uEQoWticG09BTj7pdvNI1ULpr99vDiP8G47PrkPnQ5OgRA2cur9c6MnEruxhrSE/5JFmZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:12:40.496965Z"},"content_sha256":"f54d27ae2aba7de35a6700db9d465178d9f76d132ec85cde2fe96b66e7f12463","schema_version":"1.0","event_id":"sha256:f54d27ae2aba7de35a6700db9d465178d9f76d132ec85cde2fe96b66e7f12463"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XBULE7IZRBQ52Z4L2N75AY65KO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isotropic Torsors on Smooth Algebras over Pr\\\"ufer Rings","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arnab Kundu","submitted_at":"2025-05-07T19:39:38Z","abstract_excerpt":"The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of \\v{C}esnavi\\v{c}ius and Fedorov, we prove a non-noetherian analogue of this conjecture for rings $A$ that are semilocalisations of smooth schemes over valuation rings of rank one, and for reductive $A$-group schemes $G$ that are totally isotropic. Roughly speaking, such group schemes are characterised by the existence of a parabolic subgroup of their adjoint quotients. Since quasi-split groups are totally isotropic, our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04760","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.04760/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":"2026-07-05T11:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxO58nyEhWG+/z2YeIHjvLadFaBFqQf4ilbuuYVPLbJy0KNjRzHj90sEc+aZn/z/2FI8xmprnm87ejwJfPDYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:12:40.497455Z"},"content_sha256":"65663637d3ecaf7f11fe949e48c6a96f373d72b2e5782825a3144620234d3d84","schema_version":"1.0","event_id":"sha256:65663637d3ecaf7f11fe949e48c6a96f373d72b2e5782825a3144620234d3d84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBULE7IZRBQ52Z4L2N75AY65KO/bundle.json","state_url":"https://pith.science/pith/XBULE7IZRBQ52Z4L2N75AY65KO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBULE7IZRBQ52Z4L2N75AY65KO/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":"2026-08-09T05:12:40Z","links":{"resolver":"https://pith.science/pith/XBULE7IZRBQ52Z4L2N75AY65KO","bundle":"https://pith.science/pith/XBULE7IZRBQ52Z4L2N75AY65KO/bundle.json","state":"https://pith.science/pith/XBULE7IZRBQ52Z4L2N75AY65KO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBULE7IZRBQ52Z4L2N75AY65KO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XBULE7IZRBQ52Z4L2N75AY65KO","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":"a13bd0ba1b8324d0fc47b1fc93857c50b074a4da207ea03ab6188c25dc6a21f5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-07T19:39:38Z","title_canon_sha256":"505eb967279d21e34ca7839d0b10dbedb23bd62208da42c41df8e58400343664"},"schema_version":"1.0","source":{"id":"2505.04760","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.04760","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2505.04760v2","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04760","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"XBULE7IZRBQ5","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"XBULE7IZRBQ52Z4L","created_at":"2026-07-05T11:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"XBULE7IZ","created_at":"2026-07-05T11:17:45Z"}],"graph_snapshots":[{"event_id":"sha256:65663637d3ecaf7f11fe949e48c6a96f373d72b2e5782825a3144620234d3d84","target":"graph","created_at":"2026-07-05T11:17:45Z","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/2505.04760/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of \\v{C}esnavi\\v{c}ius and Fedorov, we prove a non-noetherian analogue of this conjecture for rings $A$ that are semilocalisations of smooth schemes over valuation rings of rank one, and for reductive $A$-group schemes $G$ that are totally isotropic. Roughly speaking, such group schemes are characterised by the existence of a parabolic subgroup of their adjoint quotients. Since quasi-split groups are totally isotropic, our","authors_text":"Arnab Kundu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-07T19:39:38Z","title":"Isotropic Torsors on Smooth Algebras over Pr\\\"ufer Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04760","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:f54d27ae2aba7de35a6700db9d465178d9f76d132ec85cde2fe96b66e7f12463","target":"record","created_at":"2026-07-05T11:17:45Z","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":"a13bd0ba1b8324d0fc47b1fc93857c50b074a4da207ea03ab6188c25dc6a21f5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-07T19:39:38Z","title_canon_sha256":"505eb967279d21e34ca7839d0b10dbedb23bd62208da42c41df8e58400343664"},"schema_version":"1.0","source":{"id":"2505.04760","kind":"arxiv","version":2}},"canonical_sha256":"b868b27d198861dd678bd37fd063dd53aba65313087de1aa9f83ca03259c5d17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b868b27d198861dd678bd37fd063dd53aba65313087de1aa9f83ca03259c5d17","first_computed_at":"2026-07-05T11:17:45.202140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:45.202140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jjhkkyVLe+foL0f54NXOm7cHExXx47T6hUpaGedt8/z8EX9R13tsVWY7dABXAmkpuYokqJP8mjnc/irqR8y6Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:45.202685Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.04760","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f54d27ae2aba7de35a6700db9d465178d9f76d132ec85cde2fe96b66e7f12463","sha256:65663637d3ecaf7f11fe949e48c6a96f373d72b2e5782825a3144620234d3d84"],"state_sha256":"1aa6bdf9b93e2ece95e78ff51d5d51e466814393a7b0478cd7f6b822cefe1421"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"itXJOmq+GiNAEJzqLoP6vxVoRseLT08cykp4gw5ebxFReY6QDAnStHgjtt+X7ShgIHle57tuNbqGDT0XetXiCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T05:12:40.502914Z","bundle_sha256":"5c28fa183d3a5b1b88726d1f6f78416c989de75adbf5d3c9d1ef3f1da9b51809"}}