{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BCDNRYV2WDWCUVZ25CBOBH4YYG","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":"6e467c21ce05ad70c6fc74a277855814cf9ca82f3132fb12142685a2ba1cbf29","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-09T21:26:38Z","title_canon_sha256":"5b87a3edb2fefc053261bebf8437d20edca422021fbb278edd7be8e7546aa842"},"schema_version":"1.0","source":{"id":"2606.11460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11460","created_at":"2026-06-11T01:09:49Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11460v1","created_at":"2026-06-11T01:09:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11460","created_at":"2026-06-11T01:09:49Z"},{"alias_kind":"pith_short_12","alias_value":"BCDNRYV2WDWC","created_at":"2026-06-11T01:09:49Z"},{"alias_kind":"pith_short_16","alias_value":"BCDNRYV2WDWCUVZ2","created_at":"2026-06-11T01:09:49Z"},{"alias_kind":"pith_short_8","alias_value":"BCDNRYV2","created_at":"2026-06-11T01:09:49Z"}],"graph_snapshots":[{"event_id":"sha256:9511ec21a8465124e402ef4eafe02ad51d9086f785299669db49114309fdad86","target":"graph","created_at":"2026-06-11T01:09:49Z","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/2606.11460/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this note is to present a simple strategy to answer negatively a decomposition question on tori posed by Colliot-Th\\'el\\`ene and Sansuc in the article \\textit{Principal Homogeneous Spaces under Flasque Tori: Applications} of 1987. We then deduce a torus $T$ over $\\mathbb{Q}$ and a prime number $p$ such that $T(\\mathbb{Z}_p)\\,T(\\mathbb{Q})\\not=T(\\mathbb{Q}_p)$, where $T(\\mathbb{Z}_p)$ denotes the maximal compact subgroup of $T(\\mathbb{Q}_p)$.","authors_text":"Anis Zidani","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-09T21:26:38Z","title":"Answer to a decomposition question on tori raised by Colliot-Th\\'el\\`ene and Sansuc"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11460","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":"sha256:55b2fa66e5f0d7ec7092ecc6d2eda36e7b1c8ee10ffa4b6940051668baa9ad10","target":"record","created_at":"2026-06-11T01:09:49Z","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":"6e467c21ce05ad70c6fc74a277855814cf9ca82f3132fb12142685a2ba1cbf29","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-09T21:26:38Z","title_canon_sha256":"5b87a3edb2fefc053261bebf8437d20edca422021fbb278edd7be8e7546aa842"},"schema_version":"1.0","source":{"id":"2606.11460","kind":"arxiv","version":1}},"canonical_sha256":"0886d8e2bab0ec2a573ae882e09f98c18fbd43830286defa3d9e3d84a6624e29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0886d8e2bab0ec2a573ae882e09f98c18fbd43830286defa3d9e3d84a6624e29","first_computed_at":"2026-06-11T01:09:49.777457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:09:49.777457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UU0TeY2ptwcYOPt/dUk2uCo5XwJpHV/QeHGg+Dme1xmxX9R+egwo9kpSmKIkH4QGvVEWlW5fe6JTqtIyAEaDCw==","signature_status":"signed_v1","signed_at":"2026-06-11T01:09:49.778304Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55b2fa66e5f0d7ec7092ecc6d2eda36e7b1c8ee10ffa4b6940051668baa9ad10","sha256:9511ec21a8465124e402ef4eafe02ad51d9086f785299669db49114309fdad86"],"state_sha256":"0a98d8f2e973defae6f30fd355cabf45e7a4eb219bfd801472c8e10c4adaa5de"}