{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AVQ2NOHC5JZBR3DXYT3RELM6QH","short_pith_number":"pith:AVQ2NOHC","canonical_record":{"source":{"id":"1212.5889","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-24T10:18:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"200e326fa18ea736128441d1efbb00f82834d8329e1d2cdb9e5c58b200a49d6d","abstract_canon_sha256":"6dc942c1cee4f94a973e3e572b7fcaa1d8f27a7e7f8fda3a7f20d4b3728278b4"},"schema_version":"1.0"},"canonical_sha256":"0561a6b8e2ea7218ec77c4f7122d9e81e83ce779947a429a131e327e988ea5d7","source":{"kind":"arxiv","id":"1212.5889","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5889","created_at":"2026-05-18T03:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5889v2","created_at":"2026-05-18T03:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5889","created_at":"2026-05-18T03:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"AVQ2NOHC5JZB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AVQ2NOHC5JZBR3DX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AVQ2NOHC","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AVQ2NOHC5JZBR3DXYT3RELM6QH","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5889","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-24T10:18:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"200e326fa18ea736128441d1efbb00f82834d8329e1d2cdb9e5c58b200a49d6d","abstract_canon_sha256":"6dc942c1cee4f94a973e3e572b7fcaa1d8f27a7e7f8fda3a7f20d4b3728278b4"},"schema_version":"1.0"},"canonical_sha256":"0561a6b8e2ea7218ec77c4f7122d9e81e83ce779947a429a131e327e988ea5d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:56.659916Z","signature_b64":"33BcQTW/DGIPxiSlr8C0uPgyIVl+HxPAI7BHMAWZUHRN9slXhzHbZClYm2o8ryd1UcdQMdbFRGUfhzSc1pzsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0561a6b8e2ea7218ec77c4f7122d9e81e83ce779947a429a131e327e988ea5d7","last_reissued_at":"2026-05-18T03:19:56.659292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:56.659292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5889","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":"2026-05-18T03:19:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"okBDES3epZaEL4vg6vskOq+RmsxGnYBHWnoYqKuHDeykYVCqciw7vUlm0enMBoqdvoVe4mh/ZONTwhwr23OPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:35:38.558355Z"},"content_sha256":"4db2d214a2bd41dcb6bb218ccb815ade272bb9d8aaa79e34b634845bc7a37842","schema_version":"1.0","event_id":"sha256:4db2d214a2bd41dcb6bb218ccb815ade272bb9d8aaa79e34b634845bc7a37842"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AVQ2NOHC5JZBR3DXYT3RELM6QH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hasse principle and weak approximation for multinorm equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Cyril Demarche, Dasheng Wei","submitted_at":"2012-12-24T10:18:29Z","abstract_excerpt":"In this note, we are interested in local-global principles for multinorm equations of the form $\\prod_{i=1}^n N_{L_i /k}(z_i) = a$ where $k$ is a global field, $L_i/k$ are finite separable field extensions and $a \\in k^*$.\n  In particular, we prove a result relating weak approximation for this equation to weak approximation for some classical norm equation $N_{F/k}(w) = a$ where $F := \\bigcap_{i=1}^n L_i$. It provides a proof of a \"weak approximation\" analogue of a recent conjecture by Pollio and Rapinchuk about multinorm principle. We also provide a counterexample to the original conjecture c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5889","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":""},"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":"2026-05-18T03:19:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VlJlWnoX9z249GIySv2wN91NFjFi6rBLpEbRM5GAumsk5HpC+bmh+rOheDRKItWTtG0puI/FOpt5Vg1gV5yWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:35:38.558706Z"},"content_sha256":"2fb171d8d85701b89227db681ef4d99cbcff1270b9b6ac71f2e011e1d10ba8d4","schema_version":"1.0","event_id":"sha256:2fb171d8d85701b89227db681ef4d99cbcff1270b9b6ac71f2e011e1d10ba8d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AVQ2NOHC5JZBR3DXYT3RELM6QH/bundle.json","state_url":"https://pith.science/pith/AVQ2NOHC5JZBR3DXYT3RELM6QH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AVQ2NOHC5JZBR3DXYT3RELM6QH/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":"2026-06-22T21:35:38Z","links":{"resolver":"https://pith.science/pith/AVQ2NOHC5JZBR3DXYT3RELM6QH","bundle":"https://pith.science/pith/AVQ2NOHC5JZBR3DXYT3RELM6QH/bundle.json","state":"https://pith.science/pith/AVQ2NOHC5JZBR3DXYT3RELM6QH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AVQ2NOHC5JZBR3DXYT3RELM6QH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AVQ2NOHC5JZBR3DXYT3RELM6QH","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":"6dc942c1cee4f94a973e3e572b7fcaa1d8f27a7e7f8fda3a7f20d4b3728278b4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-24T10:18:29Z","title_canon_sha256":"200e326fa18ea736128441d1efbb00f82834d8329e1d2cdb9e5c58b200a49d6d"},"schema_version":"1.0","source":{"id":"1212.5889","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5889","created_at":"2026-05-18T03:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5889v2","created_at":"2026-05-18T03:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5889","created_at":"2026-05-18T03:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"AVQ2NOHC5JZB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AVQ2NOHC5JZBR3DX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AVQ2NOHC","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:2fb171d8d85701b89227db681ef4d99cbcff1270b9b6ac71f2e011e1d10ba8d4","target":"graph","created_at":"2026-05-18T03:19:56Z","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":"In this note, we are interested in local-global principles for multinorm equations of the form $\\prod_{i=1}^n N_{L_i /k}(z_i) = a$ where $k$ is a global field, $L_i/k$ are finite separable field extensions and $a \\in k^*$.\n  In particular, we prove a result relating weak approximation for this equation to weak approximation for some classical norm equation $N_{F/k}(w) = a$ where $F := \\bigcap_{i=1}^n L_i$. It provides a proof of a \"weak approximation\" analogue of a recent conjecture by Pollio and Rapinchuk about multinorm principle. We also provide a counterexample to the original conjecture c","authors_text":"Cyril Demarche, Dasheng Wei","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-24T10:18:29Z","title":"Hasse principle and weak approximation for multinorm equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5889","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":"sha256:4db2d214a2bd41dcb6bb218ccb815ade272bb9d8aaa79e34b634845bc7a37842","target":"record","created_at":"2026-05-18T03:19:56Z","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":"6dc942c1cee4f94a973e3e572b7fcaa1d8f27a7e7f8fda3a7f20d4b3728278b4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-24T10:18:29Z","title_canon_sha256":"200e326fa18ea736128441d1efbb00f82834d8329e1d2cdb9e5c58b200a49d6d"},"schema_version":"1.0","source":{"id":"1212.5889","kind":"arxiv","version":2}},"canonical_sha256":"0561a6b8e2ea7218ec77c4f7122d9e81e83ce779947a429a131e327e988ea5d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0561a6b8e2ea7218ec77c4f7122d9e81e83ce779947a429a131e327e988ea5d7","first_computed_at":"2026-05-18T03:19:56.659292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:56.659292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"33BcQTW/DGIPxiSlr8C0uPgyIVl+HxPAI7BHMAWZUHRN9slXhzHbZClYm2o8ryd1UcdQMdbFRGUfhzSc1pzsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:56.659916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5889","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4db2d214a2bd41dcb6bb218ccb815ade272bb9d8aaa79e34b634845bc7a37842","sha256:2fb171d8d85701b89227db681ef4d99cbcff1270b9b6ac71f2e011e1d10ba8d4"],"state_sha256":"31e380b561acfec6bf6544440a94f0b6ec27b2e4e9c304bc514b2272391f773d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Evu4LtpK5HIpsu3z6DY/lshJ8PzlpFyLj3XPb81SpbvrGkvhP3R3Kqq2POIC50ip1VAuQsXswcHia0AT3nzhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:35:38.560543Z","bundle_sha256":"77423a0b07d197480dd18f2dc1a7021453320f2b5ad00dd1807f55eb4e55be13"}}