{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AFBGZC5YQ7WSEX6EIX5UO446NN","short_pith_number":"pith:AFBGZC5Y","canonical_record":{"source":{"id":"1401.0915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-05T17:31:53Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"cc93d7cf57855d7f533c41e527a2d52161b000d6e12d9d289dc188f3328f5513","abstract_canon_sha256":"1c20dc1a3103417aea0ea105309a1f337c84b441deb4780ddee073636963000f"},"schema_version":"1.0"},"canonical_sha256":"01426c8bb887ed225fc445fb47739e6b5236448a4db3329c084ae26582bf4a51","source":{"kind":"arxiv","id":"1401.0915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0915","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0915v1","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0915","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"AFBGZC5YQ7WS","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AFBGZC5YQ7WSEX6E","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AFBGZC5Y","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AFBGZC5YQ7WSEX6EIX5UO446NN","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-05T17:31:53Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"cc93d7cf57855d7f533c41e527a2d52161b000d6e12d9d289dc188f3328f5513","abstract_canon_sha256":"1c20dc1a3103417aea0ea105309a1f337c84b441deb4780ddee073636963000f"},"schema_version":"1.0"},"canonical_sha256":"01426c8bb887ed225fc445fb47739e6b5236448a4db3329c084ae26582bf4a51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:11.691686Z","signature_b64":"xaWf2QVfp4jCnnYDOg0MZ4VpLMskafMj5pN/rc3aEjutIsPoMDVHz0H8sWJpdos9llISXb1tvpSr7Z5bMANjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01426c8bb887ed225fc445fb47739e6b5236448a4db3329c084ae26582bf4a51","last_reissued_at":"2026-05-18T01:29:11.690959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:11.690959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0915","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":"2026-05-18T01:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufhxdOSpqiC+9xhxWg8IpJrZpK3WjdYOhx98+mUrmlvbob6PUFkAu6o8Jtrm4ClBxCYAr7Vt8MMjHESagezdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:14:00.412840Z"},"content_sha256":"9c82830e7c13158b89a028ffc63a248fcfff3f72ac0edbbb74b26a4837a89900","schema_version":"1.0","event_id":"sha256:9c82830e7c13158b89a028ffc63a248fcfff3f72ac0edbbb74b26a4837a89900"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AFBGZC5YQ7WSEX6EIX5UO446NN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Le compl\\'ementaire des puissances $n$-i\\`emes dans un corps de nombres est un ensemble diophantien","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jan Van Geel, Jean-Louis Colliot-Th\\'el\\`ene","submitted_at":"2014-01-05T17:31:53Z","abstract_excerpt":"Given a number field $k$ and a positive integer $n$, there exists an algebraic variety $X$ over $k$ and a function $f$ on $X$ whose set of values $f(X(k))$ on the set of $k$-points of $X$ is the complement in $k$ of the set of $n$-th powers. This result had been proved by B. Poonen (2009) for $n$ a power of $2$. For $n$ arbitrary, under Schinzel's hypothesis, it has been given a conditional proof by T. V\\'arilly-Alvarado and B. Viray (2012). Instead of Schinzel's hypothesis, we use \"Salberger's trick\", as developed in papers of Skorobogatov, Swinnerton-Dyer and one of the authors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0915","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":""},"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":"2026-05-18T01:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQ7JecSz4Ws9CZ76SNvNjDHcVdoH330TTGpC8YIUZIAn26HcweXcFu6T0tO7m/rN3Evaj798GAJUohjrFx9eAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:14:00.413190Z"},"content_sha256":"8655599bb6137b7d33bd180255ce070ada7a3f2801f9be6cd5508afa1a0af9bf","schema_version":"1.0","event_id":"sha256:8655599bb6137b7d33bd180255ce070ada7a3f2801f9be6cd5508afa1a0af9bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AFBGZC5YQ7WSEX6EIX5UO446NN/bundle.json","state_url":"https://pith.science/pith/AFBGZC5YQ7WSEX6EIX5UO446NN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AFBGZC5YQ7WSEX6EIX5UO446NN/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":"2026-05-31T06:14:00Z","links":{"resolver":"https://pith.science/pith/AFBGZC5YQ7WSEX6EIX5UO446NN","bundle":"https://pith.science/pith/AFBGZC5YQ7WSEX6EIX5UO446NN/bundle.json","state":"https://pith.science/pith/AFBGZC5YQ7WSEX6EIX5UO446NN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AFBGZC5YQ7WSEX6EIX5UO446NN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AFBGZC5YQ7WSEX6EIX5UO446NN","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":"1c20dc1a3103417aea0ea105309a1f337c84b441deb4780ddee073636963000f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-05T17:31:53Z","title_canon_sha256":"cc93d7cf57855d7f533c41e527a2d52161b000d6e12d9d289dc188f3328f5513"},"schema_version":"1.0","source":{"id":"1401.0915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0915","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0915v1","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0915","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"AFBGZC5YQ7WS","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AFBGZC5YQ7WSEX6E","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AFBGZC5Y","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:8655599bb6137b7d33bd180255ce070ada7a3f2801f9be6cd5508afa1a0af9bf","target":"graph","created_at":"2026-05-18T01:29:11Z","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":"Given a number field $k$ and a positive integer $n$, there exists an algebraic variety $X$ over $k$ and a function $f$ on $X$ whose set of values $f(X(k))$ on the set of $k$-points of $X$ is the complement in $k$ of the set of $n$-th powers. This result had been proved by B. Poonen (2009) for $n$ a power of $2$. For $n$ arbitrary, under Schinzel's hypothesis, it has been given a conditional proof by T. V\\'arilly-Alvarado and B. Viray (2012). Instead of Schinzel's hypothesis, we use \"Salberger's trick\", as developed in papers of Skorobogatov, Swinnerton-Dyer and one of the authors.","authors_text":"Jan Van Geel, Jean-Louis Colliot-Th\\'el\\`ene","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-05T17:31:53Z","title":"Le compl\\'ementaire des puissances $n$-i\\`emes dans un corps de nombres est un ensemble diophantien"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0915","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":"sha256:9c82830e7c13158b89a028ffc63a248fcfff3f72ac0edbbb74b26a4837a89900","target":"record","created_at":"2026-05-18T01:29:11Z","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":"1c20dc1a3103417aea0ea105309a1f337c84b441deb4780ddee073636963000f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-05T17:31:53Z","title_canon_sha256":"cc93d7cf57855d7f533c41e527a2d52161b000d6e12d9d289dc188f3328f5513"},"schema_version":"1.0","source":{"id":"1401.0915","kind":"arxiv","version":1}},"canonical_sha256":"01426c8bb887ed225fc445fb47739e6b5236448a4db3329c084ae26582bf4a51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01426c8bb887ed225fc445fb47739e6b5236448a4db3329c084ae26582bf4a51","first_computed_at":"2026-05-18T01:29:11.690959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:11.690959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xaWf2QVfp4jCnnYDOg0MZ4VpLMskafMj5pN/rc3aEjutIsPoMDVHz0H8sWJpdos9llISXb1tvpSr7Z5bMANjBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:11.691686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c82830e7c13158b89a028ffc63a248fcfff3f72ac0edbbb74b26a4837a89900","sha256:8655599bb6137b7d33bd180255ce070ada7a3f2801f9be6cd5508afa1a0af9bf"],"state_sha256":"8a213fed8a427dde738a026703af5e7af305ec416ec9eb1c3754c6eb002b0373"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/kP2ghDh96CIpUTFLUQn+QjYNSIbOejyqQe9Dv7cRDgSMGGRv4iEtn/Gr/lwW3Ebhgq4aZDYsuMHRY6Ofg/VDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:14:00.415165Z","bundle_sha256":"b0d355adc79528d66da1b2c87682336af6bfcbc1e827dfcdeabec12d5dc152aa"}}