{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XZVPGGLFK7IZNCLCGTI3FTBQKA","short_pith_number":"pith:XZVPGGLF","canonical_record":{"source":{"id":"1303.1921","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-08T09:49:19Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"cae3c3423bb9c21729420b4c1bebeec9f62fd09c6057f07ffab4045217b7e6b2","abstract_canon_sha256":"c82f5567435a52d47523c4eb1e6a3a7702c6594943cfd788448b5db40d6d6af1"},"schema_version":"1.0"},"canonical_sha256":"be6af3196557d196896234d1b2cc30500611cdf2ed7209260cc23177c6ac362e","source":{"kind":"arxiv","id":"1303.1921","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1921","created_at":"2026-05-18T00:49:25Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1921v4","created_at":"2026-05-18T00:49:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1921","created_at":"2026-05-18T00:49:25Z"},{"alias_kind":"pith_short_12","alias_value":"XZVPGGLFK7IZ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XZVPGGLFK7IZNCLC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XZVPGGLF","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XZVPGGLFK7IZNCLCGTI3FTBQKA","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1921","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-08T09:49:19Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"cae3c3423bb9c21729420b4c1bebeec9f62fd09c6057f07ffab4045217b7e6b2","abstract_canon_sha256":"c82f5567435a52d47523c4eb1e6a3a7702c6594943cfd788448b5db40d6d6af1"},"schema_version":"1.0"},"canonical_sha256":"be6af3196557d196896234d1b2cc30500611cdf2ed7209260cc23177c6ac362e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:25.440672Z","signature_b64":"flBGigiwj0GiQFFPtrutQkXgfsZwY+Akyo7CcjDxIZwIpEcO0t6A6bafLGIjTXM5nfSbL6QpTEU2eaZ3J08vBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be6af3196557d196896234d1b2cc30500611cdf2ed7209260cc23177c6ac362e","last_reissued_at":"2026-05-18T00:49:25.439942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:25.439942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1921","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ol8bhoCLPQ61Xbbfx7ZegNsVagf+sZ5xPx9pRL9VMmM0P8lGpDWDofjqVVpkkw6T7B/mKDqYUxl1ZWGMpp67DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:41:27.406621Z"},"content_sha256":"d3e199b45f5b52672062caf8b817ce783b6a415a2b5933c933d1ec6c71cf4385","schema_version":"1.0","event_id":"sha256:d3e199b45f5b52672062caf8b817ce783b6a415a2b5933c933d1ec6c71cf4385"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XZVPGGLFK7IZNCLCGTI3FTBQKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"About the algebraic closure of the field of power series in several variables in characteristic zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.AC","authors_text":"Guillaume Rond","submitted_at":"2013-03-08T09:49:19Z","abstract_excerpt":"We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and are constructed via the Newton-Puiseux method. Then we study more carefully the case of monomial valuations and we give a result generalizing the Abhyankar-Jung Theorem for monic polynomials whose discriminant is weighted homogeneous."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1921","kind":"arxiv","version":4},"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":"2026-05-18T00:49:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LNGfIbsalQU2zfG82vkD0X06hbCEuZJBZJ1JunL4wb1zd5/+2MSt30ZMspmbooI4Z0XxXAI0InwoVK09+s6wBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:41:27.407301Z"},"content_sha256":"e279fabab6b3914c18d8d0df4917507a5cec07d4da26fafcee3f3dc3843fd93d","schema_version":"1.0","event_id":"sha256:e279fabab6b3914c18d8d0df4917507a5cec07d4da26fafcee3f3dc3843fd93d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZVPGGLFK7IZNCLCGTI3FTBQKA/bundle.json","state_url":"https://pith.science/pith/XZVPGGLFK7IZNCLCGTI3FTBQKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZVPGGLFK7IZNCLCGTI3FTBQKA/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":"2026-06-08T01:41:27Z","links":{"resolver":"https://pith.science/pith/XZVPGGLFK7IZNCLCGTI3FTBQKA","bundle":"https://pith.science/pith/XZVPGGLFK7IZNCLCGTI3FTBQKA/bundle.json","state":"https://pith.science/pith/XZVPGGLFK7IZNCLCGTI3FTBQKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZVPGGLFK7IZNCLCGTI3FTBQKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XZVPGGLFK7IZNCLCGTI3FTBQKA","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":"c82f5567435a52d47523c4eb1e6a3a7702c6594943cfd788448b5db40d6d6af1","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-08T09:49:19Z","title_canon_sha256":"cae3c3423bb9c21729420b4c1bebeec9f62fd09c6057f07ffab4045217b7e6b2"},"schema_version":"1.0","source":{"id":"1303.1921","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1921","created_at":"2026-05-18T00:49:25Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1921v4","created_at":"2026-05-18T00:49:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1921","created_at":"2026-05-18T00:49:25Z"},{"alias_kind":"pith_short_12","alias_value":"XZVPGGLFK7IZ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XZVPGGLFK7IZNCLC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XZVPGGLF","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:e279fabab6b3914c18d8d0df4917507a5cec07d4da26fafcee3f3dc3843fd93d","target":"graph","created_at":"2026-05-18T00:49:25Z","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":"We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and are constructed via the Newton-Puiseux method. Then we study more carefully the case of monomial valuations and we give a result generalizing the Abhyankar-Jung Theorem for monic polynomials whose discriminant is weighted homogeneous.","authors_text":"Guillaume Rond","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-08T09:49:19Z","title":"About the algebraic closure of the field of power series in several variables in characteristic zero"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1921","kind":"arxiv","version":4},"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:d3e199b45f5b52672062caf8b817ce783b6a415a2b5933c933d1ec6c71cf4385","target":"record","created_at":"2026-05-18T00:49:25Z","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":"c82f5567435a52d47523c4eb1e6a3a7702c6594943cfd788448b5db40d6d6af1","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-03-08T09:49:19Z","title_canon_sha256":"cae3c3423bb9c21729420b4c1bebeec9f62fd09c6057f07ffab4045217b7e6b2"},"schema_version":"1.0","source":{"id":"1303.1921","kind":"arxiv","version":4}},"canonical_sha256":"be6af3196557d196896234d1b2cc30500611cdf2ed7209260cc23177c6ac362e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be6af3196557d196896234d1b2cc30500611cdf2ed7209260cc23177c6ac362e","first_computed_at":"2026-05-18T00:49:25.439942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:25.439942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"flBGigiwj0GiQFFPtrutQkXgfsZwY+Akyo7CcjDxIZwIpEcO0t6A6bafLGIjTXM5nfSbL6QpTEU2eaZ3J08vBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:25.440672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1921","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3e199b45f5b52672062caf8b817ce783b6a415a2b5933c933d1ec6c71cf4385","sha256:e279fabab6b3914c18d8d0df4917507a5cec07d4da26fafcee3f3dc3843fd93d"],"state_sha256":"ed5c493080fd4a8952a0fe9b92da9231663166ba964cc0c09f6bc206d72e8479"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lEntm0IpoST9EugLonTUWxPMRT8BnfNya7I6aK2wFbKZtxXK1WAv9U+G5xqPuqA6+f5TwUXeDkId0y+N6h+OAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:41:27.411228Z","bundle_sha256":"4d1636d58f1f14fffd24674606d169d2b3befe080221c7ecf552e47d141f2f80"}}