{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XUNUPM4SKVWC43EKHH7PESMLJH","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":"d57dc4c7f0fdd524a9ff0772f3b4f0e260518b49182aa3f1a440f5f3b405ba6c","cross_cats_sorted":["math.AG","math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-20T12:28:52Z","title_canon_sha256":"4450ae288a8e1cd20b1bbfd5dea1d6a1012f0c22b7da5bef0b79305725e4e05a"},"schema_version":"1.0","source":{"id":"1802.07083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07083","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07083v2","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07083","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"pith_short_12","alias_value":"XUNUPM4SKVWC","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XUNUPM4SKVWC43EK","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XUNUPM4S","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:1a4ce686b582d3aa64ab906422a1545f76c5d0e57b83808480bcfcf9865cbd54","target":"graph","created_at":"2026-05-18T00:06:40Z","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":"This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of the support of such a Laurent series. As an application of this result we provide a gap theorem for Laurent series which are algebraic over the field of formal power series. We also relate these results to diophantine properties of the fields of Laurent series.","authors_text":"Fuensanta Aroca, Guillaume Rond","cross_cats":["math.AG","math.CO","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-20T12:28:52Z","title":"Support of Laurent series algebraic over the field of formal power series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07083","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:c30260acb4d436971799fc40e25f7fcc1e91f882b2b388dcae3ee67dced0b393","target":"record","created_at":"2026-05-18T00:06:40Z","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":"d57dc4c7f0fdd524a9ff0772f3b4f0e260518b49182aa3f1a440f5f3b405ba6c","cross_cats_sorted":["math.AG","math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-20T12:28:52Z","title_canon_sha256":"4450ae288a8e1cd20b1bbfd5dea1d6a1012f0c22b7da5bef0b79305725e4e05a"},"schema_version":"1.0","source":{"id":"1802.07083","kind":"arxiv","version":2}},"canonical_sha256":"bd1b47b392556c2e6c8a39fef2498b49d5492bf35ba7b6a8860807b578bc4b10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd1b47b392556c2e6c8a39fef2498b49d5492bf35ba7b6a8860807b578bc4b10","first_computed_at":"2026-05-18T00:06:40.639430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:40.639430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gz2crxldLvEenLfMbDu2nThTyeFi+RxNyQrjPdnSkTP+Pt31nzrJwKH72nYnWsk4PwQYj6O/9YWdm4wAbySiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:40.639855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c30260acb4d436971799fc40e25f7fcc1e91f882b2b388dcae3ee67dced0b393","sha256:1a4ce686b582d3aa64ab906422a1545f76c5d0e57b83808480bcfcf9865cbd54"],"state_sha256":"5e9423610750bb22f79d2ad2b8b706343b63828e56460adaadc116d8ffd76523"}