{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4MVNINMRKPAJEKPJFXGOKECKIO","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":"f766506872472ca2f686390478deeffe47c1a11c7e2395c944ef37e181a2fadf","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-02-20T12:25:20Z","title_canon_sha256":"6cffca4b338bb68e527c8e59900a4e59a030bdadf0693643d80daed73c4bfb23"},"schema_version":"1.0","source":{"id":"1202.4301","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4301","created_at":"2026-05-18T04:01:51Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4301v1","created_at":"2026-05-18T04:01:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4301","created_at":"2026-05-18T04:01:51Z"},{"alias_kind":"pith_short_12","alias_value":"4MVNINMRKPAJ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4MVNINMRKPAJEKPJ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4MVNINMR","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:585ae7596809952ef10ffbfb21ff58cb67022985e335848a1cc82fa7ba992622","target":"graph","created_at":"2026-05-18T04:01:51Z","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":"A set of multivariate polynomials, over a field of zero or large characteristic, can be tested for algebraic independence by the well-known Jacobian criterion. For fields of other characteristic p>0, there is no analogous characterization known. In this paper we give the first such criterion. Essentially, it boils down to a non-degeneracy condition on a lift of the Jacobian polynomial over (an unramified extension of) the ring of p-adic integers.\n  Our proof builds on the de Rham-Witt complex, which was invented by Illusie (1979) for crystalline cohomology computations, and we deduce a natural","authors_text":"Johannes Mittmann, Nitin Saxena, Peter Scheiblechner","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-02-20T12:25:20Z","title":"Algebraic Independence in Positive Characteristic -- A p-Adic Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4301","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":"sha256:8d695c5dd79c662ef9adf8a204d9dd86614b0f9c7174748034c5649861969e17","target":"record","created_at":"2026-05-18T04:01:51Z","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":"f766506872472ca2f686390478deeffe47c1a11c7e2395c944ef37e181a2fadf","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-02-20T12:25:20Z","title_canon_sha256":"6cffca4b338bb68e527c8e59900a4e59a030bdadf0693643d80daed73c4bfb23"},"schema_version":"1.0","source":{"id":"1202.4301","kind":"arxiv","version":1}},"canonical_sha256":"e32ad4359153c09229e92dcce5104a4395e4032dd9bc5366d1a81ffd97ff3663","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e32ad4359153c09229e92dcce5104a4395e4032dd9bc5366d1a81ffd97ff3663","first_computed_at":"2026-05-18T04:01:51.831574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:51.831574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tna/FnL1C2pAn4+j4GG7dicPsdaDfN9+F6GovnOomyFRbcFNhFKbaYCtOb1zDkQmSYwiUJhRCc8YH0ne6psFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:51.832018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4301","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d695c5dd79c662ef9adf8a204d9dd86614b0f9c7174748034c5649861969e17","sha256:585ae7596809952ef10ffbfb21ff58cb67022985e335848a1cc82fa7ba992622"],"state_sha256":"db8fb0a20d511e4800f4db3629fbc6978f4549b78d378c55a1986c92e8013d86"}