{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NZLDGKHYETK6QG6MLELY5XIGNF","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":"c6eae7b13e55958ac240461670936efae04adbd152a722960a402ccccf14dc7b","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-08T21:08:08Z","title_canon_sha256":"e6e1dc3fe6fab189766033073a3196b14342f7759b8397637d9836a94609fa4a"},"schema_version":"1.0","source":{"id":"2112.04592","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.04592","created_at":"2026-07-05T06:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"2112.04592v1","created_at":"2026-07-05T06:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04592","created_at":"2026-07-05T06:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"NZLDGKHYETK6","created_at":"2026-07-05T06:03:52Z"},{"alias_kind":"pith_short_16","alias_value":"NZLDGKHYETK6QG6M","created_at":"2026-07-05T06:03:52Z"},{"alias_kind":"pith_short_8","alias_value":"NZLDGKHY","created_at":"2026-07-05T06:03:52Z"}],"graph_snapshots":[{"event_id":"sha256:b1dd2d7b7e104d23c7c73c8adf034cffd7bff60617b5335b35410d811a2f8f53","target":"graph","created_at":"2026-07-05T06:03:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.04592/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"One can compute the local $\\mathbb{A}^1$-degree at points with separable residue field by base changing, working rationally, and post-composing with the field trace. We show that for endomorphisms of the affine line, one can compute the local $\\mathbb{A}^1$-degree at points with inseparable residue field by taking a suitable lift of the polynomial and transferring its local degree. We also discuss the general set-up and strategy in terms of the six functor formalism. As an application, we show that trace forms of number fields are local $\\mathbb{A}^1$-degrees.","authors_text":"Stephen McKean, Thomas Brazelton","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-08T21:08:08Z","title":"Lifts, transfers, and degrees of univariate maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04592","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":"sha256:86a0082ca66798df24ae035bd9b2019780ed1ca0f63cd7418decb26058729da7","target":"record","created_at":"2026-07-05T06:03:52Z","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":"c6eae7b13e55958ac240461670936efae04adbd152a722960a402ccccf14dc7b","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-08T21:08:08Z","title_canon_sha256":"e6e1dc3fe6fab189766033073a3196b14342f7759b8397637d9836a94609fa4a"},"schema_version":"1.0","source":{"id":"2112.04592","kind":"arxiv","version":1}},"canonical_sha256":"6e563328f824d5e81bcc59178edd06695fe70d7369cfecf8c705e019970c0264","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e563328f824d5e81bcc59178edd06695fe70d7369cfecf8c705e019970c0264","first_computed_at":"2026-07-05T06:03:52.304482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:03:52.304482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ekKNvl6/uhaHfSuueX+PaAGcTV4PndoQl9GeVhjniR+nJry9n4T+DW00k+taRYrckA2s+uC+QdN20EVHuJmbDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:03:52.304833Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.04592","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86a0082ca66798df24ae035bd9b2019780ed1ca0f63cd7418decb26058729da7","sha256:b1dd2d7b7e104d23c7c73c8adf034cffd7bff60617b5335b35410d811a2f8f53"],"state_sha256":"322c623cc806904b99b5e08133441a08c8ff13dc1638c7198636bc88a73148d7"}