{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W2QUWRHFEKGXT6MOFE56PVRBU7","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":"729825f6d3b9447c237308a23d0232c8a98b89d09edca782ac3746862d8f3eb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-29T16:26:04Z","title_canon_sha256":"d4ea305569218c8e9f9ec7d04c06c266d019e6e16487b4761b4769ae2b06d86a"},"schema_version":"1.0","source":{"id":"1405.7608","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7608","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7608v3","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7608","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"W2QUWRHFEKGX","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2QUWRHFEKGXT6MO","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2QUWRHF","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:b70645b40d833d5803be434cd3840be240aba06d862bd4d1749051ae4a93b0c9","target":"graph","created_at":"2026-05-18T02:31:02Z","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":"Let $p$ be prime. Let $L/K$ be a finite, totally ramified, purely inseparable extension of local fields, $\\left[ L:K\\right] =p^{n},\\;n\\geq2.$ It is known that $L/K$ is Hopf Galois for numerous Hopf algebras $H,$ each of which can act on the extension in numerous ways. For a certain collection of such $H$ we construct \"Hopf Galois scaffolds\" which allow us to obtain a Hopf analogue to the Normal Basis Theorem for $L/K.$ The existence of a scaffold structure depends on the chosen action of $H$ on $L.$ We apply the theory of scaffolds to describe when the fractional ideals of $L$ are free over th","authors_text":"Alan Koch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-29T16:26:04Z","title":"Scaffolds and integral Hopf Galois module structure on purely inseparable extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7608","kind":"arxiv","version":3},"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":"sha256:8c94be6af445999a02400fa1e2fd4acf38f0fd88df7f6f064c40077e30f9d828","target":"record","created_at":"2026-05-18T02:31:02Z","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":"729825f6d3b9447c237308a23d0232c8a98b89d09edca782ac3746862d8f3eb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-29T16:26:04Z","title_canon_sha256":"d4ea305569218c8e9f9ec7d04c06c266d019e6e16487b4761b4769ae2b06d86a"},"schema_version":"1.0","source":{"id":"1405.7608","kind":"arxiv","version":3}},"canonical_sha256":"b6a14b44e5228d79f98e293be7d621a7d8704b728a527c403a2c89bc8f0bb447","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6a14b44e5228d79f98e293be7d621a7d8704b728a527c403a2c89bc8f0bb447","first_computed_at":"2026-05-18T02:31:02.222658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:02.222658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"78BGwN7K4Irts9lSlhHiZN2j/0Hod6sT7+M+CIrXWerBSNzqgf8Ek9OcyfPII4yvQRFxMfKPpmw/Eoa/1hO5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:02.223108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7608","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c94be6af445999a02400fa1e2fd4acf38f0fd88df7f6f064c40077e30f9d828","sha256:b70645b40d833d5803be434cd3840be240aba06d862bd4d1749051ae4a93b0c9"],"state_sha256":"87a693dc0ba61f99a0e3a8d13023ec9bddb15a0f42be03f9de5cafa222b12169"}