{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZMZALAHPZHWUEG2LUDYRH3B4YY","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":"dbcd89b9667e4bef8fba0ae853dbdb7ea660dce71fffc7e4fb888125b9ca4fc1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-12-04T17:37:07Z","title_canon_sha256":"c06acde5dd18b7dd5b1e797b9cc2bc8314ae6b2f99bc3a9af406ab222aed676f"},"schema_version":"1.0","source":{"id":"2512.05023","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.05023","created_at":"2026-06-12T01:09:17Z"},{"alias_kind":"arxiv_version","alias_value":"2512.05023v2","created_at":"2026-06-12T01:09:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.05023","created_at":"2026-06-12T01:09:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZMZALAHPZHWU","created_at":"2026-06-12T01:09:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZMZALAHPZHWUEG2L","created_at":"2026-06-12T01:09:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZMZALAHP","created_at":"2026-06-12T01:09:17Z"}],"graph_snapshots":[{"event_id":"sha256:c65be1440d0abc2d40ca1053221064dc36f93d701738ddd6a0aa633dc834478c","target":"graph","created_at":"2026-06-12T01:09:17Z","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/2512.05023/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify the inertial Weil-Deligne types arising from elliptic curves over all finite extensions $F/\\mathbb Q_p$. Based on this classification, we give a fully explicit description of the types and implement an algorithm that computes all inertial types of elliptic curves defined over a given $F$. As an application, we determine all inertial types arising from elliptic curves over any extension $F/\\mathbb Q_p$ of degree at most 3.","authors_text":"Enric Florit, Jose Castro-Moreno, Nuno Freitas","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-12-04T17:37:07Z","title":"On inertial types of elliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.05023","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:c291f1fcc1428c2dd601544043969f6e18bc05ae693f80c86eaf304e9107efbc","target":"record","created_at":"2026-06-12T01:09:17Z","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":"dbcd89b9667e4bef8fba0ae853dbdb7ea660dce71fffc7e4fb888125b9ca4fc1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-12-04T17:37:07Z","title_canon_sha256":"c06acde5dd18b7dd5b1e797b9cc2bc8314ae6b2f99bc3a9af406ab222aed676f"},"schema_version":"1.0","source":{"id":"2512.05023","kind":"arxiv","version":2}},"canonical_sha256":"cb320580efc9ed421b4ba0f113ec3cc61fd0f2d620e530756013a1c593975096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb320580efc9ed421b4ba0f113ec3cc61fd0f2d620e530756013a1c593975096","first_computed_at":"2026-06-12T01:09:17.403878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:17.403878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6nNHkatOK1+TfoQwPuK4q2C7y8AOwQZHJYhAc/Oa0kCeSX3Zsn6VSbs1fd1jqNlOTGT2lK1/bXvwgUiGQuOrBQ==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:17.404699Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.05023","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c291f1fcc1428c2dd601544043969f6e18bc05ae693f80c86eaf304e9107efbc","sha256:c65be1440d0abc2d40ca1053221064dc36f93d701738ddd6a0aa633dc834478c"],"state_sha256":"bee3f87fe9c3faa82a97a65e8eebdabc7661febfbfe39bd70fe04ee518cf6bc1"}