{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MSLYYYPHRRRG3WCXJSGQC5JCFD","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":"fa36a2c40c1ef622bbbd774adf8fad428db557a9df042adf8353160bbf74854d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-08-03T09:48:19Z","title_canon_sha256":"5000ec7ec2c74ecfb557ad566ea02c2ef3876883386daa5f160743c7499f0924"},"schema_version":"1.0","source":{"id":"2608.01987","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01987","created_at":"2026-08-04T02:10:26Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01987v1","created_at":"2026-08-04T02:10:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01987","created_at":"2026-08-04T02:10:26Z"},{"alias_kind":"pith_short_12","alias_value":"MSLYYYPHRRRG","created_at":"2026-08-04T02:10:26Z"},{"alias_kind":"pith_short_16","alias_value":"MSLYYYPHRRRG3WCX","created_at":"2026-08-04T02:10:26Z"},{"alias_kind":"pith_short_8","alias_value":"MSLYYYPH","created_at":"2026-08-04T02:10:26Z"}],"graph_snapshots":[{"event_id":"sha256:abc5312abd10074842c9894edfd4de3a3b02eb4ad9b2c71f0a7468d7c0dbb27a","target":"graph","created_at":"2026-08-04T02:10:26Z","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/2608.01987/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the complete extended Euclidean scheme for pairs of monic univariate polynomials over a field of characteristic zero cannot be computed by polynomial-size, constant-depth piecewise arithmetic circuits in the select-gate model of Andrews and Wigderson. In fact, the lower bound already holds for the simpler task of outputting the complete padded list of nonzero Euclidean remainders.\n  We show that a suitable Hankel determinant can be recovered from fixed coordinates of the complete Euclidean remainder sequence on a nonempty Zariski-open set. The connection is provided by a middle p","authors_text":"Amiel Ferman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-08-03T09:48:19Z","title":"The Complete Extended Euclidean Scheme Is Not in Piecewise Arithmetic $\\mathrm{AC}^0$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01987","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":"sha256:8752093bb6aaac81f4a573b253b8fc37ac2f944f05f0cd7754cf38ecabf8d0c7","target":"record","created_at":"2026-08-04T02:10:26Z","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":"fa36a2c40c1ef622bbbd774adf8fad428db557a9df042adf8353160bbf74854d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-08-03T09:48:19Z","title_canon_sha256":"5000ec7ec2c74ecfb557ad566ea02c2ef3876883386daa5f160743c7499f0924"},"schema_version":"1.0","source":{"id":"2608.01987","kind":"arxiv","version":1}},"canonical_sha256":"64978c61e78c626dd8574c8d01752228e31cda544179c4e8bbd32ad0c98e0bb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64978c61e78c626dd8574c8d01752228e31cda544179c4e8bbd32ad0c98e0bb3","first_computed_at":"2026-08-04T02:10:26.783041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:10:26.783041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KIKIbjIShvAG4h6mLOUkLc/+hsOcK6vVB+CYJZGU2yyZiUMm0udBMkY+IlwqWxxaNrswBfaHuVmW23Zz3LQHDg==","signature_status":"signed_v1","signed_at":"2026-08-04T02:10:26.784706Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.01987","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8752093bb6aaac81f4a573b253b8fc37ac2f944f05f0cd7754cf38ecabf8d0c7","sha256:abc5312abd10074842c9894edfd4de3a3b02eb4ad9b2c71f0a7468d7c0dbb27a"],"state_sha256":"47b69bc83b0cce7bcfc3431f50401a13a55355bbcbd0f7493d5a36500ecc4935"}