{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SLV6QXZQ4ZBKPBEYX4NBZAZ7PR","merge_version":"pith-open-graph-merge-v1","event_count":4,"valid_event_count":4,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e5b72b04270d0621ca510135a445ed4042f1b85a32e01b550c86c95d37977084","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2026-04-29T08:10:17Z","title_canon_sha256":"ecb40f45c99a91134019441f90fc3d582e6c1dccf247ee2be018a651eaa8499e"},"schema_version":"1.0","source":{"id":"2604.26400","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.26400","created_at":"2026-06-12T01:09:28Z"},{"alias_kind":"arxiv_version","alias_value":"2604.26400v2","created_at":"2026-06-12T01:09:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.26400","created_at":"2026-06-12T01:09:28Z"},{"alias_kind":"pith_short_12","alias_value":"SLV6QXZQ4ZBK","created_at":"2026-06-12T01:09:28Z"},{"alias_kind":"pith_short_16","alias_value":"SLV6QXZQ4ZBKPBEY","created_at":"2026-06-12T01:09:28Z"},{"alias_kind":"pith_short_8","alias_value":"SLV6QXZQ","created_at":"2026-06-12T01:09:28Z"}],"graph_snapshots":[{"event_id":"sha256:2f062fe53428bdd75572f9a8ee1daa3c55abc99c594e768e0263804a990feef2","target":"graph","created_at":"2026-06-12T01:09:28Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a reduction to real quantifier elimination followed by a heuristic reinterpretation of the results within our complex framework."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The heuristic reinterpretation step correctly and completely maps results from real quantifier elimination back into the pseudo-complex language without introducing errors or incompleteness."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A quantifier elimination framework for complex numbers is designed via reduction to real QE followed by heuristic reinterpretation, with examples in the Logic1 system."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Quantifier elimination for the complex numbers reduces to real quantifier elimination followed by heuristic reinterpretation in a language with imaginary unit, real parts, imaginary parts, and conjugates."}],"snapshot_sha256":"fd99e6e2ee47111e645b47a2eb223289e09720bcb6f1735401f2e38803b8a132"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":false,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-21T00:37:25.391252Z","status":"completed","version":"1.0.0"},{"findings_count":2,"name":"doi_compliance","ran_at":"2026-05-19T20:11:48.589342Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2604.26400/integrity.json","findings":[{"audited_at":"2026-05-19T20:11:48.589342Z","detected_arxiv_id":null,"detected_doi":"10.1007/978-3-7091-9459-1_20.21","detector":"doi_compliance","finding_type":"recoverable_identifier","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/978-3-7091-9459-1_20.21) was visible in the surrounding text but could not be confirmed against doi.org as printed.","ref_index":42,"severity":"advisory","verdict_class":"incontrovertible"},{"audited_at":"2026-05-19T20:11:48.589342Z","detected_arxiv_id":null,"detected_doi":"10.1016/S0747-7171(88","detector":"doi_compliance","finding_type":"recoverable_identifier","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1016/S0747-7171(88) was visible in the surrounding text but could not be confirmed against doi.org as printed.","ref_index":21,"severity":"advisory","verdict_class":"incontrovertible"}],"snapshot_sha256":"5850dba0b3362159f67bb9346c085f96e8c85d66afc12a6bee7dda33d64c0cc0","summary":{"advisory":2,"by_detector":{"doi_compliance":{"advisory":2,"critical":0,"informational":0,"total":2}},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a reduction to real quantifier elimination followed by a heuristic reinterpretation of the results within our complex framework. We present computational examples using a prototypical implementation of our approach in our Python-based open-source system Logic1.","authors_text":"Nicolas Faro{\\ss}, Thomas Sturm","cross_cats":["cs.LO"],"headline":"Quantifier elimination for the complex numbers reduces to real quantifier elimination followed by heuristic reinterpretation in a language with imaginary unit, real parts, imaginary parts, and conjugates.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2026-04-29T08:10:17Z","title":"Pseudo-Complex Quantifier Elimination"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.26400","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-07T12:39:25.325716Z","id":"8198e441-41c2-4388-9e5f-64f0cc3ac1be","model_set":{"reader":"grok-4.3"},"one_line_summary":"A quantifier elimination framework for complex numbers is designed via reduction to real QE followed by heuristic reinterpretation, with examples in the Logic1 system.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Quantifier elimination for the complex numbers reduces to real quantifier elimination followed by heuristic reinterpretation in a language with imaginary unit, real parts, imaginary parts, and conjugates.","strongest_claim":"We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a reduction to real quantifier elimination followed by a heuristic reinterpretation of the results within our complex framework.","weakest_assumption":"The heuristic reinterpretation step correctly and completely maps results from real quantifier elimination back into the pseudo-complex language without introducing errors or incompleteness."}},"verdict_id":"8198e441-41c2-4388-9e5f-64f0cc3ac1be"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f96a10bc38825c0f698fa6b9a963b53d0d5372b48def413d04c52e1af9bfe734","target":"record","created_at":"2026-06-12T01:09:28Z","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":"e5b72b04270d0621ca510135a445ed4042f1b85a32e01b550c86c95d37977084","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2026-04-29T08:10:17Z","title_canon_sha256":"ecb40f45c99a91134019441f90fc3d582e6c1dccf247ee2be018a651eaa8499e"},"schema_version":"1.0","source":{"id":"2604.26400","kind":"arxiv","version":2}},"canonical_sha256":"92ebe85f30e642a78498bf1a1c833f7c5bcf8d8e00ae6cfa916d333bee991135","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92ebe85f30e642a78498bf1a1c833f7c5bcf8d8e00ae6cfa916d333bee991135","first_computed_at":"2026-06-12T01:09:28.117915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:28.117915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E1zDCOKIDMi8E0VjgtAaI/DvRFTuwNqRv/FhHJP+YGvpCCooYRkHhLp0gy8yiXr/IW9DtOYY0GQ5GEdCMIK4CQ==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:28.118347Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.26400","source_kind":"arxiv","source_version":2}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:1c42f4956df142a96a254c708b92c3dd5152fa5428de89e3a0fc63c42a8479b0","sha256:4d8eba81324233a4670e8af1560ad327b1471e70fa8a1b5562e8e6670ef699f0"]}],"invalid_events":[],"applied_event_ids":["sha256:f96a10bc38825c0f698fa6b9a963b53d0d5372b48def413d04c52e1af9bfe734","sha256:2f062fe53428bdd75572f9a8ee1daa3c55abc99c594e768e0263804a990feef2"],"state_sha256":"a5a98d57fb3f6ba56b1b22abd37ab86ee6829c80684b6f727821bce8b84c562e"}