{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:APK77DHHQVNIEB2FWXD34EBXXP","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":"b9740182e4dd36b7540337198c39bc9d5f586afabb0c602dc33cfb1a72593a5b","cross_cats_sorted":["cs.AI","cs.CL","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-01-02T18:49:37Z","title_canon_sha256":"22baddb73e28275f45c63105c26e4bf492da4dca90968ed7b89788b9f0c7dc0d"},"schema_version":"1.0","source":{"id":"2601.00791","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.00791","created_at":"2026-06-11T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"2601.00791v2","created_at":"2026-06-11T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.00791","created_at":"2026-06-11T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"APK77DHHQVNI","created_at":"2026-06-11T01:09:25Z"},{"alias_kind":"pith_short_16","alias_value":"APK77DHHQVNIEB2F","created_at":"2026-06-11T01:09:25Z"},{"alias_kind":"pith_short_8","alias_value":"APK77DHH","created_at":"2026-06-11T01:09:25Z"}],"graph_snapshots":[{"event_id":"sha256:a6fc21468f4aa5c7014f99e9e46d6db0b23a8ebcbd1e969dbfef9283ba5319be","target":"graph","created_at":"2026-06-11T01:09:25Z","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/2601.00791/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Verifying whether a language model is genuinely reasoning or pattern-matching remains an open problem: learned verifiers are expensive, and output-based heuristics are brittle. We show that valid mathematical reasoning induces a measurable, training-free spectral signature in transformer attention. By treating each attention matrix as a weighted token graph, we extract four diagnostics: Fiedler value, High-Frequency Energy Ratio (HFER), spectral entropy, and smoothness, that require no learned parameters. Experiments across seven models from four architectural families yield effect sizes up to","authors_text":"Valentin No\\\"el","cross_cats":["cs.AI","cs.CL","cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-01-02T18:49:37Z","title":"Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.00791","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:cd9d62b4aa2080a56312fbec05d3b76d7e4ed0f01eb73f069f2f937d7d21baa3","target":"record","created_at":"2026-06-11T01:09:25Z","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":"b9740182e4dd36b7540337198c39bc9d5f586afabb0c602dc33cfb1a72593a5b","cross_cats_sorted":["cs.AI","cs.CL","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-01-02T18:49:37Z","title_canon_sha256":"22baddb73e28275f45c63105c26e4bf492da4dca90968ed7b89788b9f0c7dc0d"},"schema_version":"1.0","source":{"id":"2601.00791","kind":"arxiv","version":2}},"canonical_sha256":"03d5ff8ce7855a820745b5c7be1037bbf70cca4e84c4dbc8db5e053a05bcb7ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03d5ff8ce7855a820745b5c7be1037bbf70cca4e84c4dbc8db5e053a05bcb7ac","first_computed_at":"2026-06-11T01:09:25.824443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:09:25.824443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aqsG0XRLzTPCJDBkdfHppd9lIVRPLoFoT27ZAkccyoSadCI41GfAffdy3VCnMJ58M8GutRir/VA3rt2HggXTAw==","signature_status":"signed_v1","signed_at":"2026-06-11T01:09:25.825435Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.00791","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd9d62b4aa2080a56312fbec05d3b76d7e4ed0f01eb73f069f2f937d7d21baa3","sha256:a6fc21468f4aa5c7014f99e9e46d6db0b23a8ebcbd1e969dbfef9283ba5319be"],"state_sha256":"3f2e290d8727053e9a5a75807ba490853821be01f2a62a6f26f84a32f2179ef8"}