{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_3855a42981baccb0f990c42bb40283b9afab816800ade82fd2d2e4ee1a2b9d1b","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_3855a42981baccb0f990c42bb40283b9afab816800ade82fd2d2e4ee1a2b9d1b","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"7c2943a5509d19ecc7b656defb030fe1f4ce7489e943990f18f1e4bc9929af48","published":"Thu, 11 Jun 2026 00:00:00 -0400","receipt_hash":"7c2943a5509d19ecc7b656defb030fe1f4ce7489e943990f18f1e4bc9929af48","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"7c2943a5509d19ecc7b656defb030fe1f4ce7489e943990f18f1e4bc9929af48","observed_at":"2026-06-11T04:43:37.662146Z","parent_run_hash":"5267801b61ae0d882196b5f37208a9a1633905a64ca7d933f1fa5075cd861491","published":"Thu, 11 Jun 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2601.00791v2 Announce Type: replace-cross \nAbstract: 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 Cohen's $d = 3.30$ ($p < 10^{-116}$), enabling $85$--$96\\%$ single-threshold classification accuracy. Two findings sharpen the interpretation. First, \\emph{Platonic validity}: the spectral signal tracks logical coherence rather than compiler acceptance, proofs rejected for timeouts or missing imports are correctly classified as valid, a d","title":"Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning","url":"https://arxiv.org/abs/2601.00791","vendor":"arxiv_cs_ai"},"summary":"arXiv:2601.00791v2 Announce Type: replace-cross \nAbstract: 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 Cohen's $d = 3.30$ ($p < 10^{-116}$), enabling $85$--$96\\%$ single-threshold classification accuracy. Two findings sharpen the interpretation. First, \\emph{Platonic validity}: the spectral signal tracks logical coherence rather than compiler acceptance, proofs rejected for timeouts or missing imports are correctly classified as valid, a d","title":"Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-11T04:43:37Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2601.00791"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:0b308467e11eeddb3938bad7aa8e97d424a5771616e7bb8f750c136cc9377e901286ba107474e5c35a92482aeae1d99428111d2e2ffdbae6fbafe27edbdb5007","signer":"crovia.substrate","subject":{"observed_at":"2026-06-11T04:43:37Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2601.00791"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"d297b280a8d01d712299bfac29a3c849c3da787620420353da280a8fb2e987a3","leaf_index":227592,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"de085ef26daa2bbbc0436cefe536817e6ddc863d98303c986e11a28745b23b88","side":"right"},{"sibling":"b4201b2eadddad5b5654196ef48ea8391e35c77239f45809dad069f551f25fab","side":"right"},{"sibling":"b1da466e17f260c09e898c2107fd96a8c6a2beaa8139a917a5173d345393d241","side":"right"},{"sibling":"170799a1ee62bbbaa86fab857e29aa393f101ea2f3c551622adb35b5af3f0665","side":"left"},{"sibling":"5b1a8d3a19b408b22f0222f3e6a2674cddb013f8eb56811fa1077de01797f42a","side":"right"},{"sibling":"5c7c8be4e170a73031eb1c9f46ffbf81872d59bfe0f3853c100cd36ce5cd30a4","side":"right"},{"sibling":"b3e44c169468247ff310527cf2f90f2c6c7fb8fa20f54d288a0ad8da5e1aeaae","side":"right"},{"sibling":"8a3e5c7ea49dd66cd71ed0760cc762c1e6d233215488abe34cb40cd8d01bc326","side":"right"},{"sibling":"f76de2250b6d1132375cb2a9c157faf5c22b74a7ca5c8df342d778d0e08e1216","side":"left"},{"sibling":"04e399458c5b36988cae0bf1c6dbe1b01349003b15cb5aa43f95c55acffe4ec3","side":"right"},{"sibling":"1383228337d54218bd8e5563aebb0b0dfe15c5269e3d5138e64c261d6130a88b","side":"right"},{"sibling":"57cb49c192550231071a0bf53a0821da2f79c585ec6c8d0fc76cebd62ccd78b2","side":"left"},{"sibling":"cdb58f86163046d3b15f857b03372ec75e1ad9ea4548e086793d528b9eed364d","side":"left"},{"sibling":"533d82482604463aa4a281b9d8b85917b383b7c5f924b2b494039524c55e8797","side":"left"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"6cea4964f32722eb370847c2f7c9d6a9f0622c239538b07e6815a59d6fd8d49c","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":228173,"merkle_root":"7e416202c0bfd759bd2eea4236713b403993d99793fe8badb5065040080bece3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260611T143708Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-11T21:59:35Z","sig_algorithm":"ed25519","signature":"231c80024bc3982dd493c45b31af95097e97aabc6d712a4e5bad7d0cbdd3c08e01ff395b0f8e72754bac97016e0cd0eed88b8a13cb71edbbcb9b6d72c10a7b03","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_3855a42981baccb0f990c42bb40283b9afab816800ade82fd2d2e4ee1a2b9d1b"}}