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Despite these advances, their reasoning processes remain largely latent, making them difficult to interpret, verify, replay, debug, and transfer across domains. Existing approaches such as chain-of-thought, tree-of-thoughts, graph-of-thoughts, and tool-augmented reasoning expose intermediate reasoning artifacts but typically lack explicit execution semantics, formal state representations, and verifiable reasoning structures.\n  We introduce Theorem-Grounded Execution Ontologies (TGEO), a framework that models reasoning as an executable state-transition process rather than a sequence of generated tokens. Given an input problem, TGEO identifies relevant theorem families, binds the problem to a domain ontology, discovers semantic objects, instantiates states and operators, constructs predicate","title":"Theorem-Grounded Execution Ontologies for Interpretable Machine Reasoning","url":"https://arxiv.org/abs/2606.16010","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.16010v1 Announce Type: cross \nAbstract: Large language models have achieved impressive performance on reasoning tasks spanning mathematics, science, programming, and commonsense inference. Despite these advances, their reasoning processes remain largely latent, making them difficult to interpret, verify, replay, debug, and transfer across domains. Existing approaches such as chain-of-thought, tree-of-thoughts, graph-of-thoughts, and tool-augmented reasoning expose intermediate reasoning artifacts but typically lack explicit execution semantics, formal state representations, and verifiable reasoning structures.\n  We introduce Theorem-Grounded Execution Ontologies (TGEO), a framework that models reasoning as an executable state-transition process rather than a sequence of generated tokens. Given an input problem, TGEO identifies relevant theorem families, binds the problem to a domain ontology, discovers semantic objects, instantiates states and operators, constructs predicate","title":"Theorem-Grounded Execution Ontologies for Interpretable Machine Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-16T04:43:43Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.16010"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:8f589f1f5dfd070ff8fdb775b50b7aa3239e0a983aa7f51a9df8f8fad547cb6de17d6b17ce86338dd3c4b8f5ea659ec87d656c1ba912bc3c9b1787f74b4ec301","signer":"crovia.substrate","subject":{"observed_at":"2026-06-16T04:43:43Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.16010"},"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":"125ef58acc9c8ab17e562c38a67980fd8aa03b6e6985287c35d9cb53225cf761","leaf_index":230499,"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":"fe88ba66a22381e70290a38bc9319b7930d20741fe92f3df59a1ec024f1335c8","side":"left"},{"sibling":"3d7b92565dac926b9692d9a4fed986dd77a5d63fbcbf6d13e59cd874d3c713b2","side":"left"},{"sibling":"603a37c937545c203181cfb39a40f16a4fe8b4a63eb0cb4b9f0e069ac7c548bf","side":"right"},{"sibling":"689376851f96e983c86ab058f3f419993fd7280731063ae6bd158421d5e9095a","side":"right"},{"sibling":"a3e74522344c32d69b32309b121af7ffa7c08c0d14577e2c90218dc7e834818d","side":"right"},{"sibling":"14f88507fc4a5da54f418340bec85cece14b836401357c37733eb2594bb758a8","side":"left"},{"sibling":"96d9b7ee6d46d2c6d0078e6f6295557abfed0d62f449449bf4962d81989410dc","side":"left"},{"sibling":"5e70a98340dea4a4509e7050c42e3706fa23334d35ad282b0e9f997e7ba855f2","side":"right"},{"sibling":"63d6b9d8af7ae8348285d3493af29f64992ecec42f5f1cae99c8604cd1703487","side":"right"},{"sibling":"0c5669692381d605223c74b8d30f70cd308e77e33d5e40ea84bb7b4f84f2d4d9","side":"right"},{"sibling":"d5b9f8b1a2c9f6a46e17982dfbe6ce1f3b5fa4e730220397f2253d114dcc8486","side":"left"},{"sibling":"d10d772a4984cae00e65ab24af21d1d260e475bbaae3f17871859eb705bd3999","side":"right"},{"sibling":"e79159853f2f35ddae8e3247d515e433c534277b287d65bbd77ae989aa4992fa","side":"right"},{"sibling":"3054319f1840cce0eaaf0bc4b1ae38e5bf8b6210927d924a750775cc7d77cca6","side":"right"},{"sibling":"0fd8b5059f279c4a4a6688de2472fdbc25543fee183df19b21dacca880354cff","side":"right"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"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":232015,"merkle_root":"62bfb7809bb55667ad7eeebdb48267b9b2c1ee89bb808ea1e6d3a814a15aa402","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260617T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-17T13:39:59Z","sig_algorithm":"ed25519","signature":"930a3563c643cc7518d048b12a1f5392a96a5edce49533ba0a56f11b6cc69319bb1c800aacc46b52a6941c4d05dae255a45cac757d6093c971b96852c24f140e","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_c45ad3ce341a2f2817b961b0f0bf4be33a1d7d6d38e2f1046fd3471d7e4a1df9"}}