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We present a benchmark of 350 question families (1,750 total questions) for Controlled Reformulation Testing (CRTBench) to evaluate logical invariance. In this benchmark, we investigate LLMs' ability to maintain consistent answers across controlled reformulations, which include contrapositive rewriting, double negation, negation flipping, and passive voice. We evaluate several frontier LLMs and observe an accuracy-consistency gap where GPT-5.4-mini achieves $98.9\\%$ base accuracy but only $60.3\\%$ family-level consistency, while reasoning-optimized o4-mini achieves $96.9\\%$ consistency. From our experiments, we observe that failures cluster around logically nontrivial transformations such as contrapositive rewriting ($72.4\\%$ for GPT-5.4-mini) and double negation ($84.6\\%$), while surface-level rephrasing rema","title":"Controlled Reformulation Testing for Logical Consistency in Large Language Models","url":"https://arxiv.org/abs/2607.14528","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.14528v1 Announce Type: cross \nAbstract: Large language models (LLMs) frequently contradict themselves when the surface form of a logically equivalent question changes. We present a benchmark of 350 question families (1,750 total questions) for Controlled Reformulation Testing (CRTBench) to evaluate logical invariance. In this benchmark, we investigate LLMs' ability to maintain consistent answers across controlled reformulations, which include contrapositive rewriting, double negation, negation flipping, and passive voice. 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From our experiments, we observe that failures cluster around logically nontrivial transformations such as contrapositive rewriting ($72.4\\%$ for GPT-5.4-mini) and double negation ($84.6\\%$), while surface-level rephrasing rema","title":"Controlled Reformulation Testing for Logical Consistency in Large Language Models","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-17T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.14528"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:4924e0db205c8d351adc0239e38ac3ecf60b23914cd9a75b2c2212c44997a9da6b07b62a42d2bae652e49dea0b571b0d1d8c677e30c026cc908d40dc71ba9d05","signer":"crovia.substrate","subject":{"observed_at":"2026-07-17T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.14528"},"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":"2e7a104d765af34e2ae2799d7ea9b75b2302b79742846a0445a92498a5becfe9","leaf_index":323118,"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":"41aa00c17b7104b26e4a5318ae31e153cdbe582faed9275bb3d94000e49b7b75","side":"right"},{"sibling":"a635fe0e696a0bef3cc764fecd8cebeb03b3082f11f32d6a8d31eab0f1bca4ae","side":"left"},{"sibling":"3e917bb662ec2f0621e6e7e24d5eddf4a815868ac756626e75c7780f7c31bd57","side":"left"},{"sibling":"108deaedec1deba87f0ba9fd11c7aecf247fd29f6ce10b916e5130be322b7463","side":"left"},{"sibling":"a0984b60e42ee195cfb45a266ade7b16a3b101425f6344c4b782f71eed8db68d","side":"right"},{"sibling":"86ed41f2483d0f15afaf14a254cf1f1f4f99b34c1507bbc0f1be3b355c369b6d","side":"left"},{"sibling":"5ff315166458d1adbaa358c18de4128f9e9bbf19a8a9158ad86b1f0230dee929","side":"right"},{"sibling":"de6ef12c0ebc7e3e48430c64265163103eb92448efd698dbc2b104ada5a5389d","side":"right"},{"sibling":"4242cc570ec8c36a37f3f6f20dcae20b49fccc17c7b53ba47d8715e465bec585","side":"right"},{"sibling":"be025f48721bfc0ca7107f0454bda3ab460e50539f0caeb1bf839a8dabcf036c","side":"left"},{"sibling":"05a09763743cdc09fc45cf454e4e3ea4a0d1cd74f9c8162b2a57e2c873160908","side":"left"},{"sibling":"de3120ef2488b8a791a686b47257da4e612256abdfcdda7519265e7edd47d041","side":"left"},{"sibling":"e86f56a4883492da5b5e7b0201324c52946e865e69b99ebb532f41fe3c658ee4","side":"right"},{"sibling":"34d85f6ad6cc7dfa79d90e2b9ff99a561bcdc75b0301bbbd3e83861f54535c1e","side":"left"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"9b11714124b9b951ff9450b0ee9d625a0b70b6da2cf388bd3df1475eec0b17ba","side":"right"},{"sibling":"a4523a9014d45df43e006e9210a73428c380d771f2c650a1b986910759b0cdf7","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":323382,"merkle_root":"2f4d32419c80a9600aba5a480fc3fb7012ec0a695c91a1b055048e78760b65ca","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260717T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-17T05:38:31Z","sig_algorithm":"ed25519","signature":"495308c7bf004117807331d3f71d0b079f6bd7ed7737faa58c773b1b3e80ee84928d2d8519cc7d2b809506501aada1be6546f72c7ecda3dad5445cbb44502209","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_898fa82e6bb3f09b61648f25ac0049a95eedcf91498ec51890a535231bb233ed"}}