{"_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_394c4c1c26e06994a418bf38d92b24998efd34552f74a93e85ebe0bf028630aa","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_394c4c1c26e06994a418bf38d92b24998efd34552f74a93e85ebe0bf028630aa","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"c0e6329325b6b5b1b3c48d6ac9fef5a319aa5e6972f0942cc07d76165c4fe86e","published":"Fri, 24 Jul 2026 00:00:00 -0400","receipt_hash":"c0e6329325b6b5b1b3c48d6ac9fef5a319aa5e6972f0942cc07d76165c4fe86e","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":"c0e6329325b6b5b1b3c48d6ac9fef5a319aa5e6972f0942cc07d76165c4fe86e","observed_at":"2026-07-24T04:43:08.456021Z","parent_run_hash":"b018378f86139a28e6209ec008b31c1282cd1b5c1632dbd43b054c17aa88ab96","published":"Fri, 24 Jul 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:2607.20520v1 Announce Type: new \nAbstract: Large language models (LLMs) are increasingly evaluated on mathematical problem solving, yet prior work often treats representationally equivalent formulations as interchangeable and conflates reasoning errors with interface failures. This paper investigates representation robustness in LLM-based mathematical problem solving by systematically varying surface representations of the same underlying problems, including story problems, word-equations, symbolic equations, and isomorphic paraphrases. Using a curated dataset of mathematically equivalent problems, we evaluate five contemporary LLMs under a direct answer generation condition. We find substantial representational sensitivity: models frequently change correctness across equivalent formulations, with nontrivial flip rates across story, symbolic, and word-equation variants. We also observe systematic regressions under isomorphic reformulations, showing that even subtle paraphrase-lev","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","url":"https://arxiv.org/abs/2607.20520","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.20520v1 Announce Type: new \nAbstract: Large language models (LLMs) are increasingly evaluated on mathematical problem solving, yet prior work often treats representationally equivalent formulations as interchangeable and conflates reasoning errors with interface failures. This paper investigates representation robustness in LLM-based mathematical problem solving by systematically varying surface representations of the same underlying problems, including story problems, word-equations, symbolic equations, and isomorphic paraphrases. Using a curated dataset of mathematically equivalent problems, we evaluate five contemporary LLMs under a direct answer generation condition. We find substantial representational sensitivity: models frequently change correctness across equivalent formulations, with nontrivial flip rates across story, symbolic, and word-equation variants. We also observe systematic regressions under isomorphic reformulations, showing that even subtle paraphrase-lev","title":"Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-24T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.20520"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:f0cf0b36963bcc7c10684ead6dceca85ebe89c5d2047de272e9267a89289abcf3e89243e81b6448aae2c51031e22da829dcaa53782229aee9f1fc7e976536403","signer":"crovia.substrate","subject":{"observed_at":"2026-07-24T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.20520"},"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":"05baf933a845beb3a3b6a6ded37f47d2108f669a66967177bd5424a942975a62","leaf_index":346990,"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":"80f9db47b914b6f4196f7c96fde5a6a135ffc63dd3bf6106038ecef62be35f41","side":"right"},{"sibling":"bff95b26520073b8ff47983e5dcd29e3c795a10d8610bee93349a672b5ede155","side":"left"},{"sibling":"7773492b9dd9561f5e8df01bb08ea429b78b85e8865eedf09fc5967ac371081c","side":"left"},{"sibling":"723c7649b109b5cb9292354a31b349e5056f72c73102da6592605e50477e3909","side":"left"},{"sibling":"0222a459a14f16bc313fb527b643c2f09817c6cca93ded8a3d93a9f324d80550","side":"right"},{"sibling":"2d8571a85ef8db282687baf52c678be7c1e616f7a8b798c9f0b7c1f94ce5acd7","side":"left"},{"sibling":"6149df3d1da13abe8a81da069f7bd406a0badf8b62cfc2d62ba645f403037400","side":"left"},{"sibling":"ffd3a55995db3d94b2e5c6432ae18b8c5c13fa05a460ebe646d97e4cfd4c196c","side":"right"},{"sibling":"c212fcc83c532c0321804b72fe72b546946bb055d3d482aab19c43f5bebfbf3f","side":"left"},{"sibling":"da189c159d0789c2229cf3731890cc753832dab1aa83e4bbf0fac01955c22cd8","side":"left"},{"sibling":"3a02ed8ea41a09957282e4e27db74ed88cd675156461abb02acb28e2cd257e63","side":"right"},{"sibling":"d3139af8c5ce235438e1c69e4b7afa44ba09129fd86674968434f23e546f423e","side":"left"},{"sibling":"cb89775a838ee16d10fc8da3213420c2012b4d96e8d55cd49939b0887a4b92d3","side":"right"},{"sibling":"252d30ea8052c3bb6b40bc5cc29fc9b9725343d212f84c08fbbae4215a125b00","side":"right"},{"sibling":"f3e45bceed774d2402fa45d41ff5190f295823bd2f216eb90157884150034693","side":"left"},{"sibling":"3cfa2102c0224815c6f3bf73e6710e24103f43f7bf5da1ca2abad1416d9c0890","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"e871fd7edf9b2ad89bce1609a028f5225eea4d14372169bac242420830f86530","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":347413,"merkle_root":"9efe042c5dd6583dfd3b6a58fbfc289807f60bcf2bd2927f10488a54a8ba11fc","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260724T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-24T05:38:42Z","sig_algorithm":"ed25519","signature":"8633c55f558d42994850505218b2862c6134bad2b1c80d4b80736c2fd3ea7a19690ca3498727a8adbdc47791176128a8d64bef0883b888db809f0477355bd00c","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_394c4c1c26e06994a418bf38d92b24998efd34552f74a93e85ebe0bf028630aa"}}