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When this grounding step is not certifying, there is no way of knowing that the obtained solutions actually correspond to the original problem specification, resulting in a trust gap. \n  In this paper, we close the trust gap between the user's high-level specification and the solver's low-level input by introducing a novel certifying grounding framework for first-order logic model expansion (FOX) over finite domains. We present CertiFOX, a framework consisting of: (1) a proof format for grounding derivations, (2) GroundFOX, a certifying grounder operating on theories in Grounding Normal Form (GNF)--a new normal form designed for compact, domain-aware grounding--and (3) CheckFOX, an independent proof checker.\n  Our approach guarantees that the ground","title":"Towards a Certifying Grounder","url":"https://arxiv.org/abs/2607.21199","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.21199v1 Announce Type: cross \nAbstract: Grounding, the translation of high-level theories into equivalent quantifier-free formulas, is a crucial step in declarative solving, yet it has so far escaped the proof-logging revolution. When this grounding step is not certifying, there is no way of knowing that the obtained solutions actually correspond to the original problem specification, resulting in a trust gap. \n  In this paper, we close the trust gap between the user's high-level specification and the solver's low-level input by introducing a novel certifying grounding framework for first-order logic model expansion (FOX) over finite domains. We present CertiFOX, a framework consisting of: (1) a proof format for grounding derivations, (2) GroundFOX, a certifying grounder operating on theories in Grounding Normal Form (GNF)--a new normal form designed for compact, domain-aware grounding--and (3) CheckFOX, an independent proof checker.\n  Our approach guarantees that the ground","title":"Towards a Certifying Grounder","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/2607.21199"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:4c403040940fd72b12cc8db701730c084ea1e7c375657c221c2172b3cdf9bc2d28a6fde17f31f0e3d6e10c8b4a555cd6a5d527a8d27b44182939d1498056a608","signer":"crovia.substrate","subject":{"observed_at":"2026-07-24T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.21199"},"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":"2981434aef80bd9158488734225e3aa05c1385b397584a007d186decc497841b","leaf_index":347165,"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":"ae41b32a2f411f45c17e97c88d06f75d63c7befa0b99e33a2af14d45f3f6d7ba","side":"left"},{"sibling":"2c41f31fedd6606cecfafa8d40d9d3188fcf12573d297d2558d3c8f29c95a8da","side":"right"},{"sibling":"fce554e64a6f5d135b338a29496f5975bb06706ead0c57cc1158a05082203886","side":"left"},{"sibling":"deec06a7e0570734b622dfff7515cfe8a8615f5356412c372706d41dec8be936","side":"left"},{"sibling":"851159c4e1693c285e7d457ed28a12bf32ffb9fd5b340aaacb668afc7e106416","side":"left"},{"sibling":"b6debb6f2e4bf22e2169ef83d8bddaa57a78351013d058637030f185562dd879","side":"right"},{"sibling":"174e185d067a50aecc913edd90ba49fd072a31a09e0b3a18c0687f362c61e57b","side":"right"},{"sibling":"aa4b293ba10895bb7f8b28f0f04360b53a8fc5a7523d9a560dbb7b29d003643e","side":"right"},{"sibling":"759f431c97765cb7fb12d38ee64fd6a87076abf1b63c87d7c8c172d57b29084d","side":"right"},{"sibling":"b9cb83ecb59812b3b9270c365951fa79dead288c3923b6cf1f83ffb911b27405","side":"right"},{"sibling":"e6c9083cd0939b38f691f619de2054068654e9c77f7c7ab051e0d48b77339e5d","side":"left"},{"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_75fc99756763383afcd2688dbfd768f1475d07ff4386119b62cda8bcc1c57e9a"}}