{"_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_e4d5ba5086c8dd12ffddaba617f8f738950894b24149949b1fc8a0f1f529488a","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_e4d5ba5086c8dd12ffddaba617f8f738950894b24149949b1fc8a0f1f529488a","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"fd6ff8d8abc35bdeb29e05fe94512dd2b4259836f928b6bbde0e8812dcfcd355","published":"Tue, 14 Jul 2026 00:00:00 -0400","receipt_hash":"fd6ff8d8abc35bdeb29e05fe94512dd2b4259836f928b6bbde0e8812dcfcd355","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":"fd6ff8d8abc35bdeb29e05fe94512dd2b4259836f928b6bbde0e8812dcfcd355","observed_at":"2026-07-14T04:43:37.834979Z","parent_run_hash":"66b89520a448b8d9fe7d8f602ef38b82b6c95e57f532ce72de51375b41870477","published":"Tue, 14 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:2607.10880v1 Announce Type: new \nAbstract: We extend, in Isabelle/HOL, the deep-and-shallow embedding methodology of our prior work from propositional to first-order modal logic (FML) with constant-domain Kripke semantics. Three embeddings of FML into classical higher-order logic (HOL) are provided side by side: a deep embedding, a heavyweight maximal-shallow embedding, and a lightweight minimal-shallow embedding. The minimal-shallow embedding is presented as an Isabelle/HOL locale, parametrised by an accessibility relation, a world-indexed interpretation, a universe of worlds, and a variable assignment; the locale form admits a global faithfulness theorem, stating that quantifying over all minimal-shallow interpretations recovers exactly deep validity.\n  A central technical contribution is a mechanisation, for FML under constant-domain Kripke semantics, of the (countable) downward L\\\"owenheim-Skolem theorem, which underpins the automation of our faithfulness proof between the de","title":"First-Order Modal Logic in HOL: Deep and Shallow Embeddings with Automated Faithfulness (Extended Preprint)","url":"https://arxiv.org/abs/2607.10880","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.10880v1 Announce Type: new \nAbstract: We extend, in Isabelle/HOL, the deep-and-shallow embedding methodology of our prior work from propositional to first-order modal logic (FML) with constant-domain Kripke semantics. Three embeddings of FML into classical higher-order logic (HOL) are provided side by side: a deep embedding, a heavyweight maximal-shallow embedding, and a lightweight minimal-shallow embedding. The minimal-shallow embedding is presented as an Isabelle/HOL locale, parametrised by an accessibility relation, a world-indexed interpretation, a universe of worlds, and a variable assignment; the locale form admits a global faithfulness theorem, stating that quantifying over all minimal-shallow interpretations recovers exactly deep validity.\n  A central technical contribution is a mechanisation, for FML under constant-domain Kripke semantics, of the (countable) downward L\\\"owenheim-Skolem theorem, which underpins the automation of our faithfulness proof between the de","title":"First-Order Modal Logic in HOL: Deep and Shallow Embeddings with Automated Faithfulness (Extended Preprint)","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-14T04:43:37Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.10880"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:cb3ec1bd0516d8ac7b4dc6a8589a4d7b31586ba8748131ff045a3faa5d7efe4b56639184bcd22fbab574eeae576dc4e173871fa453706c53e0a377f1aa8c1d04","signer":"crovia.substrate","subject":{"observed_at":"2026-07-14T04:43:37Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.10880"},"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":"0281014dc9eb95a3b863be4935fed1d803e75917fbc8bb471cd7289ae976be44","leaf_index":312853,"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":"0dfee27c66023c5d1be65ccaf4610ef8eb361e380049edd80a95faabaa99b562","side":"left"},{"sibling":"bbec9868083d04c9d18bf87e42068cbd24486057a7a4f51a31d555ba758471ac","side":"right"},{"sibling":"db45c34d4bd1680d095ad829aa4763bf203d414d4a36765be979b302f3ff8b5d","side":"left"},{"sibling":"fac2b10acce0ba79821c023ce18a4fc03b9dba1319a30845c5d78ba4b93d821a","side":"right"},{"sibling":"104556ebfbbb3c2261ea024f7e4246161d1f09a822ab4924884f821afb1afae9","side":"left"},{"sibling":"d8d5ddf33faed2454e98d99a614566f2ea60738df94d7b4292db5dde7abf666c","side":"right"},{"sibling":"04a12e88bcadd8c9e1dda8e2f91239c99fb5d20c71c964d11fa8866459755f0e","side":"right"},{"sibling":"b6420221ab220053217910d6a61ccf0d6e8ca1f1eb9e0cc40a25723c21042168","side":"right"},{"sibling":"ca17e703a3fca19bfbb090cbed9e2450594a9c237665dd9a566195d3ef3072f7","side":"right"},{"sibling":"8393dc03644000353c5d503b6ec261c022cd2aa85a649223916153bc8af2dc75","side":"left"},{"sibling":"1627ce6908965f2e5fbc7c16bc8e247867478c587014561d0de1359dc2dc0afc","side":"left"},{"sibling":"74e1ba9fd48bdd0f52777dd5b56c10706e73f42629013748eca13ef113cd59db","side":"right"},{"sibling":"682fd39539db5bce908d0ab6f180374728fed6b34a9a8c87c7b4eb5a726e30b8","side":"right"},{"sibling":"184927f71d667ac0c6ebeadb33394626973738b9107c6dc3c0c4949b44acf295","side":"right"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"c4c189d79669979b59d9aa976ee249c54a7e065b4a05bf49463459cc7f37428e","side":"right"},{"sibling":"19475e206bdf2698769a286db2c97c4d3f089741319f9b29a139038c6e511975","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":313381,"merkle_root":"5f7d48580373d0ab0bc6bdf34f26de442f9a86d130946f7ee45addd1a55cb9f4","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260714T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-14T05:38:23Z","sig_algorithm":"ed25519","signature":"97364224142ed1b2a8925fed1bfba2e0a8a6a15f8ca0999b934846ad83584a78c7f0f5cd09dbc1c938b35383fcc5c8fa4b723118e30916628879d1c5fd3a9908","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_e4d5ba5086c8dd12ffddaba617f8f738950894b24149949b1fc8a0f1f529488a"}}