{"_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_d4ec57f4535ff84b667cedec26f91a52a93477f4dbdc117c6cefe4de34eeebe2","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_d4ec57f4535ff84b667cedec26f91a52a93477f4dbdc117c6cefe4de34eeebe2","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"7a12ed11334aa9ae698dba499e9c1f68687f399d7582de772f1b557048477dfa","published":"Wed, 17 Jun 2026 00:00:00 -0400","receipt_hash":"7a12ed11334aa9ae698dba499e9c1f68687f399d7582de772f1b557048477dfa","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":"7a12ed11334aa9ae698dba499e9c1f68687f399d7582de772f1b557048477dfa","observed_at":"2026-06-17T04:43:17.968423Z","parent_run_hash":"8f56c4deb22b28178ba7974d6ffc5ff17336d44c95dd94de80095705245fa113","published":"Wed, 17 Jun 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:2606.17851v1 Announce Type: new \nAbstract: A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $\\sigma$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases. This account is built on sets, and a set deliberately forgets two things that are important for NeSy: when two $\\sigma$-structures are the same up to a symmetry of the theory, and how many distinct proofs witness a query. Replacing the underlying sets by types, in the sense of homotopy type theory, preserves this information, and turns this functional into a belief-weighted homotopy cardinality, a notion of size that counts each object in inverse proportion to its symmetries. We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind ","title":"A homotopy-type-theoretic generalization of neurosymbolic inference","url":"https://arxiv.org/abs/2606.17851","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.17851v1 Announce Type: new \nAbstract: A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $\\sigma$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases. This account is built on sets, and a set deliberately forgets two things that are important for NeSy: when two $\\sigma$-structures are the same up to a symmetry of the theory, and how many distinct proofs witness a query. Replacing the underlying sets by types, in the sense of homotopy type theory, preserves this information, and turns this functional into a belief-weighted homotopy cardinality, a notion of size that counts each object in inverse proportion to its symmetries. We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind ","title":"A homotopy-type-theoretic generalization of neurosymbolic inference","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-17T04:43:17Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.17851"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:7faaa7d288e113b9511262205d5601f3cb5548a86a64a784d24d8a1797fa85904dfe0f245b087c11aa5690c9f4daf0273fe1aec82b0c30fbcbd4257ebbfb7300","signer":"crovia.substrate","subject":{"observed_at":"2026-06-17T04:43:17Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.17851"},"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":"40be3c741d4a88d672578a6bb4282b27d3f624565c5b1360b2537d6c8609a11b","leaf_index":230877,"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":"f62618a5c75eda8dfec3e66ba840335e00859f327655225ef5afe2f6b9601d9f","side":"left"},{"sibling":"e2715e9a0470fa05abe3ee30194409bd95f14d215170055b7f9ae0ab9710dd1d","side":"right"},{"sibling":"1da0f437425b3bba581d3a68653fbc97615daacebfbed1c18830bd6ebed6ee54","side":"left"},{"sibling":"38054516521a1afb51ef23edcffe1a9375c95d0095401f8961a9a0ebe166e09e","side":"left"},{"sibling":"a011eed65a011c5f09f35b365315daa3efe52202fe1f717062f18edb32070310","side":"left"},{"sibling":"505980e02b3a22a962e22e6151b370e9aa9ce58f596e99b446b88c8236da18aa","side":"right"},{"sibling":"70b54557b0f44aae58967d06c700194d1d2cf17d2bbbb2ad9632da8cf5919c79","side":"left"},{"sibling":"46f3925bb1c995570704f74c45315769d7303b87cc2d1f176bed247b9cc9fdad","side":"left"},{"sibling":"ee59602dad0bf74c97a32a93f0a1a19e7a12f2800791988a6fdf35611febe031","side":"left"},{"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_d4ec57f4535ff84b667cedec26f91a52a93477f4dbdc117c6cefe4de34eeebe2"}}