{"_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_2e3986c02b553440741b952e5cad610325e2c37c4b92656fb70e74db66e1f3d5","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_2e3986c02b553440741b952e5cad610325e2c37c4b92656fb70e74db66e1f3d5","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"09ba60da36eac81558f216bbb9d62d4d36a3ed93914f9002def9124bdec34f6f","published":"Fri, 19 Jun 2026 00:00:00 -0400","receipt_hash":"09ba60da36eac81558f216bbb9d62d4d36a3ed93914f9002def9124bdec34f6f","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":"09ba60da36eac81558f216bbb9d62d4d36a3ed93914f9002def9124bdec34f6f","observed_at":"2026-06-19T04:43:39.497162Z","parent_run_hash":"942f204649bd8fb7e5f3ac68f64dc64a5a02624b49ac200c0f629f6ff3a211f3","published":"Fri, 19 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:2606.19610v1 Announce Type: cross \nAbstract: Recent work on Kan-Do-Calculus (KDC) has established that the boundary between passive observation and active intervention in causal inference is a category-theoretic bi-adjunction, with interventions modeled by left Kan extensions and conditioning by right Kan extensions. This paper introduces two causal discovery algorithms under latent confounding, building on the information-geometric and categorical consequences of KDC. In smooth statistical settings, Radon-Nikodym derivatives between observational and interventional measures induce local causal vector fields; failures of these fields to close under Lie brackets become computable Frobenius residuals, which we interpret as witnesses of failed visible integrability and possible latent or unmodeled structure. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines an interventional density or Radon-Nikodym-ratio engine with a ge","title":"Latent Confounded Causal Discovery via Lie Bracket Geometry","url":"https://arxiv.org/abs/2606.19610","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.19610v1 Announce Type: cross \nAbstract: Recent work on Kan-Do-Calculus (KDC) has established that the boundary between passive observation and active intervention in causal inference is a category-theoretic bi-adjunction, with interventions modeled by left Kan extensions and conditioning by right Kan extensions. This paper introduces two causal discovery algorithms under latent confounding, building on the information-geometric and categorical consequences of KDC. In smooth statistical settings, Radon-Nikodym derivatives between observational and interventional measures induce local causal vector fields; failures of these fields to close under Lie brackets become computable Frobenius residuals, which we interpret as witnesses of failed visible integrability and possible latent or unmodeled structure. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines an interventional density or Radon-Nikodym-ratio engine with a ge","title":"Latent Confounded Causal Discovery via Lie Bracket Geometry","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-19T04:43:39Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.19610"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:e6019e52a7a73c470347f3ddcd94008a8bfcd1eb0d5e8adcb8a5c06c1f0d461fe0e015f1b6b130e371f83437a824d4ee63bcc06b744759585da411ec51adf000","signer":"crovia.substrate","subject":{"observed_at":"2026-06-19T04:43:39Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.19610"},"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":"f9e7c51269abb12906635af6e5f6c255c5730e5bfbcd32f72137b592fcc11be3","leaf_index":235574,"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":"fb029a35fb37060811b059d025248a18ff29b0498e87ed63e4352068dd673dcc","side":"right"},{"sibling":"173f7dd629f085f9862e68500a8cbb2d90b206e0b9064f16398a4ac0ba2f3258","side":"left"},{"sibling":"6beb9fe62f629f1686045f47e0d44ac85c82c4a9d32be6531ced526e7ac3552f","side":"left"},{"sibling":"bfba360d584a67ffa6cb3b0af22b3cf4e59cc20a27c40688a04cbe74f3f5440c","side":"right"},{"sibling":"6da7daead88f76db531b56568205bdbfcef4bef4a84f947a4a773e4debb120e7","side":"left"},{"sibling":"c51c58a50c9136814d4c77707235d4cb07ccd1952c8d9530f44c0a4e8d56c7b8","side":"left"},{"sibling":"6cc7ca0021a188fb7ef3325d99f198a5bb7782a033e787d0adde01b21a90e6f5","side":"right"},{"sibling":"c0ab0c7dd98a2c17ee965cb19831d49d3a82a2ba1812d8a677f78274ab6f7c98","side":"right"},{"sibling":"aa68ebe8f5e8e96388fc8d1af3aa08be7ccd27ab4cebcf5913560c48d877bc27","side":"right"},{"sibling":"8253d44cf1ed30d3ab19c2b339fb4000a1fa173182c65390e9e8dabf8173b9e9","side":"right"},{"sibling":"e2bf9b60400244c698c0196109f54323457abc5b64dee08ec33ab14cc4faaef7","side":"right"},{"sibling":"86664e7f68ba08b8dfcf77dda51a4dfa7fcfc986d4ad7c704ffb71b669202da7","side":"left"},{"sibling":"410c633928fea11c5b4bdddb431956b1d7c320db9cda00d2fe32e0fcf888d7b7","side":"left"},{"sibling":"b52a771530dd1686bca49e42088898b86da94879579cd6a995c6ab0598a665fe","side":"right"},{"sibling":"a116bb92f9b0350491155b470acc86d006c33ec558759e49e56614a54c39f242","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":241122,"merkle_root":"7a906c6a26ff6c6feabc2feaba6a1a70c515e6fd72a38c779293b0f78ff291c4","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260622T183701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-23T06:25:25Z","sig_algorithm":"ed25519","signature":"5576b1d56d5dbb0d96c780fa3ca0940d805c8de95c6251bc87297f0be058aa5e37eb53a6aa1b601381f489f093842cf674b28737ed8e46ce3a49814b5e57290c","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_2e3986c02b553440741b952e5cad610325e2c37c4b92656fb70e74db66e1f3d5"}}