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Whereas many causal-strength measures compare whole distributions after graph surgery, causal density functions provide a pointwise change-of-measure object that can be estimated, calibrated, and used to score directed influence. The basic identity\n  \\[\n  \\mathbb{E}_{\\mathrm{do}}[f(Y)]\n  =\n  \\mathbb{E}_{\\mathrm{obs}}\\!\\left[f(Y)\\rho(X,Y)\\right]\n  \\]\n  makes causal density directly testable: if the estimated density ratio is correct, observational expectations reweighted by $\\rho$ reproduce interventional expectations. We derive practical estimators for do-curves and directed edge scores, relate the construction to Radon-Nikodym/Kan semantics for conditioning and intervention, and evaluate the resulting estimators on synthetic and real perturbation benchmark","title":"Causal Density Functions","url":"https://arxiv.org/abs/2606.00754","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.00754v1 Announce Type: cross \nAbstract: We introduce causal density functions: Radon-Nikodym derivatives that compare interventional laws to observational laws and therefore act as local density ratios for causal effects. Whereas many causal-strength measures compare whole distributions after graph surgery, causal density functions provide a pointwise change-of-measure object that can be estimated, calibrated, and used to score directed influence. The basic identity\n  \\[\n  \\mathbb{E}_{\\mathrm{do}}[f(Y)]\n  =\n  \\mathbb{E}_{\\mathrm{obs}}\\!\\left[f(Y)\\rho(X,Y)\\right]\n  \\]\n  makes causal density directly testable: if the estimated density ratio is correct, observational expectations reweighted by $\\rho$ reproduce interventional expectations. We derive practical estimators for do-curves and directed edge scores, relate the construction to Radon-Nikodym/Kan semantics for conditioning and intervention, and evaluate the resulting estimators on synthetic and real perturbation benchmark","title":"Causal Density Functions","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-02T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.00754"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:cf5bba34bba67cf54a7cfe6c2219741d8cb3bf4f7e847e3d07a4668b3180392eaa290882396f2510593eda78874962de055b1a56f8a45247cac3a6d2d08e1604","signer":"crovia.substrate","subject":{"observed_at":"2026-06-02T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.00754"},"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":"7ebf38bca95311759f96c925ff497e1d029a946b184c4a19b4fa5b6cc4180364","leaf_index":205509,"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":"2b5e2f60141bc66e5e939611c49363874c9d8582a0cf3f161e361174ec77b078","side":"left"},{"sibling":"5e1f97e020b606214466b0076bb43b29e3b6ec1003fbe54fca6be1880de780e3","side":"right"},{"sibling":"ec49fe3ba7f8ab12f646615d789bc1fb448bbc5b10abd8c3326144175242ce54","side":"left"},{"sibling":"3411804ad55e8d5d4a12af0f3d014dabd336eaed5ae6eae7ce3d8a5d10041454","side":"right"},{"sibling":"ab054fd548592416e54a526f66809e978717d1eed55c33684d914c2f3e59e3dc","side":"right"},{"sibling":"eb80a4b5acb7c91157d17872a3ad0b7c31ada0d144cea1def94c6c4129d1a544","side":"right"},{"sibling":"8a2375b77c86225d72b598729749fedbe90192c1769941af16d20d15ece17150","side":"left"},{"sibling":"4c08f6d1ea280f1117880420bf5d3d8f4cfb29d16b8b643cafca9f868218668c","side":"left"},{"sibling":"24ca17172d6e9b822b45054c27a7852aa461e97a906c83736cd55c5cf9874394","side":"right"},{"sibling":"6620a5008acf732cd3e57b0f2d1437293e88366c2e5b175ebeb7d796fc1e0c62","side":"left"},{"sibling":"a82575bfb494af7afcc13aaae718afa6f74030f09d71b02819ea25efd4186fc4","side":"right"},{"sibling":"e6adead8216db4cae92f0a036d53baebf30eed95a99c0d10758aa75bb7780f2f","side":"right"},{"sibling":"1acc2b7ff453ffd8c97b80ae4db5358780f0c6796874fd75403791dbe99f8cd7","side":"right"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"5f86f58c28b1a86ae06dfff4666bb9fba8866021a81fd4f1d200aa9af4722dfb","side":"right"},{"sibling":"f6cc6f94f6944ae21390afc65ac9e91dc31f84ee6e060681bba5ae08058294bd","side":"right"},{"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":206226,"merkle_root":"d2a6d32b13cbf343fb143b21a756d0533864ae6577a376ee84ba867b949207ec","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260602T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-02T05:37:46Z","sig_algorithm":"ed25519","signature":"abd9956cfb19dd1fb8142c46a220bac2514848c6abb0e79b8b0940206cc3ebb00894d4daaf9f786427f82a7cc12482e7fda79054ebb06bceaa9b4b97e23fb30e","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_cf9a3bf6a9c2b8a3e8d994aac9fd3283a45ffc120d278f4ad2fc3a7a68195cd1"}}