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The\n  underlying Radon-Nikodym derivative and the identity\n  $\n  \\mathbb{E}_{a}[f(Z)]\n  =\n  \\mathbb{E}_{0}\\!\\left[f(Z)\\rho_a(Z)\\right]\n  $\n  are classical importance weighting, not new identification results.\n  Our narrower question is whether retaining the entire pointwise ratio is\n  useful as a reusable diagnostic across several downstream functionals.\n  We evaluate a two-density plug-in baseline through held-out moment\n  transport and overlap stress tests on synthetic and perturbation data.\n  We also report a pairwise graph-scoring heuristic as a negative result:\n  its F1 is \\(0.10\\) on a synthetic DAG, \\(0.12\\) on Sachs, an","title":"Causal Density Functions","url":"https://arxiv.org/abs/2606.00754","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.00754v2 Announce Type: replace-cross \nAbstract: We study the full density ratio between a specified intervention regime\n  $P_a$ and an observational regime $P_0$,\n  $\\rho_a=dP_a/dP_0$, under the prerequisite $P_a\\ll P_0$.\n  We call the regime-indexed ratio a causal density function when\n  $P_a$ is an identified or directly observed interventional law. The\n  underlying Radon-Nikodym derivative and the identity\n  $\n  \\mathbb{E}_{a}[f(Z)]\n  =\n  \\mathbb{E}_{0}\\!\\left[f(Z)\\rho_a(Z)\\right]\n  $\n  are classical importance weighting, not new identification results.\n  Our narrower question is whether retaining the entire pointwise ratio is\n  useful as a reusable diagnostic across several downstream functionals.\n  We evaluate a two-density plug-in baseline through held-out moment\n  transport and overlap stress tests on synthetic and perturbation data.\n  We also report a pairwise graph-scoring heuristic as a negative result:\n  its F1 is \\(0.10\\) on a synthetic DAG, \\(0.12\\) on Sachs, an","title":"Causal Density Functions","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-28T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.00754"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:d922e6f6a61160edcf45d9220d4848f733b0ee4e5c40c78ba8785ecb0258a3c537cb9a883825fb21dcd88dc41d618f10eb9dd5617301af3100d364e3e50f7307","signer":"crovia.substrate","subject":{"observed_at":"2026-07-28T04:43:08Z","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":"488be21b3ea1ab875750b7fefca54517ba464bbd170f481b29f301cbd7924bf9","leaf_index":360844,"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":"bdde649ed3921e18d18e1311546daeb5ef6d5bbe55addb65f1aa118db5a237e9","side":"right"},{"sibling":"71ebb5a0606f6406d8d02cefa321c3cca9b013625fdf18118458f6f1e91e5af2","side":"right"},{"sibling":"b7f471419181a754863942c4267bcbd4d261f141c0d1ba6f26b16baba61beb10","side":"left"},{"sibling":"03af08636759bc9d3f535f5ce4480edf00119c9dd96879531983469ca3127af7","side":"left"},{"sibling":"ab62974ef9211c062979594e9763579d86b0e270ce9c340b362e75c2f72065a8","side":"right"},{"sibling":"bdc833b2540ff1e8ae92dc6e82d8d0df1d4888e6edf0625716acaf4fff369c1e","side":"right"},{"sibling":"3624810eba28b73089ab25eb96ab3b98f4fccbf630cdc8ce257ab18ffa11f60a","side":"right"},{"sibling":"2269d88b8ead175347e1333136f38876970c71eeededc634500c20d221068882","side":"left"},{"sibling":"f05fa4d2088913dc5410109b6c9f2c28b5e413f06a98f46cd68973c567c3b416","side":"left"},{"sibling":"fe03c6d0b083c4097049d7fc6d7d08dfdb05d9c198b2786336689712d66eabf0","side":"right"},{"sibling":"590ea76fdfc1b9e8072055c378be3182f916709e8d06bd955232e650a7188b86","side":"right"},{"sibling":"d92781c59301ffd5bfb0bad75d9fdf6d73879f715518149d383f7362213e0daf","side":"right"},{"sibling":"f315303d4402b57497416d48eb4c4bb50405b40862d41c7caf318cb3d29c5237","side":"right"},{"sibling":"36973eb5f586cd67e0c0dc055dd87e734aa544c35d4400d2c9f932f8ef8fb27f","side":"right"},{"sibling":"e39f7900355489c4718b21cc2d3d06382e1d2f22b864d10be9ebc9d498b279a1","side":"right"},{"sibling":"1f9a970b25dd938c98cabc9e0a55c5a6f46292b9fa37cc89d90ef0cbb1e05a8c","side":"left"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"3b50864499c874394ea0928567747666eaf59b01380e46cd52164ec5acec0f71","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":361008,"merkle_root":"3065e8369ea437c06beba806dc4e4bb159979adeb21fe632242c1906a7204647","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260728T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-28T05:38:48Z","sig_algorithm":"ed25519","signature":"9141644407577a82611c1579110f667de2d46dc6b93c6322edf26f4c3056ea99f0e56502853908e30d87c38bcf95eb6e0ab5130525aa51505bd6f61938120609","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_fcba6847f04b6145a2486ccdde372f3f223ec2e5a27976f6b1b1840cab6b0cb2"}}