{"_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_5b4c13f2abde2759c8ae970ae239ee7a3f7d439c21d723f0dbabd69e849e8095","bitcoin_anchor":{"bitcoin_attestations":["bitcoin_block_949451"],"calendar_attestations":["https://finney.calendar.eternitywall.com","https://btc.calendar.catallaxy.com","https://alice.btc.calendar.opentimestamps.org","https://bob.btc.calendar.opentimestamps.org"],"ots_url":"/registry/data/substrate/anchors/77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3.ots","stamped_at":"2026-05-15T03:00:03Z","status":"bitcoin"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_5b4c13f2abde2759c8ae970ae239ee7a3f7d439c21d723f0dbabd69e849e8095","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"59d21f52c27ff41e70952047ac77f1014266938185db7c4f6426b00cdf05f314","published":"Tue, 12 May 2026 00:00:00 -0400","receipt_hash":"59d21f52c27ff41e70952047ac77f1014266938185db7c4f6426b00cdf05f314","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":"59d21f52c27ff41e70952047ac77f1014266938185db7c4f6426b00cdf05f314","observed_at":"2026-05-12T04:43:42.564879Z","parent_run_hash":"4cc5aca0c1b8116c9ab92405e0260204f01cf7ce2e49dea9d7e123236f5dc13b","published":"Tue, 12 May 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:2605.05743v2 Announce Type: replace-cross \nAbstract: Gaussian process (GP) marginal likelihood scores and kernel conditional independence tests are theoretically appealing for nonlinear causal discovery but computationally prohibitive at scale. We present three complementary RFF-based methods forming a practical toolkit for score-based, constraint-based, and hybrid causal discovery.\n  The Fourier Feature Marginal Likelihood (FFML) score approximates the exact GP marginal likelihood by replacing the $n x n$ kernel Gram matrix with a finite-dimensional feature representation, reducing cost to $O(nm^2 + m^3)$ while retaining the probabilistic interpretation and automatic complexity penalty of the exact score. FFML extends to mixed (continuous and discrete) parent sets via a product-kernel construction, with a Kronecker path for small discrete parent sets and a Hadamard-product path otherwise.\n  The Tetrad Random Fourier Feature (TRFF) score is a complementary BIC-style alternative u","title":"Fourier Feature Methods for Nonlinear Causal Discovery: FFML Scoring, TRFF Scoring, and FFCI Testing in Mixed Data","url":"https://arxiv.org/abs/2605.05743","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.05743v2 Announce Type: replace-cross \nAbstract: Gaussian process (GP) marginal likelihood scores and kernel conditional independence tests are theoretically appealing for nonlinear causal discovery but computationally prohibitive at scale. We present three complementary RFF-based methods forming a practical toolkit for score-based, constraint-based, and hybrid causal discovery.\n  The Fourier Feature Marginal Likelihood (FFML) score approximates the exact GP marginal likelihood by replacing the $n x n$ kernel Gram matrix with a finite-dimensional feature representation, reducing cost to $O(nm^2 + m^3)$ while retaining the probabilistic interpretation and automatic complexity penalty of the exact score. FFML extends to mixed (continuous and discrete) parent sets via a product-kernel construction, with a Kronecker path for small discrete parent sets and a Hadamard-product path otherwise.\n  The Tetrad Random Fourier Feature (TRFF) score is a complementary BIC-style alternative u","title":"Fourier Feature Methods for Nonlinear Causal Discovery: FFML Scoring, TRFF Scoring, and FFCI Testing in Mixed Data","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-12T04:43:42Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.05743"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:adc0abfba2ef63f98498cafb37db6e8e420154fdf5e6b697720bdcaba660bd68fbfc8d4b69cab8845fd37293c980e6d4217c5195fa90de7f7d215fc664e94209","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.05743"},"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":"279f35cb9dbff41744f2d5b54d384703ab40b6836556bdb765c6d5a6a17603d3","leaf_index":129232,"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":"3cf79ceffe67aa507391da6e1d61b20435b5b12d3fb1d5ded95929ba3e1efdcd","side":"right"},{"sibling":"cf895b6c7131f644a48b66f4fd99a2a10c58ee3cdc911fb2b0f8142be7ad2be0","side":"right"},{"sibling":"7b47b4dced610b2c4d436a1bdea7b2b747405e44f3c162e0b5547863d86a4d7d","side":"right"},{"sibling":"e251aac24fccfe44d85a5bbdbab6675f427ea3e9de795dbb2777b8a973fe503e","side":"right"},{"sibling":"7bc94cc4a99aed9070c432d35a8c93e6e444d9942da06f15320dac94b1682b76","side":"left"},{"sibling":"191e43db195da12c527816cabaa613e34e929ed1bf82d9d6f28f6b0573edcd1c","side":"right"},{"sibling":"7bf8415be77f9b60a0ddcf8ae89d09c7702ec0a4dad8e63b9185cc233150354e","side":"left"},{"sibling":"6cffd83b66fa63950542ea9b737e53228a66f295a7ebb44ea9155b70f279094c","side":"left"},{"sibling":"bb93634b6ea81ccfb7b9c5b023ffaff85acd8b3f1ec609973d847fd93873d3ec","side":"right"},{"sibling":"9922155d12ac3db561299f0abaec57fc59dd8e711d91cd590823abd8f3e4647f","side":"right"},{"sibling":"9c71dae5b380aff58527385ccecc23b4cd8ff36395d4fc35ad5236b00fcb6db8","side":"right"},{"sibling":"d32d0a951c1d7e98a8e1951a587d83c97962daeeaa455643bc1d5d53744dc21e","side":"left"},{"sibling":"ffc4d51379293bc3e1910c7d612f409dc610fd9acf8241793fb89f82e1bad4ef","side":"left"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_5b4c13f2abde2759c8ae970ae239ee7a3f7d439c21d723f0dbabd69e849e8095"}}