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The bottleneck is interface, not approximation: J\\\"ackel's seminal \"Let's Be Rational\" (LBR) solver already inverts the Black-Scholes price to machine precision efficiently. What is missing is a differentiable layer that preserves LBR in the forward pass and avoids backpropagating through its branch logic. Such a layer must also confront the unavoidable singularity of the inverse map in the low-vega regime, where the sensitivity 1/vega diverges as vega -> 0.\n  We close this gap with PIVOT, the Price-Implied-Volatility Objective Translator. PIVOT keeps the LBR forward pass intact and supplies the backward pass by implicit differentiation through the smooth Black-Scholes/Black-76 price map","title":"PIVOT: Bridging Black-Scholes Implied-Volatility and Price Objectives via Differentiable J\\\"ackel Operator","url":"https://arxiv.org/abs/2606.17065","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.17065v1 Announce Type: cross \nAbstract: Modern option-learning systems operate in two coordinates: price space, where markets quote and no-arbitrage constraints are most naturally enforced, and implied volatility (IV) space, where volatility surfaces are smoothed, regularized, and evaluated. The bottleneck is interface, not approximation: J\\\"ackel's seminal \"Let's Be Rational\" (LBR) solver already inverts the Black-Scholes price to machine precision efficiently. What is missing is a differentiable layer that preserves LBR in the forward pass and avoids backpropagating through its branch logic. Such a layer must also confront the unavoidable singularity of the inverse map in the low-vega regime, where the sensitivity 1/vega diverges as vega -> 0.\n  We close this gap with PIVOT, the Price-Implied-Volatility Objective Translator. PIVOT keeps the LBR forward pass intact and supplies the backward pass by implicit differentiation through the smooth Black-Scholes/Black-76 price map","title":"PIVOT: Bridging Black-Scholes Implied-Volatility and Price Objectives via Differentiable J\\\"ackel Operator","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/2606.17065"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c32fdf1f024432e9f726c9d47354e8ab3e6533e26ee68b7b2d2c6bb0e8a911f0c4068ad45a6c8bcd78a9dc57db75a62ca7b6eba34b9eca5bc6723630b50c3802","signer":"crovia.substrate","subject":{"observed_at":"2026-06-17T04:43:17Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.17065"},"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":"6549e8ce43790e416349c4ecf0557a3276a599ec47b6a1fb8d7e1a5faf4b4672","leaf_index":230909,"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":"b01dbf76feb08027251ddbe4556c7d567f1db2230b5e5310490669089dd58924","side":"left"},{"sibling":"9fe11fabae222c9dd7e3a84f4e5da3a5236d74ac29491f23eec7e67442806830","side":"right"},{"sibling":"4acec605b2b8ce3389e04671540a5c719d888f7903912f8a926705683f6a605f","side":"left"},{"sibling":"9b6fd30be8c55b260027c28dba41281a0daf915a3c007fec59d4660b723a4f3f","side":"left"},{"sibling":"6ef59cd13612915ae8cfb063e8fd2cbcddba67e7ba1315c8d17df045cb05ee9d","side":"left"},{"sibling":"0ea7cb1318c990633617d0034c42c8725926210f070f03a1846dcf1c8d46d947","side":"left"},{"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_937cd748d26e81fc5b6cfecf2278cedee5a47a476cb72b383e8e4e929eac669d"}}