{"_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_a835ab307d7b7cd3c055c6ad631543e442ece17e4ae5dd8b3fd5497112e5b50c","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_arxiv_retraction_v1","root_at_anchor":"spider_arxiv_retraction_v1"}],"axiom_id":"axm_a835ab307d7b7cd3c055c6ad631543e442ece17e4ae5dd8b3fd5497112e5b50c","axiom_type":"AX.OBS","body":{"axiom_subtype":"research.arxiv_retraction.v1","category":"research","fingerprint":"2bb9d3941a3ba1a770c245cf6d68b9d9ba3ccc975c69806e6237feffeb0920ad","published":"2026-06-01T07:59:29Z","receipt_hash":"2bb9d3941a3ba1a770c245cf6d68b9d9ba3ccc975c69806e6237feffeb0920ad","schema":"spider.research.arxiv_retraction.v1","spider":"arxiv_retraction","spider_record":{"axiom_subtype":"research.arxiv_retraction.v1","category":"research","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"2bb9d3941a3ba1a770c245cf6d68b9d9ba3ccc975c69806e6237feffeb0920ad","observed_at":"2026-06-02T05:59:03.128606Z","parent_run_hash":"cf2c506e2a28a27578018b9fe1417e119d4d047eb4c60f42e6fd12e5097fbb61","published":"2026-06-01T07:59:29Z","runtime_version":"0.1.0","schema":"spider.research.arxiv_retraction.v1","source_status":200,"source_url":"http://export.arxiv.org/api/query?search_query=cat:cs.LG+AND+%28abs:withdrawn+OR+abs:retracted%29&max_results=20&sortBy=submittedDate&sortOrder=descending","spider":"arxiv_retraction","summary_excerpt":"Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\\mathbb{R}^{12}$ vectors. This approximation induces (1) manifold drift violating SO(3) constraints, (2) broken equivariance under coordinate transformations, and (3) non-geodesic trajectories with excessive kinematic cost. We introduce $\\textbf{Lie Diffuser Actor (LDA)}$, a diffusion framework operating intrinsically on SE(3). Our method injects noise through left-invariant SDEs, predicts scores in the tangent space, and retracts samples via the exponential map. This formulation eliminates manifold drift by construction while guaranteeing coordinate-frame equivariance and geodesic optimality. On CALVIN ABC$\\rightarrow$D, LDA improves average task length from $3.27$ to $3.51$ ($+7.3\\%$). We further validate our method on real robot and the results show that our methodology","title":"The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space","url":"https://arxiv.org/pdf/2606.01847v1","vendor":"arxiv"},"summary":"Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\\mathbb{R}^{12}$ vectors. This approximation induces (1) manifold drift violating SO(3) constraints, (2) broken equivariance under coordinate transformations, and (3) non-geodesic trajectories with excessive kinematic cost. We introduce $\\textbf{Lie Diffuser Actor (LDA)}$, a diffusion framework operating intrinsically on SE(3). Our method injects noise through left-invariant SDEs, predicts scores in the tangent space, and retracts samples via the exponential map. This formulation eliminates manifold drift by construction while guaranteeing coordinate-frame equivariance and geodesic optimality. On CALVIN ABC$\\rightarrow$D, LDA improves average task length from $3.27$ to $3.51$ ($+7.3\\%$). We further validate our method on real robot and the results show that our methodology","title":"The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space","vendor":"arxiv"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-02T05:59:03Z","notes":"Spider arxiv_retraction (research) research.arxiv_retraction.v1","object":{"captured_by":"crovia.spider.arxiv_retraction","primary_source_url":"https://arxiv.org/pdf/2606.01847v1"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:f062d6d6de6f87a57a556d4b1b700e7cc81398ee44bc41f65e359f7bcdef758ede094c6f250fd810cf868b5cac254baa109aebb5818c43b8a7b835ad28fa1806","signer":"crovia.substrate","subject":{"observed_at":"2026-06-02T05:59:03Z","source_collector":"spider:arxiv_retraction","target_id":"https://arxiv.org/pdf/2606.01847v1"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/research/arxiv_retraction_v1.jsonl\",\"source_seal_merkle_root\":\"spider_arxiv_retraction_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"694faf2f1b930f3c983a0b01cdeb6db71281ad8f7c720b3f6f0165b579dd0caf","leaf_index":206448,"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":"5df6596d4d91ba15f3efd882e1293afc84beef0d562655466aea53289246583f","side":"right"},{"sibling":"a9aa33c1bb6893acafd351c6e3725e0648bbc0b4da0103cd5d9cbaf8bfdfde7b","side":"right"},{"sibling":"5bc678ee9bfc493b69cbd4e38ff46cd52cc3073e3c541553186e59d0f002da4c","side":"right"},{"sibling":"a068819a29565faebd8a81dabb7481ea7e6a6723d8b43681f2e7dca74006e0ab","side":"right"},{"sibling":"3a67bf6bbf91ec30a8890f1084967697d3859b46009a19a8b132e3f9e02a1605","side":"left"},{"sibling":"34cafbe6451011dc2a7496bd932eccc9686d7a3e3f4a56b8fbf82bbbb825c29e","side":"left"},{"sibling":"20709dfcd56a8de655dc8ceb7f8ac4b8fc8233f2aae3466290002d17c679f534","side":"left"},{"sibling":"4003c9b715c4234bc58bc032831082d6adb17664fbb0675cd5a0d1d69a074d1b","side":"right"},{"sibling":"fba0df0f2006a9867063bdbf595b4dab0da3114f9d704fea047e8f211dd854f9","side":"right"},{"sibling":"dd3aa5e6086fa8c9b534debea14a99067b0f16d024e8684fba98544626bbb6e1","side":"left"},{"sibling":"e4bd1aaaf3f336d9b072b4d1fc234246fc3cf2874ca873b7741c03eaf97911f2","side":"left"},{"sibling":"568a7d55a0f581132d7cf0cc37265b86efb6c54d244e760cfbc4b837e4b2cccc","side":"right"},{"sibling":"eceedf82a379874cec4f9a8b776cec5c5f37c7aaaeba1f4887d211b9400ea6ff","side":"right"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"955efa64c284d754310e5921432a2db907919aae5ad2eda9c967f1bcf7a487c0","side":"right"},{"sibling":"accf1221b27ed6b0c41abb48141f2b9ab2d2fcaaf83eaa92c5bfa99fe4f19c28","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":206562,"merkle_root":"de3a1a98487dbbf0f767ce1fa148783fa66c07dcbf715dabcbbe10a49949b9d8","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260602T073701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-02T07:37:47Z","sig_algorithm":"ed25519","signature":"c757edc7a15c3e07e09f59540ff0763636d112253c9819218647725565b0968c31d61617cf5bb2faf49ff7d0138565ac86b4205481247ebd3d972158ca160e08","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_a835ab307d7b7cd3c055c6ad631543e442ece17e4ae5dd8b3fd5497112e5b50c"}}