{"_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_136e7511a3e05829eaf781da02da6ca1eb0af56afd445c281b44c7bf582cd15b","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_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_136e7511a3e05829eaf781da02da6ca1eb0af56afd445c281b44c7bf582cd15b","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"f50db73a6877d7d6d121d2ac6d798d85b67c88fbb5fc0c68e5b5266e01112698","published":"Fri, 29 May 2026 00:00:00 -0400","receipt_hash":"f50db73a6877d7d6d121d2ac6d798d85b67c88fbb5fc0c68e5b5266e01112698","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":"f50db73a6877d7d6d121d2ac6d798d85b67c88fbb5fc0c68e5b5266e01112698","observed_at":"2026-05-29T04:43:58.478092Z","parent_run_hash":"0fcd87efcfe67ccb9952f747541debc16793919a4d20fd71ca0ad5516a0a13ee","published":"Fri, 29 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:2605.25413v2 Announce Type: replace-cross \nAbstract: Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error accumulation over long-horizon rollouts. In this work, we propose Autoregression-Free Neural Operators (AFNO), which map the time evolution of PDEs into a latent space and model continuous-time vector fields within it. AFNO uses flow matching to learn the latent vector field, thereby enabling continuous evolution over extended horizons, avoiding autoregressive rollout and capturing dyna","title":"Autoregression-Free Neural Operators for Time-Dependent PDEs","url":"https://arxiv.org/abs/2605.25413","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.25413v2 Announce Type: replace-cross \nAbstract: Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error accumulation over long-horizon rollouts. In this work, we propose Autoregression-Free Neural Operators (AFNO), which map the time evolution of PDEs into a latent space and model continuous-time vector fields within it. AFNO uses flow matching to learn the latent vector field, thereby enabling continuous evolution over extended horizons, avoiding autoregressive rollout and capturing dyna","title":"Autoregression-Free Neural Operators for Time-Dependent PDEs","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-29T04:43:58Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.25413"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:275630d2d95ceec2e62d431c61c93bcf0aaf054a07d03adc9c8f19030d66574f325702f443fc21480985ed081cf89f43f6d774c3eadca5da7da9c2ead05bb807","signer":"crovia.substrate","subject":{"observed_at":"2026-05-29T04:43:58Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.25413"},"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":"cde1435d592242718f8de1aae31c07e5765eed9d0dbc1fb416559ba8d8e101f6","leaf_index":158186,"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":"99bb6949ff8cf93b2c7c9680d593f92cc5d6c1f8dc95dd99e8a0b8916830b697","side":"right"},{"sibling":"cc71ca0ad06f5335697995d720dc01ac467ae054b5714ff85b4fcc3233ee8c04","side":"left"},{"sibling":"5513625558bd803ee2f7f02e407deee627e286007753ebf1c70e60d91de15177","side":"right"},{"sibling":"a9ad3b2a6f31764abee5e3be03ec01ecf4e4c3f2ccd141487550904770014ea2","side":"left"},{"sibling":"9490e3b60f7c33ffe83725c1ff81136aedde2518ea53ee2f9bc8ea5c1e71ed43","side":"right"},{"sibling":"682a65c5be3c1bc5d64a09340a34e0702bf499b96139c8bf17318babc5920016","side":"left"},{"sibling":"2496d8181c3184c4ea7973d99293dedbb754d677261137e3c8c5546635804645","side":"left"},{"sibling":"463d4726f68bda2bbf724c72553fd53d88ea99a3d4a713f9b8a1b2d9fde12933","side":"left"},{"sibling":"002471ff5893cd2a2890119cbfe4a9456bfb46cf31fa6aee377650afe6ae0c92","side":"left"},{"sibling":"1dcc44e23fbb0218b13591e4b584eca3600dcf365769cb741e0ecd33b25b8c56","side":"right"},{"sibling":"fcf16a6f44025801f5b83e928acce764352ddbc06ae3043d8cde9a409933e6d8","side":"right"},{"sibling":"78982294dee68f9db9288c64d7e507c7865fda96e1b6f7ccff5c8bb152e93c49","side":"left"},{"sibling":"995b421824624a8282c7f44e64c64ee35344800f477ae1845b41be14d3fab94c","side":"right"},{"sibling":"66331bac84ca0f8983eb09fac7eaf95af234f1b82680b793eabff4ee25caac40","side":"left"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"eef0e8906a749d3470f89beeedc723f37a5737010bbb0dcc7cf91515338e5a3e","side":"right"},{"sibling":"1a07e481a9407d71aad078ce854cdeee362163c887fe10f889b0ecf0b5e749ad","side":"right"},{"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":158251,"merkle_root":"485e6b31fe60c8beba5b394808c7e4c32448b2ff65c2482c480ca0e2a2eda718","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260529T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-29T05:37:37Z","sig_algorithm":"ed25519","signature":"bbf9f005201182fce4f9d94c7a9d01a508b56daf7d9611bd73514f5f616bc059d0e5e1f2edfc95716e6fe08ef5fae38b558cbf7f2fd8f9d5dfe4c34a54c83005","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_136e7511a3e05829eaf781da02da6ca1eb0af56afd445c281b44c7bf582cd15b"}}