{"_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_e74a3ac1e9989790ffe1f36ee3ddd7e268bf07b5facae753aa192d81666072df","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_arxiv_retraction_v1","root_at_anchor":"spider_arxiv_retraction_v1"}],"axiom_id":"axm_e74a3ac1e9989790ffe1f36ee3ddd7e268bf07b5facae753aa192d81666072df","axiom_type":"AX.OBS","body":{"axiom_subtype":"research.arxiv_retraction.v1","category":"research","fingerprint":"4713ff04a0409292c858e54d172ebda2f94940ba2522e4e33ed6052ce17fd307","published":"2026-05-01T13:30:23Z","receipt_hash":"4713ff04a0409292c858e54d172ebda2f94940ba2522e4e33ed6052ce17fd307","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":"4713ff04a0409292c858e54d172ebda2f94940ba2522e4e33ed6052ce17fd307","observed_at":"2026-05-04T05:51:15.429844Z","parent_run_hash":"b820e1a785ef2b5287cdf8b4331180ef61462b84b48082898446c6ba89a1437c","published":"2026-05-01T13:30:23Z","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withdrawn+OR+abs:retracted%29&max_results=20&sortBy=submittedDate&sortOrder=descending","spider":"arxiv_retraction","summary_excerpt":"Assigning one of K options to each of N groups under a total cost budget is a recurring problem in machine learning, appearing in mixed-precision quantization, non-uniform pruning, and expert selection. The objective (model loss) depends jointly on all assignments and does not decompose across groups, which prevents combinatorial solvers from optimizing the true objective directly and limits them to proxy objectives. Evolutionary search evaluates the actual loss but lacks gradient information, while penalty-based methods provide gradients but enforce the budget only approximately and require sensitive hyperparameter tuning. We observe that under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with particularly simple geometry: the normal vector is available in closed form, shifting logits along the cost vector changes expected cost monotonically, allowing binary-search retraction, and vector transport reduces to a single inner product. Buil","title":"Budget Constraints as Riemannian Manifolds","url":"https://arxiv.org/pdf/2605.00649v1","vendor":"arxiv"},"summary":"Assigning one of K options to each of N groups under a total cost budget is a recurring problem in machine learning, appearing in mixed-precision quantization, non-uniform pruning, and expert selection. The objective (model loss) depends jointly on all assignments and does not decompose across groups, which prevents combinatorial solvers from optimizing the true objective directly and limits them to proxy objectives. Evolutionary search evaluates the actual loss but lacks gradient information, while penalty-based methods provide gradients but enforce the budget only approximately and require sensitive hyperparameter tuning. We observe that under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with particularly simple geometry: the normal vector is available in closed form, shifting logits along the cost vector changes expected cost monotonically, allowing binary-search retraction, and vector transport reduces to a single inner product. Buil","title":"Budget Constraints as Riemannian Manifolds","vendor":"arxiv"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-04T05:51:15Z","notes":"Spider arxiv_retraction (research) research.arxiv_retraction.v1","object":{"captured_by":"crovia.spider.arxiv_retraction","primary_source_url":"https://arxiv.org/pdf/2605.00649v1"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:bb09f34bbb7234ea857c04dd9ac51e41ae686d9606dcbe6824f1b0b3544560e1d6d8ab2b0f986ff58eef0180047d9f4086cfc250891c2e9af12ffb1769ae6509","signer":"crovia.substrate","subject":{"observed_at":"2026-05-04T05:51:15Z","source_collector":"spider:arxiv_retraction","target_id":"https://arxiv.org/pdf/2605.00649v1"},"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":"fefa5d3686f986b3b59e8c387981e0bf7c1fbb331ed22833e992df4cb245eee3","leaf_index":112842,"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":"90ddacdeaec4144cb1d2d65358a03b7eb423c3eca5c416a1d476296a0cae04d4","side":"right"},{"sibling":"0bf87ec30206cb978f1f5ac587c34fa43cd402726ab128cb92e9d31b26e68cb6","side":"left"},{"sibling":"d11b7de87084a30c767a680124774df9351a640533581392429d604a0222a786","side":"right"},{"sibling":"d860ccfcaec0dddd0590cdd0bbc3dd9681de67441c1b85b15c5009856d068a45","side":"left"},{"sibling":"8f2144ca77c8e35f5136c28d72bbf9856a01919955b9cca7fc7a1c7323ff4b56","side":"right"},{"sibling":"bd60ed35ff2b36c1cb0a4f41849a5ea83dea4314be378de40fa932291f796114","side":"right"},{"sibling":"7e97a18e3f0a778f0a420e6add4c64f50cab93ce5b15fe47b3c3568512717c6b","side":"left"},{"sibling":"23812954b6ef686d296d2f09de3cb207c0537f7ee28517df834cce2af77835a9","side":"left"},{"sibling":"567fba8b7605b46fb02359d53be2bf36001180fd89b2987ff5b19acfca573bf3","side":"right"},{"sibling":"d74f3a62630438aecc36029a34840a064f38e84be3f2a6bb15029b0b2debc8af","side":"right"},{"sibling":"732d4a75425fb5538d14685ba705b2dd88f7ba5b73b89571ed5ea3b6a6024f2c","side":"right"},{"sibling":"673cd6d27b696232f7f65e7a0733c7df6bc9fac3bcb569907ebb0de1c72c4bb2","side":"left"},{"sibling":"76d7c4385d71ae8104107105be66eddb792e01ed6e493db5a9b4eec5441abb76","side":"left"},{"sibling":"b03f005860bf95148ea89c703a32ca19ab7a2ca71b58bb628ff94a9edb8703b0","side":"left"},{"sibling":"21d1e30b556f553dc939fddc23e6367f0a7755ebe3dd489dc0001cef017beb7f","side":"right"},{"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_e74a3ac1e9989790ffe1f36ee3ddd7e268bf07b5facae753aa192d81666072df"}}