{"_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_11c31021301c9ed82960f08151b4e05a83347b9d6a8f053888581988507528d5","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_11c31021301c9ed82960f08151b4e05a83347b9d6a8f053888581988507528d5","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"4bd1d878c53e83bd735beedf87592291ec9c3605661a716889e2ac48b111ac59","published":"Wed, 08 Jul 2026 00:00:00 -0400","receipt_hash":"4bd1d878c53e83bd735beedf87592291ec9c3605661a716889e2ac48b111ac59","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":"4bd1d878c53e83bd735beedf87592291ec9c3605661a716889e2ac48b111ac59","observed_at":"2026-07-08T04:43:57.834712Z","parent_run_hash":"46ab019f0b0f0bfcde5e14ed7c256069c6fa8c8079b9f87fd3a8a6d9259e3864","published":"Wed, 08 Jul 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:2602.22600v2 Announce Type: replace-cross \nAbstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function. Studying any single trained neural network thus risks describing accidents of one training run rather than the computation itself. This work shifts focus from what transformers happen to do to what they must do by extracting algorithmic cores, compact subspaces that are necessary and sufficient for a task and that recur across independently trained models. Here, Algorithmic Core Extraction (ACE) is introduced to isolate these subspaces, causally validate them, and recover the algorithms they implement across settings ranging from synthetic tasks to large-scale pretrained models. Markov-chain transformers embed three-dimensional cores in nearly orthogonal subspaces yet recover identical transition spectra. Modular-addition transformers form compact cyclic cores at grokking that later inflate under continued regularization, r","title":"Transformers converge to invariant algorithmic cores","url":"https://arxiv.org/abs/2602.22600","vendor":"arxiv_cs_ai"},"summary":"arXiv:2602.22600v2 Announce Type: replace-cross \nAbstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function. Studying any single trained neural network thus risks describing accidents of one training run rather than the computation itself. This work shifts focus from what transformers happen to do to what they must do by extracting algorithmic cores, compact subspaces that are necessary and sufficient for a task and that recur across independently trained models. Here, Algorithmic Core Extraction (ACE) is introduced to isolate these subspaces, causally validate them, and recover the algorithms they implement across settings ranging from synthetic tasks to large-scale pretrained models. Markov-chain transformers embed three-dimensional cores in nearly orthogonal subspaces yet recover identical transition spectra. Modular-addition transformers form compact cyclic cores at grokking that later inflate under continued regularization, r","title":"Transformers converge to invariant algorithmic cores","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-08T04:43:57Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2602.22600"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:4f63fe7d46c267a5ecfdfaaf79f145cb21b928f66f558c627a8a198249f544153b10c4fe08cecf3266774a05a2c4ee35cda3decf100f14d39694b991d74cb704","signer":"crovia.substrate","subject":{"observed_at":"2026-07-08T04:43:57Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2602.22600"},"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":"06ca90a9f50b17148783bc13e4c3f9416ba14d4f7dcf6b3fea3adc947ef772a2","leaf_index":292841,"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":"e4e0db4aed63c2f095f6898b3768e6fe30c0636134a70e365ea8a396cf82c73d","side":"left"},{"sibling":"b7bba9fdd05c8e90f4f58c67a038bd07e0176eb013b622a53f2b8c8e66dd5ef1","side":"right"},{"sibling":"f5c31eabc8361c56e2f9584e78e5ac51133742ca69ba1cadff5804017b566ce2","side":"right"},{"sibling":"eb69990a0d55e44a86a43599123534211c0a46338021e872cb3459f5c6c30e73","side":"left"},{"sibling":"0202c453a3948e9013eb5a6cb389c144d27f22e10ea2037f465ba4bfa492d55c","side":"right"},{"sibling":"2209adb7e32bdc00faa3455b10e6e84ea7382544d1d0331dbeed97777453e5be","side":"left"},{"sibling":"b68effed96c9c760c6a644ba421552cb75cab0f5269153819ebc6ee58c6e16f1","side":"left"},{"sibling":"6e4b9570930ece9a9ba8eab260493982ccceb0060de1dddb4ef505f9f3d00598","side":"left"},{"sibling":"1515812edbf9903d3d787f20218b8577e2f1fef32592508ce01a3b3ebe75f507","side":"left"},{"sibling":"d4b475beae71e5b4d5ab7e66f7144e7b8e1356fcd32339e49df234b455659fef","side":"left"},{"sibling":"cead64e0790e8871aeea2334210146b5e35fe7e4bc10748acdf76da0c565be05","side":"left"},{"sibling":"d1231ac6e6bd7d6867a9109fbdadede0b1631e97866ddde70f7ac2d52c28e15f","side":"right"},{"sibling":"76855b4804c75c52bf97aa34358950d42d6103cdc1a86be5f0a2c8de4d65c106","side":"left"},{"sibling":"a75ab4319e241beeddb1b3f5705febe0422937926c3479923ccfb0b0082fa4e3","side":"left"},{"sibling":"bd04fa605f883bfb2b81510d045b1e85e555a03da3be083619f61384dfe40ff8","side":"left"},{"sibling":"9e75f2ab0ddf2dc9e92af7049244c21b909734ab57906a35dfad2853ca9966e2","side":"right"},{"sibling":"e6cd4cad39a4b6ca6647d1b0ad2db86e57e5fa6240f65966c10093e91140769b","side":"right"},{"sibling":"90a7efc6b94ec8913fbdf03f4927a821b9fb89921d526716f5ee28f015303779","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":292998,"merkle_root":"f533b7efebdfd8fb6ba3e7cc158ee55261fd53a7985f234cfea359170dad4d5a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260708T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-08T05:38:17Z","sig_algorithm":"ed25519","signature":"07ebb10c732bbffb28b55a5db01d5525f6b8ab7ef36e1e0a68c35c96ded99f7040c277edba75eb6b15c77feda30bd5321e31ada6f572b674d06f4f8e24bd2f07","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_11c31021301c9ed82960f08151b4e05a83347b9d6a8f053888581988507528d5"}}