{"_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_2053a778f1b2c656a22580691160fb574dae7129fc75db5ad234e54e71d15b77","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_2053a778f1b2c656a22580691160fb574dae7129fc75db5ad234e54e71d15b77","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"a7750d1d6670b547d6e6ab5ad4e609664a69e7fdea703265babc03479d485cb6","published":"Fri, 10 Jul 2026 00:00:00 -0400","receipt_hash":"a7750d1d6670b547d6e6ab5ad4e609664a69e7fdea703265babc03479d485cb6","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":"a7750d1d6670b547d6e6ab5ad4e609664a69e7fdea703265babc03479d485cb6","observed_at":"2026-07-10T04:43:53.465232Z","parent_run_hash":"06997be187ba20932a2030c56de194579eacf484085252a25bee544eab183e91","published":"Fri, 10 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:2604.22951v2 Announce Type: replace \nAbstract: Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models better learn these long-tail skills, we find a counterintuitive result: across a wide range of compositional reasoning tasks, such as state tracking and multi-step arithmetic, training under power-law distributions consistently outperforms training under uniform distributions. To understand this advantage, we introduce a minimalist skill-composition task and show that learning under a power-law distribution provably requires significantly less training data. Our theoretical analysis reveals that power law sampling induces a beneficial asymmetry that improves the pathological loss landscape, which enables models to first acquire high-frequency skill compositions with low data complexity, which in turn se","title":"The Power of Power Law: Asymmetry Enables Compositional Reasoning","url":"https://arxiv.org/abs/2604.22951","vendor":"arxiv_cs_ai"},"summary":"arXiv:2604.22951v2 Announce Type: replace \nAbstract: Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models better learn these long-tail skills, we find a counterintuitive result: across a wide range of compositional reasoning tasks, such as state tracking and multi-step arithmetic, training under power-law distributions consistently outperforms training under uniform distributions. To understand this advantage, we introduce a minimalist skill-composition task and show that learning under a power-law distribution provably requires significantly less training data. Our theoretical analysis reveals that power law sampling induces a beneficial asymmetry that improves the pathological loss landscape, which enables models to first acquire high-frequency skill compositions with low data complexity, which in turn se","title":"The Power of Power Law: Asymmetry Enables Compositional Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-10T04:43:53Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2604.22951"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:e897ed30da77de2edcc5537454a8b2a5a4ec46ebc4c188e710fd4f4605aaa9da51ea2e4a0e1d180dce479fd96ffa3cc294c6d39e70bd5f8e3faedd8660ca610b","signer":"crovia.substrate","subject":{"observed_at":"2026-07-10T04:43:53Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2604.22951"},"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":"3c87df4136541a6aca10d4a85c6c0883a02cf4d991a4ffe18a16222b969bfb4b","leaf_index":299518,"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":"134fbee8ee307238a6e86ec51ac65b29e8bf231da97f2cea41a5deecf69e3a4a","side":"right"},{"sibling":"5dd4311c7b29842bd93fd412d03886476d34e1054bf353e6e4eafde9d3875ae5","side":"left"},{"sibling":"f265feb388275e5cc1be5a77d946f6bbb4582d727eec2932e8b9ca9d55a7bc92","side":"left"},{"sibling":"845287bd8324015e00fb64eb0a9db929e8d2c35f3341053251eb8890860556cf","side":"left"},{"sibling":"c21f29407248633afb08c2a86e6963f642dccb36cb2a7d3734060791238527d3","side":"left"},{"sibling":"1e8021b095c74bdab85562264f566a914165bb59331cdb96722f48e8df9f939a","side":"left"},{"sibling":"7a96803ed93140d8d4c0e1fe53c891fc73447ccfce6e55b7c43e7a06979f307a","side":"left"},{"sibling":"b1b72243c904808d4df9b283c65832a729a411520c97fd9d17f891f214971a0a","side":"left"},{"sibling":"2c5ce75ad134aa442d7fbb5dc9968b0f2e48097c2ffaa2111d405de1c4a9c48b","side":"left"},{"sibling":"36a2c507282befad57202dd10278a66d37b402692f195a22d2275b3d1b2488d8","side":"right"},{"sibling":"f80e8d47e0860527b906fc2dba9a52609f7f623f2772479ae922cc019bab36d9","side":"right"},{"sibling":"cae83500ab2c25555aa6b5eaf9232696d15a868d91b34f7531dd955daadf70f7","side":"right"},{"sibling":"64dab64d51bdcb909e2a5e37efb8909d6704ecf824be484b5d2b60ee6e518890","side":"left"},{"sibling":"576f134a23c19a758ae5efd53016092a74b9900e878cf6eb4f3dab6be682b395","side":"right"},{"sibling":"3c65f53d7c3e4feba7c745e8df1327760ffa768eec84336db14d515a31731532","side":"right"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"8728642cdb98496d916cc653f0d919d7eb2e89d0c529927c9e89091074ad584c","side":"right"},{"sibling":"8025674cb002a22ae243ca0c295c18c1d0ee119189ea88e08ac14a3a1468b8e3","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":299721,"merkle_root":"f7115d63193d3285ca28cb9f741ecea2513f9b3e492e785f97076f3cf8f9bb98","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260710T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-10T05:38:19Z","sig_algorithm":"ed25519","signature":"4eeedeb744885bff6523d66b1cb86bde62b36917696367addfd980d90b31011daece2e01b20608e4c0870ec31dd0bcb57d297447f01f153bf0716ad527142b00","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_2053a778f1b2c656a22580691160fb574dae7129fc75db5ad234e54e71d15b77"}}