{"_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_d9e010a249d4fd517eed246feb5abe663b26007b4908cf6dd1c03f991bec35d8","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_d9e010a249d4fd517eed246feb5abe663b26007b4908cf6dd1c03f991bec35d8","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"e901766c8651bbce08cbe619ce539cf9584c374201851fe3a33255177c011e0e","published":"Sat, 06 Jun 2026 00:00:00 -0400","receipt_hash":"e901766c8651bbce08cbe619ce539cf9584c374201851fe3a33255177c011e0e","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":"e901766c8651bbce08cbe619ce539cf9584c374201851fe3a33255177c011e0e","observed_at":"2026-06-06T04:43:19.193968Z","parent_run_hash":"550d5b02674822f43975c282be668ca76a4d9c7c957eb1601ba8b07dcb67715e","published":"Sat, 06 Jun 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:2605.30747v2 Announce Type: replace \nAbstract: Logical rules constitute a cornerstone of knowledge graph (KG) reasoning, valued for their interpretability and ability to model relational patterns. However, existing rule mining methods predominantly focus on simple chain-like rules and therefore neglect the richer relational information encoded in graph-like structures, such as cycles and branches. This limitation is further exacerbated by computational bottlenecks caused by the combinatorial explosion of the search space, which is especially challenging for graph-like rules. Meanwhile, generative approaches such as diffusion models, despite their success in other domains, cannot be directly applied to rule mining because their training objectives are not aligned with the goal of learning high-quality rules, and non-differentiable KG rule quality metrics cannot directly guide model optimization. To address these limitations, we propose GRiD, a framework that reformulates graph-lik","title":"Generating Graph-Like Logical Rules for Knowledge Graph Reasoning via Diffusion Models","url":"https://arxiv.org/abs/2605.30747","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.30747v2 Announce Type: replace \nAbstract: Logical rules constitute a cornerstone of knowledge graph (KG) reasoning, valued for their interpretability and ability to model relational patterns. However, existing rule mining methods predominantly focus on simple chain-like rules and therefore neglect the richer relational information encoded in graph-like structures, such as cycles and branches. This limitation is further exacerbated by computational bottlenecks caused by the combinatorial explosion of the search space, which is especially challenging for graph-like rules. Meanwhile, generative approaches such as diffusion models, despite their success in other domains, cannot be directly applied to rule mining because their training objectives are not aligned with the goal of learning high-quality rules, and non-differentiable KG rule quality metrics cannot directly guide model optimization. To address these limitations, we propose GRiD, a framework that reformulates graph-lik","title":"Generating Graph-Like Logical Rules for Knowledge Graph Reasoning via Diffusion Models","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-06T04:43:19Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.30747"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:93c0dcce5ef69dd1538b8057a0ea3fdde81363a47dc19b12fd1c0dc4db5c476a82de12d641e54f068decccd0a9c5ab31d953e4141e49c5ef46510a96795eb70c","signer":"crovia.substrate","subject":{"observed_at":"2026-06-06T04:43:19Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.30747"},"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":"ddc66b61f75c678949364745f63ee4019f39fe8203304a42698dc9348ee57b4d","leaf_index":219451,"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":"ba2a56d29fd42bef92d48e4d146353550d424256c7778d84b9813f9ea9388609","side":"left"},{"sibling":"79e3ab4ea83bbc37d89f48cc7ee2caa06b105090e3264b38dabaf7e38ab6b0c3","side":"left"},{"sibling":"b435e6c96148b6d1b4407aa96e08b83d6fab315ee71f2da81becf6e6904cafca","side":"right"},{"sibling":"924986411f7e63a3992ab06b5099d0a99a5adf652879b36e09ea7fe0fac5dafc","side":"left"},{"sibling":"a9fb24083dd30e49c07d1b9506502e8308b57e61814dfa0154b8e77e38c2340f","side":"left"},{"sibling":"0533945d48fc5cfd005a76d7e01ac78a1ad97725a2e0650037feaf4a36bde567","side":"left"},{"sibling":"c6d85f421226f83ff8cf32aaff89929d6dc9d5d94759254073631ced17a73907","side":"right"},{"sibling":"242ec7690d5995e1b5c2e94f2a8cedd5416b170d2db6fb44c95d0f9fb134a235","side":"right"},{"sibling":"42875175baa73c49869c927a23711e8bef732331ce49af85fa7e86d0903b1066","side":"left"},{"sibling":"84d2509eab51047589142ed6da8c496305d2fbcbe148e0e6755163db2c7a4bc4","side":"right"},{"sibling":"9e3ea17e834fab022f2eabcfedb8ea0ac95c1f9fb57edc5004dded68522d3c9e","side":"right"},{"sibling":"41d58fea95a95071715ee23ef8bcd15f5867a3639da28e62a0641bc95eb83094","side":"left"},{"sibling":"27ad9d6a9ab792d708709017242a61b9ca519da4e035f87a342811aae221d000","side":"left"},{"sibling":"5f303e2a7840c60038ff2d035b1cd911feefb0fba880de2d737c6671ace594d4","side":"right"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"1a61eadbf0217d063ab78291ccafdc0c92907f7d6ccdc3357534ef89f07d78ae","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":219672,"merkle_root":"d3e32d3a61ca02ce6b1f0b2db86721107770b250e8a5bf762a2c225d2f03c870","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260606T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-06T05:38:35Z","sig_algorithm":"ed25519","signature":"dab214c2d4d857f01383c8e93a521a774b1aba60eaee5677d4e43e4074f0342b2c6a9b9bfcff0eba74f7ac81fcb490dd0e43727979c1a7e8979c7e11547fb101","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_d9e010a249d4fd517eed246feb5abe663b26007b4908cf6dd1c03f991bec35d8"}}