{"_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_c4749ff1dff886a63e9ae553d8f19724008fc2a2c1916f735c01b08b98478292","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_c4749ff1dff886a63e9ae553d8f19724008fc2a2c1916f735c01b08b98478292","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"0e81107ffa90cc4e21646f8045c34a4101d7afae2566a4aa7eef4b537dfb93c7","published":"Tue, 21 Jul 2026 00:00:00 -0400","receipt_hash":"0e81107ffa90cc4e21646f8045c34a4101d7afae2566a4aa7eef4b537dfb93c7","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":"0e81107ffa90cc4e21646f8045c34a4101d7afae2566a4aa7eef4b537dfb93c7","observed_at":"2026-07-21T04:43:35.036805Z","parent_run_hash":"03e944014de2697434479833d15ea9303e014945afc230ecc7f207824493b589","published":"Tue, 21 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:2607.17240v1 Announce Type: new \nAbstract: When does a committed intermediate stage in an LLM reasoning pipeline earn its cost? Constrained Path Reasoning (CPR) pairs a source-aware path hypothesis with stage-level accounting. Search generates provisional states; trusted or validated invariants can constrain hard, while other proposals remain soft and revisable. CPR predicts that task-compatible commitments can factor transitions, concentrate candidate mass, induce regularity, and expose feedback when their gains exceed propagated error and execution cost. The formalism covers discrete commitments and continuous flows and measures effective branching, endpoint concentration, and cost per usable output. Across 1,180 generated QCQPs and 40 engineered degenerate polynomial instances (2,140 endpoints), residual triage recovers 63.0% of repair-all's additional feasible yield with 17.7% of its attempts. Fixed-LLM accounting (270 unique calls shared across nested arms) finds usable yiel","title":"Constrained Path Reasoning: Measuring When Committed Stages Earn Their Cost","url":"https://arxiv.org/abs/2607.17240","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.17240v1 Announce Type: new \nAbstract: When does a committed intermediate stage in an LLM reasoning pipeline earn its cost? Constrained Path Reasoning (CPR) pairs a source-aware path hypothesis with stage-level accounting. Search generates provisional states; trusted or validated invariants can constrain hard, while other proposals remain soft and revisable. CPR predicts that task-compatible commitments can factor transitions, concentrate candidate mass, induce regularity, and expose feedback when their gains exceed propagated error and execution cost. The formalism covers discrete commitments and continuous flows and measures effective branching, endpoint concentration, and cost per usable output. Across 1,180 generated QCQPs and 40 engineered degenerate polynomial instances (2,140 endpoints), residual triage recovers 63.0% of repair-all's additional feasible yield with 17.7% of its attempts. Fixed-LLM accounting (270 unique calls shared across nested arms) finds usable yiel","title":"Constrained Path Reasoning: Measuring When Committed Stages Earn Their Cost","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-21T04:43:35Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.17240"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:8d1212413368cfff9bcd40727753792236c2cef2e00695aabc9e4234dfa0b62bd6d67c4e2bf09fe5eac0c2a7f34910fe5653450661b5adf9e621ac79a3e71d0b","signer":"crovia.substrate","subject":{"observed_at":"2026-07-21T04:43:35Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.17240"},"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":"f1a9eb5d05ff5d4afedc995161968c76fd641e04b0806859446f57382dde8550","leaf_index":336569,"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":"740162c9989097fcf2587f5e9348838359f045e010abb74116f5d9beb335c467","side":"left"},{"sibling":"dff0df966fd0a114e91d1326123456037336ff1de7640985e23e375d8b211602","side":"right"},{"sibling":"b92aab770b7f95b87d527bc15e2d7343886c8f34aa67229115dcbc1d5f316610","side":"right"},{"sibling":"7d9a39b6f50e52a7cccdd4dd44969ac5c72f0a7b98ab3b44d1bd9877f9f7136a","side":"left"},{"sibling":"66bc434e6e19a9c80aa166a7e64214e7beacadeb9c643c50e05aaa4d312b52d1","side":"left"},{"sibling":"b3158e349ba0fe21d8867fdb1b0601bb48823d15155801611bab72f2e5d722d7","side":"left"},{"sibling":"a2ec0c96e7ee9134cdcbfc3f3d7279dabbae2ae36687e5158bdb5f7e8fc549cb","side":"right"},{"sibling":"e6f9d6d6c760446a7b30dd4e30a28f58c0817f4bee09529ee009c470d86f5564","side":"left"},{"sibling":"38e5827f7c9f72ad34a2b97042f2fb5f7e868db899d074b7819af4f2209b9caa","side":"right"},{"sibling":"7b927551b5db06b6571913b4e6792ffcce5291a3eca5a0df4a3b6e296271105f","side":"left"},{"sibling":"b77a0b5ae4607c8fe6ba73449d46b35076e3dedc0c82a2c65a05780d42a7bc2e","side":"right"},{"sibling":"9eb5077edfb3dc553857d4794b925bfce117e0f8a1d049af5d0dd9026b470eef","side":"right"},{"sibling":"414b1a70fd1dcb25489a194714b97492b066684b15d0b7a48a176c4b9b5bc713","side":"right"},{"sibling":"21d66dd41003813f710b7617944f1bfba3258658a5d3370c21cad8f9e945bc99","side":"left"},{"sibling":"613f015699131eb89bd755dee67133be95af25cf5f16c1c8ce4b99d963b8dd86","side":"right"},{"sibling":"a729b574b1135956436ded5eef1fe8f08014ff6a0729749d307ab1bca93fcdc9","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"4bf21052e085e8ac81f1dec1d2b310bd12bf948992de6177d12e9d2fda8d39f0","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":337144,"merkle_root":"5e969cc01afa67e4dbe5d37b712cdb10f4aa1fd74404e02eab724cf487c8d6d9","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260721T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-21T05:38:38Z","sig_algorithm":"ed25519","signature":"5c0c1a8dd2793d787ccd5e49e8b4d70eed136352555518589f05c74be357fc171702e42a76c3a556d90e3d51ff36cb3d292aaac83c66566de7b943f318bda50c","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_c4749ff1dff886a63e9ae553d8f19724008fc2a2c1916f735c01b08b98478292"}}