{"_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_345105f498a4065055aee4f25d63d140b1e817cc0e4fc32dd089c41735b0ba58","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_345105f498a4065055aee4f25d63d140b1e817cc0e4fc32dd089c41735b0ba58","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"866df1793ae53603a281697ac7931bdbc5d3aeb71b0232e673c0c3be305f73ed","published":"Tue, 09 Jun 2026 00:00:00 -0400","receipt_hash":"866df1793ae53603a281697ac7931bdbc5d3aeb71b0232e673c0c3be305f73ed","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":"866df1793ae53603a281697ac7931bdbc5d3aeb71b0232e673c0c3be305f73ed","observed_at":"2026-06-09T04:43:45.619596Z","parent_run_hash":"f2344865fd128464efd1bacba326b5a7ccea707694b8c5650dd51ae8c46ac8a1","published":"Tue, 09 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:2606.04227v2 Announce Type: replace-cross \nAbstract: We present an algorithmic framework for incremental maintenance of first sheaf cohomology $H^1(X; \\mathcal{F})$ on dynamically evolving 1-dimensional cellular complexes equipped with finite-dimensional cellular sheaves. The classical computation of $H^1$ via factorization of the coboundary matrix requires $O(n^3)$ time; when the complex evolves with a stream of $m$ edits, full recomputation after each edit costs $O(mn^3)$.\n  Under a bounded local geometry assumption -- bounded cell size $v_{\\max}$, bounded stalk dimension $d$, and bounded nerve degree $D$ -- each edit (vertex insertion, edge insertion, restriction map update) affects only a bounded set of local coboundary blocks. The algorithm therefore processes lazy streaming edits in $O(1)$ time with respect to the total complex size $n$ (with cost polynomial in the local geometry parameters $v_{\\max}$, $d$, and $D$, which are treated as constants independent of $n$), deferr","title":"Incremental Sheaf Cohomology on Cellular Complexes: O(1)-in-n Lazy Edit Processing under Bounded Local Geometry","url":"https://arxiv.org/abs/2606.04227","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.04227v2 Announce Type: replace-cross \nAbstract: We present an algorithmic framework for incremental maintenance of first sheaf cohomology $H^1(X; \\mathcal{F})$ on dynamically evolving 1-dimensional cellular complexes equipped with finite-dimensional cellular sheaves. The classical computation of $H^1$ via factorization of the coboundary matrix requires $O(n^3)$ time; when the complex evolves with a stream of $m$ edits, full recomputation after each edit costs $O(mn^3)$.\n  Under a bounded local geometry assumption -- bounded cell size $v_{\\max}$, bounded stalk dimension $d$, and bounded nerve degree $D$ -- each edit (vertex insertion, edge insertion, restriction map update) affects only a bounded set of local coboundary blocks. The algorithm therefore processes lazy streaming edits in $O(1)$ time with respect to the total complex size $n$ (with cost polynomial in the local geometry parameters $v_{\\max}$, $d$, and $D$, which are treated as constants independent of $n$), deferr","title":"Incremental Sheaf Cohomology on Cellular Complexes: O(1)-in-n Lazy Edit Processing under Bounded Local Geometry","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-09T04:43:45Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.04227"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:3d410b6344c88f3a7c7087b4acc6802a005e905bdfbfdb809527fcc4ea215b11ec8d6d4916e57c1de601ebbe83f2b8e9776736b4e9260f39309aee202adcf00b","signer":"crovia.substrate","subject":{"observed_at":"2026-06-09T04:43:45Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.04227"},"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":"b526f4f3cd6a90c1705be374dc048a6efda7238dce68fef7994f861ef482cd43","leaf_index":224690,"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":"70dabbb123034408968b0e40be0d4fc3d23d122306d68478f98649954505a5fa","side":"right"},{"sibling":"4909bf1f4b98e5d7c178891297949054c8c91c16d79d1d8afd981ae0decf4a2a","side":"left"},{"sibling":"7ccc920884e4b9bc3c74b1574445780965c00e0e06976c013494977b34a7d909","side":"right"},{"sibling":"0bf3f4f23ad15064f1dc963444f51f575d9b7759c01f84d4bf0ff2e8e02fb418","side":"right"},{"sibling":"e3bf0df763dd4580cc1e1abd1f639ab33997dcef21ad1fd14cae8f7fff7aad75","side":"left"},{"sibling":"9dfd4d3f39a1bf5e5705287678bd50c01bc0d905a0fb2b521f834d05098ec8b2","side":"left"},{"sibling":"4cbc852b1c806f43d24027ee52115a44c6a67dd27328071cc246f77bbd500a57","side":"right"},{"sibling":"61f5edd06f165b7eb528418b7a3a490a1a565a01078352981f9463fd513fc29e","side":"left"},{"sibling":"f54580a307d4bb82e453931aa73e9a0c590486cb8df06af79ad4674f1c4f6963","side":"left"},{"sibling":"b2df6a4bb3e928f0b447931cc688ae01d2415773a2b07cfed0b1cba689078aed","side":"right"},{"sibling":"b1c9ec856caa0fd46bb47b46f18c59ebcd295d774ca17adb3b46f05d394a6a5d","side":"left"},{"sibling":"24fdc29d461691aedb6fa920758206b5bb43851f477ef7a04c34aaed84b8971b","side":"left"},{"sibling":"036922da4e1e2c46d948f070454bfad299b7406fb00735ea9d8bd1e687f5f445","side":"right"},{"sibling":"533d82482604463aa4a281b9d8b85917b383b7c5f924b2b494039524c55e8797","side":"left"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"87c6b850dfec08ac35a693d9db3a3315250a68adb1cfab9b1015f212b63b15bd","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":224761,"merkle_root":"e9f7b49b652e869ab97ffba9c5a31356b2d0e3dc5d00bb28944adf737c46b1e7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260609T103805Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-09T14:15:34Z","sig_algorithm":"ed25519","signature":"8ad8076fb12c8e486ae1d1559a9a7ba8e2ee996a9ad3d8ba7bcdbdbd88ab3a15bcb429707aca6d3e9d8b97e2ba755b3dcc77b1abb6601ccb829842719a6fb30d","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_345105f498a4065055aee4f25d63d140b1e817cc0e4fc32dd089c41735b0ba58"}}