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We study which graph value extensions are planner-admissible under the operational argmin-Q planner. Our main result is a local action-gap certificate: if the surrogate value error along the rollout stays below half the true action gap, then the greedy rollout reaches the goal. Absolutely Minimal Lipschitz Extension (AMLE), the p=infinity endpoint of the graph p-Laplacian family, instantiates this certificate through a comparison-principle fill-distance bound. Harmonic extension, by contrast, can mis-rank local actions because its values reflect boundary hitting probabilities rather than shortest-path greedy order.\n  On 120 AntMaze layout-derived graph configurations, harmonic extension achieves 0.584 a","title":"Planner-Admissible Graph-PDE Value Extensions for Sparse Goal-Conditioned Planning","url":"https://arxiv.org/abs/2605.19185","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.19185v1 Announce Type: cross \nAbstract: Sparse goal-conditioned planning with few cost-to-go labels can be viewed as a graph-PDE Dirichlet extension problem: extend sparse labels on a goal-dependent boundary to unlabelled graph vertices so that greedy rollouts reach the goal. We study which graph value extensions are planner-admissible under the operational argmin-Q planner. Our main result is a local action-gap certificate: if the surrogate value error along the rollout stays below half the true action gap, then the greedy rollout reaches the goal. Absolutely Minimal Lipschitz Extension (AMLE), the p=infinity endpoint of the graph p-Laplacian family, instantiates this certificate through a comparison-principle fill-distance bound. Harmonic extension, by contrast, can mis-rank local actions because its values reflect boundary hitting probabilities rather than shortest-path greedy order.\n  On 120 AntMaze layout-derived graph configurations, harmonic extension achieves 0.584 a","title":"Planner-Admissible Graph-PDE Value Extensions for Sparse Goal-Conditioned Planning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-20T04:43:44Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.19185"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c2dd055c1990b1a32aea169f20ef015e6aa87a93d782ca0b4b618b2e4ea6374a2a08dff4c52506ee4aac7c832fe8dcd6dacc90e1c8637e1277a97dcd5f4bc90d","signer":"crovia.substrate","subject":{"observed_at":"2026-05-20T04:43:44Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.19185"},"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":"23ff7ba0c18b3eb45cd166eae1b12b40dda7fa561e04030ea96ed7301ae16ad9","leaf_index":145086,"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":"af73c678c63701fe0f292cb6a838448918f1ce1a8bd1dd7543b385a00434ebe5","side":"right"},{"sibling":"e12e63d018c0bff9d65345395e9390907b0cac133fb06e28cb24bfa7775630cf","side":"left"},{"sibling":"70bb782e9ad669b2b4e2a91ee630035512397fed9fee601414ef1351f33f4803","side":"left"},{"sibling":"9cf4a0e9ee02e6d8cca45a64d2e0810236fcbc986fa412ce0439039255d39cfa","side":"left"},{"sibling":"224bed9cafef62f1104019003daf8283dc33b820202293989f0d7d19434d49cf","side":"left"},{"sibling":"6498b36e278698012393fb252639299d44ff76d3bbc2b98f93604927ea46e4ae","side":"left"},{"sibling":"3c054fc9610e75398c84d6602026026e93d4cc85db18f6da86b0e99184718c59","side":"right"},{"sibling":"3047d0cbdc103ff93a1a073ea940e12ff062595dae419513748ed63fbcb3359c","side":"left"},{"sibling":"9db04d2181fb869f16a5baf7dcfe999cc93a7e9beef8493d0cc71f57470fe5e1","side":"right"},{"sibling":"1526885f19d1fadf6955cf519dbc4e62d593a4bba99d741e8c301740a7068233","side":"left"},{"sibling":"e3a7d5c07f161682d61bd453ffc02ecdf87cfeda70f986d6650017f9d2d6b265","side":"left"},{"sibling":"edbc49f08e5b92291934c05c9e6efd270a6b0698d8d2fa474006366027dfe098","side":"right"},{"sibling":"3e4df6e7457cecbf36f350375e72dcab336a3984422e4c406ef809e4e2944e96","side":"left"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"be08fedc4e72a6fb56606f66812fae7317e09690b9acb18385f4ab117a981238","side":"right"},{"sibling":"0534329a7475dc9df51998c83c16892126679dade0fa34182f21e869599386c7","side":"right"},{"sibling":"2d24720928ead0e7670650eb55f558c4f20e4c18df376f47ba72cfa8cf0ed344","side":"right"},{"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":147301,"merkle_root":"08903d7159c3b38eeeeafc09eab15139ea417f1d94f02f1fbc87296b37db840a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260521T183701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-21T18:37:33Z","sig_algorithm":"ed25519","signature":"905f2924632dfa2970c8690285f5b5d4a1d891d0e0ef1cbc404ebec2fd937215ac768e16f0a9f28b18977a55ae0bfd226db6833ae7ef588729054117d2da7303","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_53455eb231ad8ebbad9d03d0c2b0d2571315dfe666206cc729627960b6e86604"}}