{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:M7LXRSPHFUOTJ3FHVZ7E3LS7MW","short_pith_number":"pith:M7LXRSPH","canonical_record":{"source":{"id":"2605.18566","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2026-05-18T15:43:59Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"67dc6df033c74eb54da5fd70fd28dfefd71dedf0ee219fa31a84844dcbad34df","abstract_canon_sha256":"55d142538f4bd0fae44a7fa3b0c2e9304b195cffdcf2adbd626a94d39223d80f"},"schema_version":"1.0"},"canonical_sha256":"67d778c9e72d1d34eca7ae7e4dae5f6599fa5303edcbf0e8f5381adcc591d0c5","source":{"kind":"arxiv","id":"2605.18566","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18566","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18566v1","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18566","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"M7LXRSPHFUOT","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"M7LXRSPHFUOTJ3FH","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"M7LXRSPH","created_at":"2026-05-20T00:06:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:M7LXRSPHFUOTJ3FHVZ7E3LS7MW","target":"record","payload":{"canonical_record":{"source":{"id":"2605.18566","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2026-05-18T15:43:59Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"67dc6df033c74eb54da5fd70fd28dfefd71dedf0ee219fa31a84844dcbad34df","abstract_canon_sha256":"55d142538f4bd0fae44a7fa3b0c2e9304b195cffdcf2adbd626a94d39223d80f"},"schema_version":"1.0"},"canonical_sha256":"67d778c9e72d1d34eca7ae7e4dae5f6599fa5303edcbf0e8f5381adcc591d0c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:06:08.011729Z","signature_b64":"qP6A6Xx3SlhjqHNlREjXyC7bA/afDmMxSDuxyYdgSSyRaN69RR5H/tKfZIAOu+O2XeV1ynDBV7c/zzs09TCmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67d778c9e72d1d34eca7ae7e4dae5f6599fa5303edcbf0e8f5381adcc591d0c5","last_reissued_at":"2026-05-20T00:06:08.010852Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:06:08.010852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.18566","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2VYsS7ZRCcLSNnjxYm0ersI+A+UOiyGBjWafwNLg4ljzNkO2OBTIXnHWRKqLGLGP4juOEsVD3VuY2sSOy6oJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:20:23.498052Z"},"content_sha256":"8a33a9fd94b8ced2e0d581c6927c6845828f4bb0e97df13e9145bd276533e968","schema_version":"1.0","event_id":"sha256:8a33a9fd94b8ced2e0d581c6927c6845828f4bb0e97df13e9145bd276533e968"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:M7LXRSPHFUOTJ3FHVZ7E3LS7MW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"HJ-Gauss: A Monte-Carlo HJ Reachability Scheme","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Lekan Molu, Namhoon Cho, Venkatraman Renganathan","submitted_at":"2026-05-18T15:43:59Z","abstract_excerpt":"Backward reachable tubes (BRTs), computed via viscous Hamilton-Jacobi (HJ) partial differential equations, provide principled safety certificates for learned controllers and planning algorithms in trustworthy machine learning. However, classical grid-based HJ solvers require $O(M^n)$ memory footprint for $M$ grid points per $n$ state dimension. This renders them impractical for high-dimensional systems. We address this bottleneck with a local PDE linearization that enables a frozen-coefficient sampling scheme for the viscous HJ PDE: a generalized Cole-Hopf-type transformation reduces the nonli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18566","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18566/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.347252Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"34cb7f41a956dcd3ee225e9f8905e08ac1cd48d9434fcbdd5d74a65794767ffe"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3o8W0r2Hz4Cqj4jSSfXwO0CnaB1S181q0sh4GHet0SvMKZYh870S25svve5/4SOZ8FJfCOi0p3KPBtn+UtIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:20:23.498485Z"},"content_sha256":"b0903eae9b1af841723191d68d7524df93caadae95ef22f3ea1417a4d143c4cf","schema_version":"1.0","event_id":"sha256:b0903eae9b1af841723191d68d7524df93caadae95ef22f3ea1417a4d143c4cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7LXRSPHFUOTJ3FHVZ7E3LS7MW/bundle.json","state_url":"https://pith.science/pith/M7LXRSPHFUOTJ3FHVZ7E3LS7MW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7LXRSPHFUOTJ3FHVZ7E3LS7MW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T00:20:23Z","links":{"resolver":"https://pith.science/pith/M7LXRSPHFUOTJ3FHVZ7E3LS7MW","bundle":"https://pith.science/pith/M7LXRSPHFUOTJ3FHVZ7E3LS7MW/bundle.json","state":"https://pith.science/pith/M7LXRSPHFUOTJ3FHVZ7E3LS7MW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7LXRSPHFUOTJ3FHVZ7E3LS7MW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:M7LXRSPHFUOTJ3FHVZ7E3LS7MW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"55d142538f4bd0fae44a7fa3b0c2e9304b195cffdcf2adbd626a94d39223d80f","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2026-05-18T15:43:59Z","title_canon_sha256":"67dc6df033c74eb54da5fd70fd28dfefd71dedf0ee219fa31a84844dcbad34df"},"schema_version":"1.0","source":{"id":"2605.18566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18566","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18566v1","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18566","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"M7LXRSPHFUOT","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"M7LXRSPHFUOTJ3FH","created_at":"2026-05-20T00:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"M7LXRSPH","created_at":"2026-05-20T00:06:08Z"}],"graph_snapshots":[{"event_id":"sha256:b0903eae9b1af841723191d68d7524df93caadae95ef22f3ea1417a4d143c4cf","target":"graph","created_at":"2026-05-20T00:06:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.347252Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.18566/integrity.json","findings":[],"snapshot_sha256":"34cb7f41a956dcd3ee225e9f8905e08ac1cd48d9434fcbdd5d74a65794767ffe","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Backward reachable tubes (BRTs), computed via viscous Hamilton-Jacobi (HJ) partial differential equations, provide principled safety certificates for learned controllers and planning algorithms in trustworthy machine learning. However, classical grid-based HJ solvers require $O(M^n)$ memory footprint for $M$ grid points per $n$ state dimension. This renders them impractical for high-dimensional systems. We address this bottleneck with a local PDE linearization that enables a frozen-coefficient sampling scheme for the viscous HJ PDE: a generalized Cole-Hopf-type transformation reduces the nonli","authors_text":"Lekan Molu, Namhoon Cho, Venkatraman Renganathan","cross_cats":["cs.SY"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2026-05-18T15:43:59Z","title":"HJ-Gauss: A Monte-Carlo HJ Reachability Scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18566","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8a33a9fd94b8ced2e0d581c6927c6845828f4bb0e97df13e9145bd276533e968","target":"record","created_at":"2026-05-20T00:06:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"55d142538f4bd0fae44a7fa3b0c2e9304b195cffdcf2adbd626a94d39223d80f","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2026-05-18T15:43:59Z","title_canon_sha256":"67dc6df033c74eb54da5fd70fd28dfefd71dedf0ee219fa31a84844dcbad34df"},"schema_version":"1.0","source":{"id":"2605.18566","kind":"arxiv","version":1}},"canonical_sha256":"67d778c9e72d1d34eca7ae7e4dae5f6599fa5303edcbf0e8f5381adcc591d0c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67d778c9e72d1d34eca7ae7e4dae5f6599fa5303edcbf0e8f5381adcc591d0c5","first_computed_at":"2026-05-20T00:06:08.010852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:06:08.010852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qP6A6Xx3SlhjqHNlREjXyC7bA/afDmMxSDuxyYdgSSyRaN69RR5H/tKfZIAOu+O2XeV1ynDBV7c/zzs09TCmBg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:06:08.011729Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a33a9fd94b8ced2e0d581c6927c6845828f4bb0e97df13e9145bd276533e968","sha256:b0903eae9b1af841723191d68d7524df93caadae95ef22f3ea1417a4d143c4cf"],"state_sha256":"d689ca87919c32e75ac69cadaa7731bc3cdaba0806b2b350390acf682a2d23dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3+drmP+psp8Z2hP+Ilbvx84GiKadw8/mnA6oN4v44ZwiLAdkbgTjf4xW+d6RnPzht9B54Ahd1cw0sq1pv1pBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:20:23.500741Z","bundle_sha256":"19024fc9d55b80432056893983b1bdfee3b168e14f2bfb83c1de6d2b53346a6a"}}