{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CIFO25MUOLYXGVNUJMISZNKPCA","short_pith_number":"pith:CIFO25MU","canonical_record":{"source":{"id":"2510.25731","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-29T17:37:27Z","cross_cats_sorted":["cs.AI","cs.NA","math.NA","physics.comp-ph"],"title_canon_sha256":"863eaca1d6a6a4ba91dec8a01adff848cde015e9acbdf6a65528115b6e79cbfd","abstract_canon_sha256":"d87f2a5f4ab97e7fcdbc51e0e517eaf1dd27306f8cdb88eeace9a6e0f97036de"},"schema_version":"1.0"},"canonical_sha256":"120aed759472f17355b44b112cb54f1033a2605d624ed17ecc9c031d92d008b4","source":{"kind":"arxiv","id":"2510.25731","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.25731","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"arxiv_version","alias_value":"2510.25731v2","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.25731","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_12","alias_value":"CIFO25MUOLYX","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_16","alias_value":"CIFO25MUOLYXGVNU","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_8","alias_value":"CIFO25MU","created_at":"2026-06-29T00:14:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CIFO25MUOLYXGVNUJMISZNKPCA","target":"record","payload":{"canonical_record":{"source":{"id":"2510.25731","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-29T17:37:27Z","cross_cats_sorted":["cs.AI","cs.NA","math.NA","physics.comp-ph"],"title_canon_sha256":"863eaca1d6a6a4ba91dec8a01adff848cde015e9acbdf6a65528115b6e79cbfd","abstract_canon_sha256":"d87f2a5f4ab97e7fcdbc51e0e517eaf1dd27306f8cdb88eeace9a6e0f97036de"},"schema_version":"1.0"},"canonical_sha256":"120aed759472f17355b44b112cb54f1033a2605d624ed17ecc9c031d92d008b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T00:14:01.170153Z","signature_b64":"5yhcHVsPZJb9Yer6xqbctZFX5DBUgAYxTyvBONaTZ/0SGRapgrA2DdhKMDw7dShw2QYeok4dlD1H+Cpd3QK+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"120aed759472f17355b44b112cb54f1033a2605d624ed17ecc9c031d92d008b4","last_reissued_at":"2026-06-29T00:14:01.169645Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T00:14:01.169645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.25731","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-29T00:14:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+y9jdpAyinC5p+6RAU8kGYjxyOvDmTCWOIcuKbxj22Xpe8GaDILI6YuxucyY8jT2aBjemc7tnEiHo/hT+3/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:16:02.429726Z"},"content_sha256":"a9bddcf65be0246ca4a007800c4d25d2eeb011276534e7fcc20d238392c7162e","schema_version":"1.0","event_id":"sha256:a9bddcf65be0246ca4a007800c4d25d2eeb011276534e7fcc20d238392c7162e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CIFO25MUOLYXGVNUJMISZNKPCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.AI","cs.NA","math.NA","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Ivan Timofeev, Johannes Frank, Jonas Naujoks, Ren\\'e P. Klausen, Sebastian Lapuschkin, Thomas Wiegand, Wojciech Samek","submitted_at":"2025-10-29T17:37:27Z","abstract_excerpt":"Initial-boundary value problems (IBVPs) provide the essential framework for modelling a wide range of phenomena in physics and engineering. We introduce a novel method for efficiently solving IBVPs using Lie symmetries to enforce the associated partial differential equation (PDE) exactly by construction. By leveraging symmetry transformations, our model embeds the underlying physical laws and learns the solution solely from initial and boundary data. Consequently, the boundary loss directly quantifies domain-wide error, enabling rigorous error estimation for well-posed IBVPs. We implement LieS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.25731","kind":"arxiv","version":2},"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/2510.25731/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-29T00:14:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"et/qMOwtkSAVjgqMFqIFOV3PyAcYtnwl91RhvGVZCi9po56NVwR6cQPod8f/EQoHjMSgmMSYqPGKaSGb7b9ZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:16:02.431144Z"},"content_sha256":"f89acce0430aa8699ace6cac1e024eacdd14b0a7ca8c75f5e20cd4c3dc294f6a","schema_version":"1.0","event_id":"sha256:f89acce0430aa8699ace6cac1e024eacdd14b0a7ca8c75f5e20cd4c3dc294f6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIFO25MUOLYXGVNUJMISZNKPCA/bundle.json","state_url":"https://pith.science/pith/CIFO25MUOLYXGVNUJMISZNKPCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIFO25MUOLYXGVNUJMISZNKPCA/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":"2026-08-08T01:16:02Z","links":{"resolver":"https://pith.science/pith/CIFO25MUOLYXGVNUJMISZNKPCA","bundle":"https://pith.science/pith/CIFO25MUOLYXGVNUJMISZNKPCA/bundle.json","state":"https://pith.science/pith/CIFO25MUOLYXGVNUJMISZNKPCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIFO25MUOLYXGVNUJMISZNKPCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CIFO25MUOLYXGVNUJMISZNKPCA","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":"d87f2a5f4ab97e7fcdbc51e0e517eaf1dd27306f8cdb88eeace9a6e0f97036de","cross_cats_sorted":["cs.AI","cs.NA","math.NA","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-29T17:37:27Z","title_canon_sha256":"863eaca1d6a6a4ba91dec8a01adff848cde015e9acbdf6a65528115b6e79cbfd"},"schema_version":"1.0","source":{"id":"2510.25731","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.25731","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"arxiv_version","alias_value":"2510.25731v2","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.25731","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_12","alias_value":"CIFO25MUOLYX","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_16","alias_value":"CIFO25MUOLYXGVNU","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_8","alias_value":"CIFO25MU","created_at":"2026-06-29T00:14:01Z"}],"graph_snapshots":[{"event_id":"sha256:f89acce0430aa8699ace6cac1e024eacdd14b0a7ca8c75f5e20cd4c3dc294f6a","target":"graph","created_at":"2026-06-29T00:14:01Z","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":[],"endpoint":"/pith/2510.25731/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Initial-boundary value problems (IBVPs) provide the essential framework for modelling a wide range of phenomena in physics and engineering. We introduce a novel method for efficiently solving IBVPs using Lie symmetries to enforce the associated partial differential equation (PDE) exactly by construction. By leveraging symmetry transformations, our model embeds the underlying physical laws and learns the solution solely from initial and boundary data. Consequently, the boundary loss directly quantifies domain-wide error, enabling rigorous error estimation for well-posed IBVPs. We implement LieS","authors_text":"Ivan Timofeev, Johannes Frank, Jonas Naujoks, Ren\\'e P. Klausen, Sebastian Lapuschkin, Thomas Wiegand, Wojciech Samek","cross_cats":["cs.AI","cs.NA","math.NA","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-29T17:37:27Z","title":"LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.25731","kind":"arxiv","version":2},"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:a9bddcf65be0246ca4a007800c4d25d2eeb011276534e7fcc20d238392c7162e","target":"record","created_at":"2026-06-29T00:14:01Z","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":"d87f2a5f4ab97e7fcdbc51e0e517eaf1dd27306f8cdb88eeace9a6e0f97036de","cross_cats_sorted":["cs.AI","cs.NA","math.NA","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-29T17:37:27Z","title_canon_sha256":"863eaca1d6a6a4ba91dec8a01adff848cde015e9acbdf6a65528115b6e79cbfd"},"schema_version":"1.0","source":{"id":"2510.25731","kind":"arxiv","version":2}},"canonical_sha256":"120aed759472f17355b44b112cb54f1033a2605d624ed17ecc9c031d92d008b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"120aed759472f17355b44b112cb54f1033a2605d624ed17ecc9c031d92d008b4","first_computed_at":"2026-06-29T00:14:01.169645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T00:14:01.169645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5yhcHVsPZJb9Yer6xqbctZFX5DBUgAYxTyvBONaTZ/0SGRapgrA2DdhKMDw7dShw2QYeok4dlD1H+Cpd3QK+Ag==","signature_status":"signed_v1","signed_at":"2026-06-29T00:14:01.170153Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.25731","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9bddcf65be0246ca4a007800c4d25d2eeb011276534e7fcc20d238392c7162e","sha256:f89acce0430aa8699ace6cac1e024eacdd14b0a7ca8c75f5e20cd4c3dc294f6a"],"state_sha256":"d551db8acefbf60bd2b04a740c33f20444f73c548c01cbf121fec1c3e223598c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZfgLu4kwbHk8/26b66COdDsTtSsilZxUfzirwSK5QtzdgdnvIx+4/0o/Kqx0AiUEdLpj36UZZ/1eQ8xS9qRAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T01:16:02.434794Z","bundle_sha256":"227b4b494857b0028a82e434688e2ffc5ad2b60b58882d95cf1a6409e48bb059"}}