{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HGSNWOE2X6VPECK7KYQLTEFSPN","short_pith_number":"pith:HGSNWOE2","canonical_record":{"source":{"id":"2608.02036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-03T10:33:34Z","cross_cats_sorted":[],"title_canon_sha256":"9b3df1503aabbc5518fc600922bd5a9dee29ef88a0b1fcea517bd7b32bc2e3e3","abstract_canon_sha256":"01b91cf7e504714a44fbc8d9f9d9c83632f37fb62d3a69b5300eb8df06f35d13"},"schema_version":"1.0"},"canonical_sha256":"39a4db389abfaaf2095f5620b990b27b73937d45e1e050aa053f8ace8d2f7722","source":{"kind":"arxiv","id":"2608.02036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.02036","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"2608.02036v1","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.02036","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"HGSNWOE2X6VP","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"pith_short_16","alias_value":"HGSNWOE2X6VPECK7","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"pith_short_8","alias_value":"HGSNWOE2","created_at":"2026-08-04T02:10:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HGSNWOE2X6VPECK7KYQLTEFSPN","target":"record","payload":{"canonical_record":{"source":{"id":"2608.02036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-03T10:33:34Z","cross_cats_sorted":[],"title_canon_sha256":"9b3df1503aabbc5518fc600922bd5a9dee29ef88a0b1fcea517bd7b32bc2e3e3","abstract_canon_sha256":"01b91cf7e504714a44fbc8d9f9d9c83632f37fb62d3a69b5300eb8df06f35d13"},"schema_version":"1.0"},"canonical_sha256":"39a4db389abfaaf2095f5620b990b27b73937d45e1e050aa053f8ace8d2f7722","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:10:33.252431Z","signature_b64":"FHq9sIiUl8g0ANKier0S9c/X1Z1HH7e/5UasLFzEE9M+Zczv0NibisIxCamtXBCyTWv+hLIyO5WhbjgVyD2aBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39a4db389abfaaf2095f5620b990b27b73937d45e1e050aa053f8ace8d2f7722","last_reissued_at":"2026-08-04T02:10:33.250221Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:10:33.250221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.02036","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":"2026-08-04T02:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzbm1jv2IU8/Q0zMU6P0yvNYBtPFoR/8N6LqUiDdcNYV+4YSaXVXNN61i7Wx9F8IBfPbyRV8QVxxEsXfOoGODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:49:23.394827Z"},"content_sha256":"01b6c01430f6de1eff52b5b3ca2265b62be7e251ba5fadafb7bd4e668f3a6baf","schema_version":"1.0","event_id":"sha256:01b6c01430f6de1eff52b5b3ca2265b62be7e251ba5fadafb7bd4e668f3a6baf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HGSNWOE2X6VPECK7KYQLTEFSPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex Neural Energy Elements: Monolithic Finite-Element Assembly of Geometry-Parameterized Neural Operators with Stability and Error Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Chenzhuo Zhang, Fan Wang, Hongyue Jiang, Jianjiang Zhan","submitted_at":"2026-08-03T10:33:34Z","abstract_excerpt":"Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, and Newton converges to spurious minima (247% error) even with 1%-accurate field predictions. We introduce convex neural energy elements: each element exports a scalar energy E(g,U), architecturally convex in its boundary degrees of freedom U and smoothly parameterized by its geometry g, realized as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02036","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/2608.02036/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":"2026-08-04T02:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zL7JORJsRpIVIRyoDQbENoyNv1/X93duNVCYA1wbJUg/VuOGZoGLhIl1WGXM5nBtcdIE5Pllx/YgtD9elCOxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:49:23.395751Z"},"content_sha256":"7c65ca08772f4f2130c309e678d87d92ff6a0cd49c3c7b8f6980c1c194a65a1f","schema_version":"1.0","event_id":"sha256:7c65ca08772f4f2130c309e678d87d92ff6a0cd49c3c7b8f6980c1c194a65a1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HGSNWOE2X6VPECK7KYQLTEFSPN/bundle.json","state_url":"https://pith.science/pith/HGSNWOE2X6VPECK7KYQLTEFSPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HGSNWOE2X6VPECK7KYQLTEFSPN/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":"2026-08-06T10:49:23Z","links":{"resolver":"https://pith.science/pith/HGSNWOE2X6VPECK7KYQLTEFSPN","bundle":"https://pith.science/pith/HGSNWOE2X6VPECK7KYQLTEFSPN/bundle.json","state":"https://pith.science/pith/HGSNWOE2X6VPECK7KYQLTEFSPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HGSNWOE2X6VPECK7KYQLTEFSPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HGSNWOE2X6VPECK7KYQLTEFSPN","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":"01b91cf7e504714a44fbc8d9f9d9c83632f37fb62d3a69b5300eb8df06f35d13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-03T10:33:34Z","title_canon_sha256":"9b3df1503aabbc5518fc600922bd5a9dee29ef88a0b1fcea517bd7b32bc2e3e3"},"schema_version":"1.0","source":{"id":"2608.02036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.02036","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"2608.02036v1","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.02036","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"HGSNWOE2X6VP","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"pith_short_16","alias_value":"HGSNWOE2X6VPECK7","created_at":"2026-08-04T02:10:33Z"},{"alias_kind":"pith_short_8","alias_value":"HGSNWOE2","created_at":"2026-08-04T02:10:33Z"}],"graph_snapshots":[{"event_id":"sha256:7c65ca08772f4f2130c309e678d87d92ff6a0cd49c3c7b8f6980c1c194a65a1f","target":"graph","created_at":"2026-08-04T02:10:33Z","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/2608.02036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, and Newton converges to spurious minima (247% error) even with 1%-accurate field predictions. We introduce convex neural energy elements: each element exports a scalar energy E(g,U), architecturally convex in its boundary degrees of freedom U and smoothly parameterized by its geometry g, realized as ","authors_text":"Chenzhuo Zhang, Fan Wang, Hongyue Jiang, Jianjiang Zhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-03T10:33:34Z","title":"Convex Neural Energy Elements: Monolithic Finite-Element Assembly of Geometry-Parameterized Neural Operators with Stability and Error Guarantees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02036","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":"sha256:01b6c01430f6de1eff52b5b3ca2265b62be7e251ba5fadafb7bd4e668f3a6baf","target":"record","created_at":"2026-08-04T02:10:33Z","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":"01b91cf7e504714a44fbc8d9f9d9c83632f37fb62d3a69b5300eb8df06f35d13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-03T10:33:34Z","title_canon_sha256":"9b3df1503aabbc5518fc600922bd5a9dee29ef88a0b1fcea517bd7b32bc2e3e3"},"schema_version":"1.0","source":{"id":"2608.02036","kind":"arxiv","version":1}},"canonical_sha256":"39a4db389abfaaf2095f5620b990b27b73937d45e1e050aa053f8ace8d2f7722","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39a4db389abfaaf2095f5620b990b27b73937d45e1e050aa053f8ace8d2f7722","first_computed_at":"2026-08-04T02:10:33.250221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:10:33.250221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FHq9sIiUl8g0ANKier0S9c/X1Z1HH7e/5UasLFzEE9M+Zczv0NibisIxCamtXBCyTWv+hLIyO5WhbjgVyD2aBA==","signature_status":"signed_v1","signed_at":"2026-08-04T02:10:33.252431Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.02036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01b6c01430f6de1eff52b5b3ca2265b62be7e251ba5fadafb7bd4e668f3a6baf","sha256:7c65ca08772f4f2130c309e678d87d92ff6a0cd49c3c7b8f6980c1c194a65a1f"],"state_sha256":"e44db429e0fca32beb2eff3d0df09458917896063b8df7746473173606e214c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YXS+Zl6KAX7N4CorrsjudSwQeX8wYoo9Pba/kif29/7wluSwvwcLkeTE5AUuCWbbng4YQjpl7qLMcm05GAjJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T10:49:23.401504Z","bundle_sha256":"eb9f076bb2fa7b0b97e9a9031c472494af5ed1443d71df7e8416670442c5ed96"}}