{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NEHDD3EXVVT5SV4IWCEKPP4D7O","short_pith_number":"pith:NEHDD3EX","canonical_record":{"source":{"id":"2606.04290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-02T23:39:23Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6173a632b8378120a534d59e96ef3c3a8ce2e75d3d2694e72948dc48f610b1e5","abstract_canon_sha256":"7b8453478e77c8f7fe7a3db739ad1cf52dfcbcb452fc7b57774fcde99ce7d8b9"},"schema_version":"1.0"},"canonical_sha256":"690e31ec97ad67d95788b088a7bf83fb9bff44b49b98695aaee3004c6f18b55f","source":{"kind":"arxiv","id":"2606.04290","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04290","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04290v1","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04290","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"pith_short_12","alias_value":"NEHDD3EXVVT5","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"pith_short_16","alias_value":"NEHDD3EXVVT5SV4I","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"pith_short_8","alias_value":"NEHDD3EX","created_at":"2026-06-04T01:09:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NEHDD3EXVVT5SV4IWCEKPP4D7O","target":"record","payload":{"canonical_record":{"source":{"id":"2606.04290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-02T23:39:23Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6173a632b8378120a534d59e96ef3c3a8ce2e75d3d2694e72948dc48f610b1e5","abstract_canon_sha256":"7b8453478e77c8f7fe7a3db739ad1cf52dfcbcb452fc7b57774fcde99ce7d8b9"},"schema_version":"1.0"},"canonical_sha256":"690e31ec97ad67d95788b088a7bf83fb9bff44b49b98695aaee3004c6f18b55f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:02.190247Z","signature_b64":"axga83FnPbsmEJs57uz9TFm7e6rZWRM9yraWw0WCJIK02tHGCyh7jnJDCM59LjReQ+SqGw9rmPFZaUYRxeC9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"690e31ec97ad67d95788b088a7bf83fb9bff44b49b98695aaee3004c6f18b55f","last_reissued_at":"2026-06-04T01:09:02.189738Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:02.189738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.04290","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":"2026-06-04T01:09:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a+52FvlfGFfu9UkKVLrfbaZ90uWp4o6h93HcYpsoscM9isG4315lsMkkFsFMkUWVLcEvgmWKhaWhzizhlZaNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:39:15.203334Z"},"content_sha256":"7ac8f4f374af8904b1b0885af0b185b987da4e6937189f847c8854adbedc02d0","schema_version":"1.0","event_id":"sha256:7ac8f4f374af8904b1b0885af0b185b987da4e6937189f847c8854adbedc02d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NEHDD3EXVVT5SV4IWCEKPP4D7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Ismail Hassaballa, Mircea Lazar","submitted_at":"2026-06-02T23:39:23Z","abstract_excerpt":"Hybrid models that combine physics-based and data-driven components have shown strong potential for achieving accuracy and interpretability in control applications. While recent methods have made progress in incorporating physical consistency, challenges remain in scalability, robustness to noise, and control of model complexity. This paper proposes a Physics-Encoded Modular Hybrid Layer (PE-MHL) framework, in which a baseline physics-based model is incrementally refined through the addition of new sub-models, where each new component adds complexity while preserving what previous components h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04290","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/2606.04290/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":"2026-06-04T01:09:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SezADy+0njFB/eDFiwXcgb//lG4eg6cT20poZz/t9ljWk11ysLfG2ZlYMq5AnImnAKNGdVIDrWdIo+ZzcImsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:39:15.203711Z"},"content_sha256":"9bce963afadce7f3c49ad1c856a82505063b1f2873272fb602a5369fdf4b2706","schema_version":"1.0","event_id":"sha256:9bce963afadce7f3c49ad1c856a82505063b1f2873272fb602a5369fdf4b2706"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NEHDD3EXVVT5SV4IWCEKPP4D7O/bundle.json","state_url":"https://pith.science/pith/NEHDD3EXVVT5SV4IWCEKPP4D7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NEHDD3EXVVT5SV4IWCEKPP4D7O/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":"2026-06-28T12:39:15Z","links":{"resolver":"https://pith.science/pith/NEHDD3EXVVT5SV4IWCEKPP4D7O","bundle":"https://pith.science/pith/NEHDD3EXVVT5SV4IWCEKPP4D7O/bundle.json","state":"https://pith.science/pith/NEHDD3EXVVT5SV4IWCEKPP4D7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NEHDD3EXVVT5SV4IWCEKPP4D7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NEHDD3EXVVT5SV4IWCEKPP4D7O","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":"7b8453478e77c8f7fe7a3db739ad1cf52dfcbcb452fc7b57774fcde99ce7d8b9","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-02T23:39:23Z","title_canon_sha256":"6173a632b8378120a534d59e96ef3c3a8ce2e75d3d2694e72948dc48f610b1e5"},"schema_version":"1.0","source":{"id":"2606.04290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04290","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04290v1","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04290","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"pith_short_12","alias_value":"NEHDD3EXVVT5","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"pith_short_16","alias_value":"NEHDD3EXVVT5SV4I","created_at":"2026-06-04T01:09:02Z"},{"alias_kind":"pith_short_8","alias_value":"NEHDD3EX","created_at":"2026-06-04T01:09:02Z"}],"graph_snapshots":[{"event_id":"sha256:9bce963afadce7f3c49ad1c856a82505063b1f2873272fb602a5369fdf4b2706","target":"graph","created_at":"2026-06-04T01:09:02Z","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/2606.04290/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hybrid models that combine physics-based and data-driven components have shown strong potential for achieving accuracy and interpretability in control applications. While recent methods have made progress in incorporating physical consistency, challenges remain in scalability, robustness to noise, and control of model complexity. This paper proposes a Physics-Encoded Modular Hybrid Layer (PE-MHL) framework, in which a baseline physics-based model is incrementally refined through the addition of new sub-models, where each new component adds complexity while preserving what previous components h","authors_text":"Ismail Hassaballa, Mircea Lazar","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-02T23:39:23Z","title":"PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04290","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":"sha256:7ac8f4f374af8904b1b0885af0b185b987da4e6937189f847c8854adbedc02d0","target":"record","created_at":"2026-06-04T01:09:02Z","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":"7b8453478e77c8f7fe7a3db739ad1cf52dfcbcb452fc7b57774fcde99ce7d8b9","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-02T23:39:23Z","title_canon_sha256":"6173a632b8378120a534d59e96ef3c3a8ce2e75d3d2694e72948dc48f610b1e5"},"schema_version":"1.0","source":{"id":"2606.04290","kind":"arxiv","version":1}},"canonical_sha256":"690e31ec97ad67d95788b088a7bf83fb9bff44b49b98695aaee3004c6f18b55f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"690e31ec97ad67d95788b088a7bf83fb9bff44b49b98695aaee3004c6f18b55f","first_computed_at":"2026-06-04T01:09:02.189738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:02.189738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"axga83FnPbsmEJs57uz9TFm7e6rZWRM9yraWw0WCJIK02tHGCyh7jnJDCM59LjReQ+SqGw9rmPFZaUYRxeC9CA==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:02.190247Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ac8f4f374af8904b1b0885af0b185b987da4e6937189f847c8854adbedc02d0","sha256:9bce963afadce7f3c49ad1c856a82505063b1f2873272fb602a5369fdf4b2706"],"state_sha256":"5204052e2fe749d88b66eda14532b2c38852972572ca3cd3ec259b1fc77c1b67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33XTTWWq0BFtSSiqR/YOv4rh+QkIhDxUF8vkXm+teGUyy5CcQ2BHiBVteWuvnZOQiIurylys5Lk4NmunbMycCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:39:15.205683Z","bundle_sha256":"87842070c243e1fc5dbfd2b0f2346e51ef0d80a5a02c95823284290243e6dd54"}}