{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TLDVSA5QR4674W35GAD5KVXSWG","short_pith_number":"pith:TLDVSA5Q","canonical_record":{"source":{"id":"2506.17242","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-06T05:37:49Z","cross_cats_sorted":["cond-mat.mtrl-sci","cs.LG"],"title_canon_sha256":"1c983f7be3adeb0153caab23317a47d857a0381ae91d76e797cc31ef0e100bca","abstract_canon_sha256":"9944203cbfa3e40dbfaa7ef6e192a667e74053d5a36362bad43b962421b07c86"},"schema_version":"1.0"},"canonical_sha256":"9ac75903b08f3dfe5b7d3007d556f2b1901c5feb0363ff23fba757c8e4f2635d","source":{"kind":"arxiv","id":"2506.17242","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.17242","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.17242v1","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17242","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"TLDVSA5QR467","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"pith_short_16","alias_value":"TLDVSA5QR4674W35","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"pith_short_8","alias_value":"TLDVSA5Q","created_at":"2026-07-05T11:25:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TLDVSA5QR4674W35GAD5KVXSWG","target":"record","payload":{"canonical_record":{"source":{"id":"2506.17242","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-06T05:37:49Z","cross_cats_sorted":["cond-mat.mtrl-sci","cs.LG"],"title_canon_sha256":"1c983f7be3adeb0153caab23317a47d857a0381ae91d76e797cc31ef0e100bca","abstract_canon_sha256":"9944203cbfa3e40dbfaa7ef6e192a667e74053d5a36362bad43b962421b07c86"},"schema_version":"1.0"},"canonical_sha256":"9ac75903b08f3dfe5b7d3007d556f2b1901c5feb0363ff23fba757c8e4f2635d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:14.133995Z","signature_b64":"r1/aSYSN4DG+ZCwd+hpXhjs0vg+8YFOjVbfuueceGkC5LISqz8/Bx4vL/gfHWNoDXGaDLlnzThRQy8fwTdZXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ac75903b08f3dfe5b7d3007d556f2b1901c5feb0363ff23fba757c8e4f2635d","last_reissued_at":"2026-07-05T11:25:14.133526Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:14.133526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.17242","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":"2026-07-05T11:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GUwTfJwcVKKCbEE2eq6/LOs71GMTMiy7K0FlwgfKwNRxjLuSXKE1oUXb5PdAZyBabds14gvEzgSewWwhJdvABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:27:33.371842Z"},"content_sha256":"cf389fea76c2342da026d4b3e15bb60ebb48c594a292af039d206274ed49befd","schema_version":"1.0","event_id":"sha256:cf389fea76c2342da026d4b3e15bb60ebb48c594a292af039d206274ed49befd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TLDVSA5QR4674W35GAD5KVXSWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentiable neural network representation of multi-well, locally-convex potentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","cs.LG"],"primary_cat":"stat.ML","authors_text":"Adrian Buganza Tepole, Jan N. Fuhg, Reese E. Jones","submitted_at":"2025-06-06T05:37:49Z","abstract_excerpt":"Multi-well potentials are ubiquitous in science, modeling phenomena such as phase transitions, dynamic instabilities, and multimodal behavior across physics, chemistry, and biology. In contrast to non-smooth minimum-of-mixture representations, we propose a differentiable and convex formulation based on a log-sum-exponential (LSE) mixture of input convex neural network (ICNN) modes. This log-sum-exponential input convex neural network (LSE-ICNN) provides a smooth surrogate that retains convexity within basins and allows for gradient-based learning and inference.\n  A key feature of the LSE-ICNN "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17242","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/2506.17242/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":"2026-07-05T11:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bjp2ERqlv9fJewdPzuZbWOSDHss6a+TEKaG+pEMSTI/SiIlEWPxgt4+iw3aU58kb6EAS+aXUf901iI+njhmQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:27:33.372439Z"},"content_sha256":"f08e45a7c77438fd7eee0eb7df44cfb2cf3e07c1747a061c8165e4907d746fd9","schema_version":"1.0","event_id":"sha256:f08e45a7c77438fd7eee0eb7df44cfb2cf3e07c1747a061c8165e4907d746fd9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLDVSA5QR4674W35GAD5KVXSWG/bundle.json","state_url":"https://pith.science/pith/TLDVSA5QR4674W35GAD5KVXSWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLDVSA5QR4674W35GAD5KVXSWG/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":"2026-08-08T15:27:33Z","links":{"resolver":"https://pith.science/pith/TLDVSA5QR4674W35GAD5KVXSWG","bundle":"https://pith.science/pith/TLDVSA5QR4674W35GAD5KVXSWG/bundle.json","state":"https://pith.science/pith/TLDVSA5QR4674W35GAD5KVXSWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLDVSA5QR4674W35GAD5KVXSWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TLDVSA5QR4674W35GAD5KVXSWG","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":"9944203cbfa3e40dbfaa7ef6e192a667e74053d5a36362bad43b962421b07c86","cross_cats_sorted":["cond-mat.mtrl-sci","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-06T05:37:49Z","title_canon_sha256":"1c983f7be3adeb0153caab23317a47d857a0381ae91d76e797cc31ef0e100bca"},"schema_version":"1.0","source":{"id":"2506.17242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.17242","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.17242v1","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17242","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"TLDVSA5QR467","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"pith_short_16","alias_value":"TLDVSA5QR4674W35","created_at":"2026-07-05T11:25:14Z"},{"alias_kind":"pith_short_8","alias_value":"TLDVSA5Q","created_at":"2026-07-05T11:25:14Z"}],"graph_snapshots":[{"event_id":"sha256:f08e45a7c77438fd7eee0eb7df44cfb2cf3e07c1747a061c8165e4907d746fd9","target":"graph","created_at":"2026-07-05T11:25:14Z","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/2506.17242/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multi-well potentials are ubiquitous in science, modeling phenomena such as phase transitions, dynamic instabilities, and multimodal behavior across physics, chemistry, and biology. In contrast to non-smooth minimum-of-mixture representations, we propose a differentiable and convex formulation based on a log-sum-exponential (LSE) mixture of input convex neural network (ICNN) modes. This log-sum-exponential input convex neural network (LSE-ICNN) provides a smooth surrogate that retains convexity within basins and allows for gradient-based learning and inference.\n  A key feature of the LSE-ICNN ","authors_text":"Adrian Buganza Tepole, Jan N. Fuhg, Reese E. Jones","cross_cats":["cond-mat.mtrl-sci","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-06T05:37:49Z","title":"Differentiable neural network representation of multi-well, locally-convex potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17242","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:cf389fea76c2342da026d4b3e15bb60ebb48c594a292af039d206274ed49befd","target":"record","created_at":"2026-07-05T11:25:14Z","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":"9944203cbfa3e40dbfaa7ef6e192a667e74053d5a36362bad43b962421b07c86","cross_cats_sorted":["cond-mat.mtrl-sci","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-06T05:37:49Z","title_canon_sha256":"1c983f7be3adeb0153caab23317a47d857a0381ae91d76e797cc31ef0e100bca"},"schema_version":"1.0","source":{"id":"2506.17242","kind":"arxiv","version":1}},"canonical_sha256":"9ac75903b08f3dfe5b7d3007d556f2b1901c5feb0363ff23fba757c8e4f2635d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ac75903b08f3dfe5b7d3007d556f2b1901c5feb0363ff23fba757c8e4f2635d","first_computed_at":"2026-07-05T11:25:14.133526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:25:14.133526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r1/aSYSN4DG+ZCwd+hpXhjs0vg+8YFOjVbfuueceGkC5LISqz8/Bx4vL/gfHWNoDXGaDLlnzThRQy8fwTdZXBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:25:14.133995Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.17242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf389fea76c2342da026d4b3e15bb60ebb48c594a292af039d206274ed49befd","sha256:f08e45a7c77438fd7eee0eb7df44cfb2cf3e07c1747a061c8165e4907d746fd9"],"state_sha256":"943e9f10ba50789775fdc9dac785f9669590e504700b3d96e893f022016af621"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7MKXiEuJgceBxtVTCR5HP0w6KIF6MZnCvygjiuVaWgH3tm91P9sHio3Uh3XjtyxurkZ3NTlUsssXSt9LXtflBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T15:27:33.378281Z","bundle_sha256":"cce510af051d73d37607e023f0fc119d29a81768e3b66c74a265f323a8567a8d"}}