{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5","short_pith_number":"pith:ZLVQ7MWV","canonical_record":{"source":{"id":"2604.20821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-04-22T17:46:35Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"6077251fb364106bfe5e3ad7b9160fea9d31aed6cfccbc84b643bb4d323367aa","abstract_canon_sha256":"fdacddce73f1edfad5f84d225c836e308351928bfce45796f6ebd094b12497c0"},"schema_version":"1.0"},"canonical_sha256":"caeb0fb2d50f31fcd1c8a622dbd311af7ed1731c2ee2d4db2c8337a61a12d348","source":{"kind":"arxiv","id":"2604.20821","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.20821","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"arxiv_version","alias_value":"2604.20821v2","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.20821","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZLVQ7MWVB4Y7","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"pith_short_16","alias_value":"ZLVQ7MWVB4Y7ZUOI","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"pith_short_8","alias_value":"ZLVQ7MWV","created_at":"2026-05-20T00:01:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5","target":"record","payload":{"canonical_record":{"source":{"id":"2604.20821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-04-22T17:46:35Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"6077251fb364106bfe5e3ad7b9160fea9d31aed6cfccbc84b643bb4d323367aa","abstract_canon_sha256":"fdacddce73f1edfad5f84d225c836e308351928bfce45796f6ebd094b12497c0"},"schema_version":"1.0"},"canonical_sha256":"caeb0fb2d50f31fcd1c8a622dbd311af7ed1731c2ee2d4db2c8337a61a12d348","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:41.714707Z","signature_b64":"k98ruhRTb5j2KUBg3TRiMh42lRZvNn/L9PQ1QKv8h/mQv0j7UA/aHbkmgO6PJO2JiwKDJWW0QHHeFb+RLp8CBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caeb0fb2d50f31fcd1c8a622dbd311af7ed1731c2ee2d4db2c8337a61a12d348","last_reissued_at":"2026-05-20T00:01:41.714107Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:41.714107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.20821","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":"2026-05-20T00:01:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x8O48cX0QNLIY/W3DVay/S/5S6cJCkcJr7jEEK2ua5NmsYk7GxGvpbXCKAKeZpt9cLZ93YPO1ymT8LQILqcmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:00:54.587974Z"},"content_sha256":"49b14f58a8cae1f7430e3713295a6a554ce83f568c1f95063747a3b84357c03c","schema_version":"1.0","event_id":"sha256:49b14f58a8cae1f7430e3713295a6a554ce83f568c1f95063747a3b84357c03c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Autonomous Emergence of Hamiltonian in Deep Generative Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A generative network trained only on spin snapshots recovers the system's exact Hamiltonian parameters via linear inversion of its score field.","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Wei-Qiang Chen, Wenjie Xi","submitted_at":"2026-04-22T17:46:35Z","abstract_excerpt":"The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or do they autonomously deduce the underlying physical laws? To address this, we introduce a rigorous algebraic framework to extract the implicit physical interactions learned by generative models. By establishing an exact equivalence between the zero-noise limit of a Riemannian diffusion score field and the thermodynamic restoring force, we utilize the traine"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Without incorporating any energetic priors, an overdetermined linear inversion successfully recovers the microscopic Hamiltonian parameters of the spin system. The inferred Hamiltonian parameters exhibit a 99.7% cosine similarity with the ground-truth interaction parameters. Furthermore, these sparse local parameters alone are sufficient to explain 87% of the variance in the continuous force field predicted by the network.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"By establishing an exact equivalence between the zero-noise limit of a Riemannian diffusion score field and the thermodynamic restoring force, we utilize the trained neural network as a direct force estimator. This equivalence is the load-bearing premise that allows the network output to be interpreted as a physical force; if it does not hold exactly for the chosen diffusion process and manifold, the subsequent linear inversion cannot recover the true Hamiltonian.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A symmetry-equivariant generative model trained on thermal snapshots of a 1D O(3) spin glass recovers the microscopic Hamiltonian parameters with 99.7% cosine similarity to ground truth through linear inversion of its learned score field.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A generative network trained only on spin snapshots recovers the system's exact Hamiltonian parameters via linear inversion of its score field.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"72a001ca299c72b929fcbf1501f67ae33b4f1303d4dd7c452c0b626776c4cba5"},"source":{"id":"2604.20821","kind":"arxiv","version":2},"verdict":{"id":"f74557ae-af07-416c-a15d-4cec9b68821a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:14:58.252582Z","strongest_claim":"Without incorporating any energetic priors, an overdetermined linear inversion successfully recovers the microscopic Hamiltonian parameters of the spin system. The inferred Hamiltonian parameters exhibit a 99.7% cosine similarity with the ground-truth interaction parameters. Furthermore, these sparse local parameters alone are sufficient to explain 87% of the variance in the continuous force field predicted by the network.","one_line_summary":"A symmetry-equivariant generative model trained on thermal snapshots of a 1D O(3) spin glass recovers the microscopic Hamiltonian parameters with 99.7% cosine similarity to ground truth through linear inversion of its learned score field.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"By establishing an exact equivalence between the zero-noise limit of a Riemannian diffusion score field and the thermodynamic restoring force, we utilize the trained neural network as a direct force estimator. This equivalence is the load-bearing premise that allows the network output to be interpreted as a physical force; if it does not hold exactly for the chosen diffusion process and manifold, the subsequent linear inversion cannot recover the true Hamiltonian.","pith_extraction_headline":"A generative network trained only on spin snapshots recovers the system's exact Hamiltonian parameters via linear inversion of its score field."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.20821/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":25,"sample":[{"doi":"","year":2024,"title":"J. Abramson, J. Adler, J. Dunger, R. Evans, T. Green, A. Pritzel, O. Ronneberger, L. Willmore, A. J. Bal- lard, J. Bambrick, S. W. Bodenstein, D. A. Evans, C.-C. Hung, M. O’Neill, D. Reiman, K. Tunyas","work_id":"d58f1684-17fd-452d-97de-1931a5cf2602","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"J. Ho, A. Jain, and P. Abbeel, Denoising diffusion prob- abilistic models (2020)","work_id":"86932763-75bb-4bbf-b363-3e755f46d20a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, Score-based generative modeling through stochastic differential equations (2020)","work_id":"0c1b1dfe-c1ac-464a-acc0-2c03067574c9","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Y. Bahri, J. Kadmon, J. Pennington, S. S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Annual Review of Con- densed Matter Physics11, 501–528 (2020)","work_id":"1d131d7e-e3cc-49c4-b276-5340f4ba2561","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1126/sciadv.aay2631","year":2020,"title":"S.-M. Udrescu and M. Tegmark, Science Advances6, 10.1126/sciadv.aay2631 (2020)","work_id":"6222c28d-2f18-4392-8cb2-0ab215b1b5d2","ref_index":6,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":25,"snapshot_sha256":"baf06e00648ca1b6b41a3a9c147bac7a846f4528ce869eab8e0e33b93db24090","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"1e909ea70e1be09f8cd38209b18db5eca54ee5e4249ca7d3f861630be514ac5f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"f74557ae-af07-416c-a15d-4cec9b68821a"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:01:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cqmJsn7CxP4QL06rLZRUZ9DK0mZc0HiQvQl0CUROIEUrPH4Y6bXER0RqbEvPlu2BOiLAvs2Nbwd+K6TKI13MDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:00:54.588629Z"},"content_sha256":"16e8fe3097aa50ce0be8361ff611b6dc3ef9619e5dcbca84ad95176ffbbcda62","schema_version":"1.0","event_id":"sha256:16e8fe3097aa50ce0be8361ff611b6dc3ef9619e5dcbca84ad95176ffbbcda62"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1103/phys-revlett.107.220601) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"J. Sohl-Dickstein, P. B. Battaglino, and M. R. De- Weese, Physical Review Letters107, 10.1103/phys- revlett.107.220601 (2011)","arxiv_id":"2604.20821","detector":"doi_compliance","evidence":{"ref_index":12,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"J. Sohl-Dickstein, P. B. Battaglino, and M. R. De- Weese, Physical Review Letters107, 10.1103/phys- revlett.107.220601 (2011)","reconstructed_doi":"10.1103/phys-revlett.107.220601"},"severity":"advisory","ref_index":12,"audited_at":"2026-05-20T01:33:20.032686Z","event_type":"pith.integrity.v1","detected_doi":"10.1103/phys-revlett.107.220601","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"63080b2a08e052f49891a7a100383881d94f156b32cd7ed02db6b8437022f39f","paper_version":2,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":4025,"payload_sha256":"f9ace5dc6b9b856a6b35d270feb9d20bdf0208d7933e5cdf4f96280b18516525","signature_b64":"ECAi4bVB1sMwQKm0UBfS3KI89czW9hQ6l1xUYlCAGNpRg8xHhiJbOxcmvWs4y0Y6mzqxWKdpERxsll9RsDc4Aw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T01:37:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tNGrSg5HAvkKXM0xTkBpxjMNgufMojFvR+sIhYUiEXS5JfGuvd8jpH+o9u1rM2KZOFldc5IJWOZ9eIJO2HcRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:00:54.589493Z"},"content_sha256":"a1e25f3896b24d728a0a1f95561d989fd1c38b1f44ad3e579fe21f156b28cc40","schema_version":"1.0","event_id":"sha256:a1e25f3896b24d728a0a1f95561d989fd1c38b1f44ad3e579fe21f156b28cc40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5/bundle.json","state_url":"https://pith.science/pith/ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5/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":"2026-06-09T13:00:54Z","links":{"resolver":"https://pith.science/pith/ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5","bundle":"https://pith.science/pith/ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5/bundle.json","state":"https://pith.science/pith/ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZLVQ7MWVB4Y7ZUOIUYRNXUYRV5","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fdacddce73f1edfad5f84d225c836e308351928bfce45796f6ebd094b12497c0","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-04-22T17:46:35Z","title_canon_sha256":"6077251fb364106bfe5e3ad7b9160fea9d31aed6cfccbc84b643bb4d323367aa"},"schema_version":"1.0","source":{"id":"2604.20821","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.20821","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"arxiv_version","alias_value":"2604.20821v2","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.20821","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZLVQ7MWVB4Y7","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"pith_short_16","alias_value":"ZLVQ7MWVB4Y7ZUOI","created_at":"2026-05-20T00:01:41Z"},{"alias_kind":"pith_short_8","alias_value":"ZLVQ7MWV","created_at":"2026-05-20T00:01:41Z"}],"graph_snapshots":[{"event_id":"sha256:16e8fe3097aa50ce0be8361ff611b6dc3ef9619e5dcbca84ad95176ffbbcda62","target":"graph","created_at":"2026-05-20T00:01:41Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Without incorporating any energetic priors, an overdetermined linear inversion successfully recovers the microscopic Hamiltonian parameters of the spin system. The inferred Hamiltonian parameters exhibit a 99.7% cosine similarity with the ground-truth interaction parameters. Furthermore, these sparse local parameters alone are sufficient to explain 87% of the variance in the continuous force field predicted by the network."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"By establishing an exact equivalence between the zero-noise limit of a Riemannian diffusion score field and the thermodynamic restoring force, we utilize the trained neural network as a direct force estimator. This equivalence is the load-bearing premise that allows the network output to be interpreted as a physical force; if it does not hold exactly for the chosen diffusion process and manifold, the subsequent linear inversion cannot recover the true Hamiltonian."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A symmetry-equivariant generative model trained on thermal snapshots of a 1D O(3) spin glass recovers the microscopic Hamiltonian parameters with 99.7% cosine similarity to ground truth through linear inversion of its learned score field."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A generative network trained only on spin snapshots recovers the system's exact Hamiltonian parameters via linear inversion of its score field."}],"snapshot_sha256":"72a001ca299c72b929fcbf1501f67ae33b4f1303d4dd7c452c0b626776c4cba5"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"1e909ea70e1be09f8cd38209b18db5eca54ee5e4249ca7d3f861630be514ac5f"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.20821/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or do they autonomously deduce the underlying physical laws? To address this, we introduce a rigorous algebraic framework to extract the implicit physical interactions learned by generative models. By establishing an exact equivalence between the zero-noise limit of a Riemannian diffusion score field and the thermodynamic restoring force, we utilize the traine","authors_text":"Wei-Qiang Chen, Wenjie Xi","cross_cats":["cond-mat.stat-mech"],"headline":"A generative network trained only on spin snapshots recovers the system's exact Hamiltonian parameters via linear inversion of its score field.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-04-22T17:46:35Z","title":"Autonomous Emergence of Hamiltonian in Deep Generative Models"},"references":{"count":25,"internal_anchors":0,"resolved_work":25,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"J. Abramson, J. Adler, J. Dunger, R. Evans, T. Green, A. Pritzel, O. Ronneberger, L. Willmore, A. J. Bal- lard, J. Bambrick, S. W. Bodenstein, D. A. Evans, C.-C. Hung, M. O’Neill, D. Reiman, K. Tunyas","work_id":"d58f1684-17fd-452d-97de-1931a5cf2602","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"J. Ho, A. Jain, and P. Abbeel, Denoising diffusion prob- abilistic models (2020)","work_id":"86932763-75bb-4bbf-b363-3e755f46d20a","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, Score-based generative modeling through stochastic differential equations (2020)","work_id":"0c1b1dfe-c1ac-464a-acc0-2c03067574c9","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Y. Bahri, J. Kadmon, J. Pennington, S. S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Annual Review of Con- densed Matter Physics11, 501–528 (2020)","work_id":"1d131d7e-e3cc-49c4-b276-5340f4ba2561","year":2020},{"cited_arxiv_id":"","doi":"10.1126/sciadv.aay2631","is_internal_anchor":false,"ref_index":6,"title":"S.-M. Udrescu and M. Tegmark, Science Advances6, 10.1126/sciadv.aay2631 (2020)","work_id":"6222c28d-2f18-4392-8cb2-0ab215b1b5d2","year":2020}],"snapshot_sha256":"baf06e00648ca1b6b41a3a9c147bac7a846f4528ce869eab8e0e33b93db24090"},"source":{"id":"2604.20821","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-19T17:14:58.252582Z","id":"f74557ae-af07-416c-a15d-4cec9b68821a","model_set":{"reader":"grok-4.3"},"one_line_summary":"A symmetry-equivariant generative model trained on thermal snapshots of a 1D O(3) spin glass recovers the microscopic Hamiltonian parameters with 99.7% cosine similarity to ground truth through linear inversion of its learned score field.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A generative network trained only on spin snapshots recovers the system's exact Hamiltonian parameters via linear inversion of its score field.","strongest_claim":"Without incorporating any energetic priors, an overdetermined linear inversion successfully recovers the microscopic Hamiltonian parameters of the spin system. The inferred Hamiltonian parameters exhibit a 99.7% cosine similarity with the ground-truth interaction parameters. Furthermore, these sparse local parameters alone are sufficient to explain 87% of the variance in the continuous force field predicted by the network.","weakest_assumption":"By establishing an exact equivalence between the zero-noise limit of a Riemannian diffusion score field and the thermodynamic restoring force, we utilize the trained neural network as a direct force estimator. This equivalence is the load-bearing premise that allows the network output to be interpreted as a physical force; if it does not hold exactly for the chosen diffusion process and manifold, the subsequent linear inversion cannot recover the true Hamiltonian."}},"verdict_id":"f74557ae-af07-416c-a15d-4cec9b68821a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:49b14f58a8cae1f7430e3713295a6a554ce83f568c1f95063747a3b84357c03c","target":"record","created_at":"2026-05-20T00:01:41Z","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":"fdacddce73f1edfad5f84d225c836e308351928bfce45796f6ebd094b12497c0","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-04-22T17:46:35Z","title_canon_sha256":"6077251fb364106bfe5e3ad7b9160fea9d31aed6cfccbc84b643bb4d323367aa"},"schema_version":"1.0","source":{"id":"2604.20821","kind":"arxiv","version":2}},"canonical_sha256":"caeb0fb2d50f31fcd1c8a622dbd311af7ed1731c2ee2d4db2c8337a61a12d348","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caeb0fb2d50f31fcd1c8a622dbd311af7ed1731c2ee2d4db2c8337a61a12d348","first_computed_at":"2026-05-20T00:01:41.714107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:41.714107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k98ruhRTb5j2KUBg3TRiMh42lRZvNn/L9PQ1QKv8h/mQv0j7UA/aHbkmgO6PJO2JiwKDJWW0QHHeFb+RLp8CBg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:41.714707Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.20821","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49b14f58a8cae1f7430e3713295a6a554ce83f568c1f95063747a3b84357c03c","sha256:16e8fe3097aa50ce0be8361ff611b6dc3ef9619e5dcbca84ad95176ffbbcda62","sha256:a1e25f3896b24d728a0a1f95561d989fd1c38b1f44ad3e579fe21f156b28cc40"],"state_sha256":"ab86142faadb2464a1bdda80c3e016671b6a115a037b0978e08a56741670c129"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UrEP0yCM0cnT+7hHrfCDfoX8GPIgcX7IaPpSdb3uUPEzZxW/6I4wYcxtJ9kKBhTeKAAiBDYSu33ix2newvFfCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:00:54.594259Z","bundle_sha256":"858b4ba7b2dc07b77adca4e694c51870ffe7c5e09e276a1aecb48a34c2856082"}}