{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AI2SPDJNYGLWMXH5XFDFCGNRCT","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":"2d078ccbe4c4c87a7ccfe7e3057aeeafbd814f7f2e888e4dc3c4aab33fd739f3","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-05-07T11:15:43Z","title_canon_sha256":"044587b378b747012ed51d07487f71dc1f109172a4f5d020c4049f36dfa141ea"},"schema_version":"1.0","source":{"id":"2605.06022","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.06022","created_at":"2026-06-25T01:18:38Z"},{"alias_kind":"arxiv_version","alias_value":"2605.06022v3","created_at":"2026-06-25T01:18:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.06022","created_at":"2026-06-25T01:18:38Z"},{"alias_kind":"pith_short_12","alias_value":"AI2SPDJNYGLW","created_at":"2026-06-25T01:18:38Z"},{"alias_kind":"pith_short_16","alias_value":"AI2SPDJNYGLWMXH5","created_at":"2026-06-25T01:18:38Z"},{"alias_kind":"pith_short_8","alias_value":"AI2SPDJN","created_at":"2026-06-25T01:18:38Z"}],"graph_snapshots":[{"event_id":"sha256:1a2ef637b4a0b39c0122c28c19d20639cafe7b5f5c8bdfc936e69396d7fe0804","target":"graph","created_at":"2026-06-25T01:18:38Z","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":"when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomial or rational approximation. [...] by changing the initial search bias, the same framework also finds a distinct solution corresponding to a Fujikawa-type generalized GW relation."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That training the neural network with the Ginsparg-Wilson relation as a soft constraint will lead to the physically correct continuum limit and correct behavior for all relevant momenta, without additional verification steps or hard enforcement of locality."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Physics-Informed Neural Networks construct lattice Dirac operators satisfying the Ginsparg-Wilson relation, reproducing overlap fermions to high accuracy and discovering a Fujikawa-type generalized relation via algebraic search."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A neural network trained to satisfy the Ginsparg-Wilson relation as a soft constraint reproduces the overlap fermion operator to high accuracy without explicit sign-function approximations."}],"snapshot_sha256":"4b2f280cbec764d0634e3dcd48b68ac76394a713dc94613dd0c7a89b645a6357"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-20T13:22:04.336204Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T08:38:43.064538Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.177815Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T13:04:16.685439Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.06022/integrity.json","findings":[],"snapshot_sha256":"1632466a74e2d320e7496e451a376543359255f3296d2c936144c5b26bbf8b48","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a novel, machine-learning-based framework for constructing lattice fermions using Physics-Informed Neural Networks (PINNs). Our approach treats the formulation of the Dirac operator as an optimization problem guided by physical requirements, such as symmetries, locality and doubler-decoupling conditions. We first demonstrate that, when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomi","authors_text":"Tatsuhiro Misumi","cross_cats":["hep-th"],"headline":"A neural network trained to satisfy the Ginsparg-Wilson relation as a soft constraint reproduces the overlap fermion operator to high accuracy without explicit sign-function approximations.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-05-07T11:15:43Z","title":"Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.06022","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-14T22:04:10.340964Z","id":"ca289d94-7a83-45c0-8a1e-066309306e3e","model_set":{"reader":"grok-4.3"},"one_line_summary":"Physics-Informed Neural Networks construct lattice Dirac operators satisfying the Ginsparg-Wilson relation, reproducing overlap fermions to high accuracy and discovering a Fujikawa-type generalized relation via algebraic search.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A neural network trained to satisfy the Ginsparg-Wilson relation as a soft constraint reproduces the overlap fermion operator to high accuracy without explicit sign-function approximations.","strongest_claim":"when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomial or rational approximation. [...] by changing the initial search bias, the same framework also finds a distinct solution corresponding to a Fujikawa-type generalized GW relation.","weakest_assumption":"That training the neural network with the Ginsparg-Wilson relation as a soft constraint will lead to the physically correct continuum limit and correct behavior for all relevant momenta, without additional verification steps or hard enforcement of locality."}},"verdict_id":"ca289d94-7a83-45c0-8a1e-066309306e3e"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:de06ae431a5c2dc287e47a5d35c7fca9a5a2fd653329aa8fd6046bc75f476e46","target":"record","created_at":"2026-06-25T01:18:38Z","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":"2d078ccbe4c4c87a7ccfe7e3057aeeafbd814f7f2e888e4dc3c4aab33fd739f3","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-05-07T11:15:43Z","title_canon_sha256":"044587b378b747012ed51d07487f71dc1f109172a4f5d020c4049f36dfa141ea"},"schema_version":"1.0","source":{"id":"2605.06022","kind":"arxiv","version":3}},"canonical_sha256":"0235278d2dc197665cfdb9465119b114f8baeb5d032008c2c9a26c700beecca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0235278d2dc197665cfdb9465119b114f8baeb5d032008c2c9a26c700beecca8","first_computed_at":"2026-06-25T01:18:38.379300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:18:38.379300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HtuQOwydMwh2M0LqUZGXDlIIi+2VWtkao2Xw7xx0OSwg+KC6k+XUnZrJLBYa4KTTTj6OAB/H783lluELI0etAQ==","signature_status":"signed_v1","signed_at":"2026-06-25T01:18:38.379948Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.06022","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de06ae431a5c2dc287e47a5d35c7fca9a5a2fd653329aa8fd6046bc75f476e46","sha256:1a2ef637b4a0b39c0122c28c19d20639cafe7b5f5c8bdfc936e69396d7fe0804"],"state_sha256":"b64ca9966e008fa401ef8ad650d44dd72e6452cf481d8f86a9b09d8d0053da3b"}