{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AI2SPDJNYGLWMXH5XFDFCGNRCT","short_pith_number":"pith:AI2SPDJN","canonical_record":{"source":{"id":"2605.06022","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-05-07T11:15:43Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"044587b378b747012ed51d07487f71dc1f109172a4f5d020c4049f36dfa141ea","abstract_canon_sha256":"2d078ccbe4c4c87a7ccfe7e3057aeeafbd814f7f2e888e4dc3c4aab33fd739f3"},"schema_version":"1.0"},"canonical_sha256":"0235278d2dc197665cfdb9465119b114f8baeb5d032008c2c9a26c700beecca8","source":{"kind":"arxiv","id":"2605.06022","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AI2SPDJNYGLWMXH5XFDFCGNRCT","target":"record","payload":{"canonical_record":{"source":{"id":"2605.06022","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-05-07T11:15:43Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"044587b378b747012ed51d07487f71dc1f109172a4f5d020c4049f36dfa141ea","abstract_canon_sha256":"2d078ccbe4c4c87a7ccfe7e3057aeeafbd814f7f2e888e4dc3c4aab33fd739f3"},"schema_version":"1.0"},"canonical_sha256":"0235278d2dc197665cfdb9465119b114f8baeb5d032008c2c9a26c700beecca8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:38.379948Z","signature_b64":"HtuQOwydMwh2M0LqUZGXDlIIi+2VWtkao2Xw7xx0OSwg+KC6k+XUnZrJLBYa4KTTTj6OAB/H783lluELI0etAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0235278d2dc197665cfdb9465119b114f8baeb5d032008c2c9a26c700beecca8","last_reissued_at":"2026-06-25T01:18:38.379300Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:38.379300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.06022","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-25T01:18:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pZepsS/TIQhlg0oVqlFci9NB0bLj+jX4HRa188CKmpQ4kg0b8M/dB5GBX7V5xF8JAd4dKWgcgzR1Ot3HFYsKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T00:52:17.426737Z"},"content_sha256":"de06ae431a5c2dc287e47a5d35c7fca9a5a2fd653329aa8fd6046bc75f476e46","schema_version":"1.0","event_id":"sha256:de06ae431a5c2dc287e47a5d35c7fca9a5a2fd653329aa8fd6046bc75f476e46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AI2SPDJNYGLWMXH5XFDFCGNRCT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions","license":"http://creativecommons.org/licenses/by/4.0/","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.","cross_cats":["hep-th"],"primary_cat":"hep-lat","authors_text":"Tatsuhiro Misumi","submitted_at":"2026-05-07T11:15:43Z","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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4b2f280cbec764d0634e3dcd48b68ac76394a713dc94613dd0c7a89b645a6357"},"source":{"id":"2605.06022","kind":"arxiv","version":3},"verdict":{"id":"ca289d94-7a83-45c0-8a1e-066309306e3e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T22:04:10.340964Z","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.","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","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.","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."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06022/integrity.json","findings":[],"available":true,"detectors_run":[{"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","findings_count":0}],"snapshot_sha256":"1632466a74e2d320e7496e451a376543359255f3296d2c936144c5b26bbf8b48"},"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":"ca289d94-7a83-45c0-8a1e-066309306e3e"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-25T01:18:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ICEqDU86IywBi2VvPgmbn2ZPFHRjyw0j3TBW87flHmJ7mFARJ1t8AqgKhHPPfHhMbLtN0aYChNMSbyf/JjLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T00:52:17.427665Z"},"content_sha256":"1a2ef637b4a0b39c0122c28c19d20639cafe7b5f5c8bdfc936e69396d7fe0804","schema_version":"1.0","event_id":"sha256:1a2ef637b4a0b39c0122c28c19d20639cafe7b5f5c8bdfc936e69396d7fe0804"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AI2SPDJNYGLWMXH5XFDFCGNRCT/bundle.json","state_url":"https://pith.science/pith/AI2SPDJNYGLWMXH5XFDFCGNRCT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AI2SPDJNYGLWMXH5XFDFCGNRCT/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":"2026-07-02T00:52:17Z","links":{"resolver":"https://pith.science/pith/AI2SPDJNYGLWMXH5XFDFCGNRCT","bundle":"https://pith.science/pith/AI2SPDJNYGLWMXH5XFDFCGNRCT/bundle.json","state":"https://pith.science/pith/AI2SPDJNYGLWMXH5XFDFCGNRCT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AI2SPDJNYGLWMXH5XFDFCGNRCT/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KoJgBgP1a1bFO/i3VynBpXW2m6WLEsF1CRpSRhJvNZQqw63XufUWZShQBlBHGY8nwnzMaRXhAZTTHqZXeBu3DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T00:52:17.432080Z","bundle_sha256":"36efc3b5a2d285e6efbf28ff54fe3f1b94eefbbd9374938b2a3c23bf13411a9e"}}