{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2QDGBVMNNS3FHTH7U6MWOCWCH6","short_pith_number":"pith:2QDGBVMN","canonical_record":{"source":{"id":"2607.14875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-16T11:46:06Z","cross_cats_sorted":["cond-mat.dis-nn","physics.comp-ph"],"title_canon_sha256":"a7fdbf0107e5c2638f5115b8ebfb5204a5676365a33cab72908f1110930d9bbe","abstract_canon_sha256":"98907c4c20ba3250bcc1d4815f8dded96a2aaa6b78fbb64ee808de986104ddec"},"schema_version":"1.0"},"canonical_sha256":"d40660d58d6cb653ccffa799670ac23fb5dafdb043106016c8d09f5d9744d5a5","source":{"kind":"arxiv","id":"2607.14875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14875","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14875v1","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14875","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"pith_short_12","alias_value":"2QDGBVMNNS3F","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"pith_short_16","alias_value":"2QDGBVMNNS3FHTH7","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"pith_short_8","alias_value":"2QDGBVMN","created_at":"2026-07-17T01:21:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2QDGBVMNNS3FHTH7U6MWOCWCH6","target":"record","payload":{"canonical_record":{"source":{"id":"2607.14875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-16T11:46:06Z","cross_cats_sorted":["cond-mat.dis-nn","physics.comp-ph"],"title_canon_sha256":"a7fdbf0107e5c2638f5115b8ebfb5204a5676365a33cab72908f1110930d9bbe","abstract_canon_sha256":"98907c4c20ba3250bcc1d4815f8dded96a2aaa6b78fbb64ee808de986104ddec"},"schema_version":"1.0"},"canonical_sha256":"d40660d58d6cb653ccffa799670ac23fb5dafdb043106016c8d09f5d9744d5a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:56.629048Z","signature_b64":"RKrDYxCoyDX4o/4b/KYZ65XHnKDnmYibuRhhosxseUNux+EVaQ17YZEk5cP/gx4F1vuEJRvivHhNpwk226/9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d40660d58d6cb653ccffa799670ac23fb5dafdb043106016c8d09f5d9744d5a5","last_reissued_at":"2026-07-17T01:21:56.628295Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:56.628295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.14875","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":"2026-07-17T01:21:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GZPGlGT84uILHNo8yq4DgEII/i2E1uk8e+kHOqrS6CcD3hdKBQyX3r8Lf/kI9VeNYUmjG7qLQjrDblg6+KOMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:05:42.298171Z"},"content_sha256":"ac31ee5de609b287fac6c1f1007986dc9a055128858a6b6099447514fa4a85e5","schema_version":"1.0","event_id":"sha256:ac31ee5de609b287fac6c1f1007986dc9a055128858a6b6099447514fa4a85e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2QDGBVMNNS3FHTH7U6MWOCWCH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimization dynamics of Transformer backflow neural quantum states for the two-dimensional Hubbard model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","physics.comp-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Jia-Qi Wang, Rong-Qiang He, Zhong-Yi Lu, Zong-Yu Liao","submitted_at":"2026-07-16T11:46:06Z","abstract_excerpt":"Building on the multi-determinant Transformer backflow neural quantum state (NQS) ansatz and the associated multi-stage training workflow for the doped two-dimensional Hubbard model, we investigate how the optimization dynamics of the NQS depend on several key optimization and architectural hyperparameters. The workflow consists of neural-network backflow (NNB) initialization, supervised Transformer pre-training, and main energy optimization using the Moment-Adaptive ReConfiguration Heuristic (MARCH) within variational Monte Carlo. Using the doped $4\\times4$ periodic Hubbard model at $U=8$ as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14875","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/2607.14875/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":"2026-07-17T01:21:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"schYJQAZemY/cUDyUWJUDPQK/RwvgxPdHPTnKq/ZQOiOSJ6E0gDs9RX1teOwcFNOUmeq/YaK0wmqWvxhYM/sDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:05:42.298700Z"},"content_sha256":"92fa4302af2bc89b98c82e8844dd465fb721703ea00c293b51326e0d631fa7d4","schema_version":"1.0","event_id":"sha256:92fa4302af2bc89b98c82e8844dd465fb721703ea00c293b51326e0d631fa7d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QDGBVMNNS3FHTH7U6MWOCWCH6/bundle.json","state_url":"https://pith.science/pith/2QDGBVMNNS3FHTH7U6MWOCWCH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QDGBVMNNS3FHTH7U6MWOCWCH6/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":"2026-08-04T17:05:42Z","links":{"resolver":"https://pith.science/pith/2QDGBVMNNS3FHTH7U6MWOCWCH6","bundle":"https://pith.science/pith/2QDGBVMNNS3FHTH7U6MWOCWCH6/bundle.json","state":"https://pith.science/pith/2QDGBVMNNS3FHTH7U6MWOCWCH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QDGBVMNNS3FHTH7U6MWOCWCH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2QDGBVMNNS3FHTH7U6MWOCWCH6","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":"98907c4c20ba3250bcc1d4815f8dded96a2aaa6b78fbb64ee808de986104ddec","cross_cats_sorted":["cond-mat.dis-nn","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-16T11:46:06Z","title_canon_sha256":"a7fdbf0107e5c2638f5115b8ebfb5204a5676365a33cab72908f1110930d9bbe"},"schema_version":"1.0","source":{"id":"2607.14875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14875","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14875v1","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14875","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"pith_short_12","alias_value":"2QDGBVMNNS3F","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"pith_short_16","alias_value":"2QDGBVMNNS3FHTH7","created_at":"2026-07-17T01:21:56Z"},{"alias_kind":"pith_short_8","alias_value":"2QDGBVMN","created_at":"2026-07-17T01:21:56Z"}],"graph_snapshots":[{"event_id":"sha256:92fa4302af2bc89b98c82e8844dd465fb721703ea00c293b51326e0d631fa7d4","target":"graph","created_at":"2026-07-17T01:21:56Z","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/2607.14875/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building on the multi-determinant Transformer backflow neural quantum state (NQS) ansatz and the associated multi-stage training workflow for the doped two-dimensional Hubbard model, we investigate how the optimization dynamics of the NQS depend on several key optimization and architectural hyperparameters. The workflow consists of neural-network backflow (NNB) initialization, supervised Transformer pre-training, and main energy optimization using the Moment-Adaptive ReConfiguration Heuristic (MARCH) within variational Monte Carlo. Using the doped $4\\times4$ periodic Hubbard model at $U=8$ as ","authors_text":"Jia-Qi Wang, Rong-Qiang He, Zhong-Yi Lu, Zong-Yu Liao","cross_cats":["cond-mat.dis-nn","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-16T11:46:06Z","title":"Optimization dynamics of Transformer backflow neural quantum states for the two-dimensional Hubbard model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14875","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:ac31ee5de609b287fac6c1f1007986dc9a055128858a6b6099447514fa4a85e5","target":"record","created_at":"2026-07-17T01:21:56Z","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":"98907c4c20ba3250bcc1d4815f8dded96a2aaa6b78fbb64ee808de986104ddec","cross_cats_sorted":["cond-mat.dis-nn","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-16T11:46:06Z","title_canon_sha256":"a7fdbf0107e5c2638f5115b8ebfb5204a5676365a33cab72908f1110930d9bbe"},"schema_version":"1.0","source":{"id":"2607.14875","kind":"arxiv","version":1}},"canonical_sha256":"d40660d58d6cb653ccffa799670ac23fb5dafdb043106016c8d09f5d9744d5a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d40660d58d6cb653ccffa799670ac23fb5dafdb043106016c8d09f5d9744d5a5","first_computed_at":"2026-07-17T01:21:56.628295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:21:56.628295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RKrDYxCoyDX4o/4b/KYZ65XHnKDnmYibuRhhosxseUNux+EVaQ17YZEk5cP/gx4F1vuEJRvivHhNpwk226/9CA==","signature_status":"signed_v1","signed_at":"2026-07-17T01:21:56.629048Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.14875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac31ee5de609b287fac6c1f1007986dc9a055128858a6b6099447514fa4a85e5","sha256:92fa4302af2bc89b98c82e8844dd465fb721703ea00c293b51326e0d631fa7d4"],"state_sha256":"51aeca1581d4912c2bcd9ad98db50a565c7d82e1a9d911b122e85b273ae68c8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KVq2x1pvv89L55GtFnuLr85yA3Di2hOViImI9aIDgizgsToXjJhd049uWSVXdkazfdJWpFKGApdOIiSQDLkTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:05:42.302505Z","bundle_sha256":"825218716fdedb65a703824269b3a2e953447fa3b6071f3619e1fafd7c680295"}}