{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:W5VAG5ZAERMLIHR4MP2UODXBR6","short_pith_number":"pith:W5VAG5ZA","schema_version":"1.0","canonical_sha256":"b76a0377202458b41e3c63f5470ee18fb59007b2198ba3811dec8ccaf522f91c","source":{"kind":"arxiv","id":"2606.22984","version":1},"attestation_state":"computed","paper":{"title":"Scalable Physics-Inspired Transformers for Spin Glasses","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG"],"primary_cat":"cond-mat.dis-nn","authors_text":"Jing Liu, Lu Zhong, Pan Zhang, Wenli Duan, Ying Tang","submitted_at":"2026-06-22T08:04:53Z","abstract_excerpt":"Efficient sampling of the Boltzmann distribution in frustrated spin glasses is central to statistical mechanics and combinatorial optimization. Despite advances in machine-learning-based approaches, two issues persist: limited understanding of why variational models fail to benefit from increased scale, unlike the monotonic scaling law of large language models; and high computational cost on large systems that negates advantages over classical sampling methods. Here, we develop a physics-inspired transformer with interpretable sparse attention and spin-tailored positional embeddings to address"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.22984","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-22T08:04:53Z","cross_cats_sorted":["cond-mat.stat-mech","cs.LG"],"title_canon_sha256":"699ce5f3429c219e93d7ad6f961afd96962b05e42737ea61fbfc9c5a04a1bb62","abstract_canon_sha256":"4b56f67b0e7b449d368a795ca58db7613cdf5252d218a921fa08a7710947c60c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:05.962559Z","signature_b64":"L+i5g9LGld1ieEZeq6VnHOpOvq19MILdEsWr8d4G8dxoylfPHF5RdgSWgbcjA4fCXL4qBdRGQs1r03lcT+SHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b76a0377202458b41e3c63f5470ee18fb59007b2198ba3811dec8ccaf522f91c","last_reissued_at":"2026-06-23T03:14:05.962181Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:05.962181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalable Physics-Inspired Transformers for Spin Glasses","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG"],"primary_cat":"cond-mat.dis-nn","authors_text":"Jing Liu, Lu Zhong, Pan Zhang, Wenli Duan, Ying Tang","submitted_at":"2026-06-22T08:04:53Z","abstract_excerpt":"Efficient sampling of the Boltzmann distribution in frustrated spin glasses is central to statistical mechanics and combinatorial optimization. Despite advances in machine-learning-based approaches, two issues persist: limited understanding of why variational models fail to benefit from increased scale, unlike the monotonic scaling law of large language models; and high computational cost on large systems that negates advantages over classical sampling methods. Here, we develop a physics-inspired transformer with interpretable sparse attention and spin-tailored positional embeddings to address"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22984","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/2606.22984/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.22984","created_at":"2026-06-23T03:14:05.962238+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22984v1","created_at":"2026-06-23T03:14:05.962238+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22984","created_at":"2026-06-23T03:14:05.962238+00:00"},{"alias_kind":"pith_short_12","alias_value":"W5VAG5ZAERML","created_at":"2026-06-23T03:14:05.962238+00:00"},{"alias_kind":"pith_short_16","alias_value":"W5VAG5ZAERMLIHR4","created_at":"2026-06-23T03:14:05.962238+00:00"},{"alias_kind":"pith_short_8","alias_value":"W5VAG5ZA","created_at":"2026-06-23T03:14:05.962238+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6","json":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6.json","graph_json":"https://pith.science/api/pith-number/W5VAG5ZAERMLIHR4MP2UODXBR6/graph.json","events_json":"https://pith.science/api/pith-number/W5VAG5ZAERMLIHR4MP2UODXBR6/events.json","paper":"https://pith.science/paper/W5VAG5ZA"},"agent_actions":{"view_html":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6","download_json":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6.json","view_paper":"https://pith.science/paper/W5VAG5ZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22984&json=true","fetch_graph":"https://pith.science/api/pith-number/W5VAG5ZAERMLIHR4MP2UODXBR6/graph.json","fetch_events":"https://pith.science/api/pith-number/W5VAG5ZAERMLIHR4MP2UODXBR6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6/action/storage_attestation","attest_author":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6/action/author_attestation","sign_citation":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6/action/citation_signature","submit_replication":"https://pith.science/pith/W5VAG5ZAERMLIHR4MP2UODXBR6/action/replication_record"}},"created_at":"2026-06-23T03:14:05.962238+00:00","updated_at":"2026-06-23T03:14:05.962238+00:00"}