{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UJMYBB644DEPTC4K4X37CMULAQ","short_pith_number":"pith:UJMYBB64","schema_version":"1.0","canonical_sha256":"a2598087dce0c8f98b8ae5f7f1328b0405d9e5e69bdde3c6dde1d2703e6d70c7","source":{"kind":"arxiv","id":"2606.07426","version":1},"attestation_state":"computed","paper":{"title":"Discovering Multiscale Deep Formulas in Complex Systems via Neural-Guided Lambda Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Cong Zhao, Hanqiao Yu, Shusen Yang, Xuebin Ren","submitted_at":"2026-06-05T16:21:12Z","abstract_excerpt":"A fundamental problem in science is identifying underlying patterns of complex systems in the form of concise mathematical formulas. Current Artificial Intelligence (AI)-based methods have shown strong performance in single-scale systems, yet remain limited in identifying scale-specific formulas in multiscale complex systems. We present Deflex, an end-to-end AI method to automatically extract multiscale formulas with potentially different forms, including invariants and distributions, from complex systems. Deflex consists of two subsystems named Deflexformer and Deflexpressor. Deflexpressor is"},"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":"2606.07426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-05T16:21:12Z","cross_cats_sorted":[],"title_canon_sha256":"ee2d2a7201ad908d8e21003c17608c0abdbd8035631b4896ba87198afc72cacb","abstract_canon_sha256":"33f2812cba2119cca9d4b8aa1d75f245a899ea6366f07e9991638207ac08148f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:05:26.453051Z","signature_b64":"OL/p+u0YWshGDQr7iH2hiIceT2zlj8unl8UO5Qk+i7TvlJS+wN0StrcTtJj0alUP/ZEmRxygPCDqhjbRPfziDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2598087dce0c8f98b8ae5f7f1328b0405d9e5e69bdde3c6dde1d2703e6d70c7","last_reissued_at":"2026-06-08T01:05:26.452559Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:05:26.452559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discovering Multiscale Deep Formulas in Complex Systems via Neural-Guided Lambda Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Cong Zhao, Hanqiao Yu, Shusen Yang, Xuebin Ren","submitted_at":"2026-06-05T16:21:12Z","abstract_excerpt":"A fundamental problem in science is identifying underlying patterns of complex systems in the form of concise mathematical formulas. Current Artificial Intelligence (AI)-based methods have shown strong performance in single-scale systems, yet remain limited in identifying scale-specific formulas in multiscale complex systems. We present Deflex, an end-to-end AI method to automatically extract multiscale formulas with potentially different forms, including invariants and distributions, from complex systems. Deflex consists of two subsystems named Deflexformer and Deflexpressor. Deflexpressor is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07426","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/2606.07426/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":"2606.07426","created_at":"2026-06-08T01:05:26.452636+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.07426v1","created_at":"2026-06-08T01:05:26.452636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07426","created_at":"2026-06-08T01:05:26.452636+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJMYBB644DEP","created_at":"2026-06-08T01:05:26.452636+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJMYBB644DEPTC4K","created_at":"2026-06-08T01:05:26.452636+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJMYBB64","created_at":"2026-06-08T01:05:26.452636+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/UJMYBB644DEPTC4K4X37CMULAQ","json":"https://pith.science/pith/UJMYBB644DEPTC4K4X37CMULAQ.json","graph_json":"https://pith.science/api/pith-number/UJMYBB644DEPTC4K4X37CMULAQ/graph.json","events_json":"https://pith.science/api/pith-number/UJMYBB644DEPTC4K4X37CMULAQ/events.json","paper":"https://pith.science/paper/UJMYBB64"},"agent_actions":{"view_html":"https://pith.science/pith/UJMYBB644DEPTC4K4X37CMULAQ","download_json":"https://pith.science/pith/UJMYBB644DEPTC4K4X37CMULAQ.json","view_paper":"https://pith.science/paper/UJMYBB64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.07426&json=true","fetch_graph":"https://pith.science/api/pith-number/UJMYBB644DEPTC4K4X37CMULAQ/graph.json","fetch_events":"https://pith.science/api/pith-number/UJMYBB644DEPTC4K4X37CMULAQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJMYBB644DEPTC4K4X37CMULAQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJMYBB644DEPTC4K4X37CMULAQ/action/storage_attestation","attest_author":"https://pith.science/pith/UJMYBB644DEPTC4K4X37CMULAQ/action/author_attestation","sign_citation":"https://pith.science/pith/UJMYBB644DEPTC4K4X37CMULAQ/action/citation_signature","submit_replication":"https://pith.science/pith/UJMYBB644DEPTC4K4X37CMULAQ/action/replication_record"}},"created_at":"2026-06-08T01:05:26.452636+00:00","updated_at":"2026-06-08T01:05:26.452636+00:00"}