{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EM4MOEQ26JTHKVO57RIDFDCEZQ","short_pith_number":"pith:EM4MOEQ2","canonical_record":{"source":{"id":"2605.16211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:26:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f335ffa2ee29b3534de6c136317a0461a3e84f8144618bc5aa99040c043ada65","abstract_canon_sha256":"0df67896596497b02fab8fca442d83f6f2a9e03387ad450a0419a681a5460421"},"schema_version":"1.0"},"canonical_sha256":"2338c7121af2667555ddfc50328c44cc3697758da8e34325571129cc6eefcf6c","source":{"kind":"arxiv","id":"2605.16211","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16211","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16211v1","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16211","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"EM4MOEQ26JTH","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_16","alias_value":"EM4MOEQ26JTHKVO5","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_8","alias_value":"EM4MOEQ2","created_at":"2026-05-20T00:01:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EM4MOEQ26JTHKVO57RIDFDCEZQ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.16211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:26:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f335ffa2ee29b3534de6c136317a0461a3e84f8144618bc5aa99040c043ada65","abstract_canon_sha256":"0df67896596497b02fab8fca442d83f6f2a9e03387ad450a0419a681a5460421"},"schema_version":"1.0"},"canonical_sha256":"2338c7121af2667555ddfc50328c44cc3697758da8e34325571129cc6eefcf6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:58.248285Z","signature_b64":"YDAeJi+oTWlcgEmrsSQEAEyd6VTJMbDsx0N91Mv2me85xeI5AU3J36jcIlIplY6GEbLobD26QrMlUWbOsIVGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2338c7121af2667555ddfc50328c44cc3697758da8e34325571129cc6eefcf6c","last_reissued_at":"2026-05-20T00:01:58.247325Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:58.247325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.16211","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":"2026-05-20T00:01:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BjeQxhiDSQMUCBHgzByW2Kykf+i82/HqkISoF4J7P0AGC4gK04Sr6/q1qM/ciL5IixOPN+Ki5nT2OrA2JmINCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:21:44.146294Z"},"content_sha256":"e75b0a5d2ba4598c9bf05360b3e9e57369f15cc358674021acc9ccc9ffa1bdc8","schema_version":"1.0","event_id":"sha256:e75b0a5d2ba4598c9bf05360b3e9e57369f15cc358674021acc9ccc9ffa1bdc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EM4MOEQ26JTHKVO57RIDFDCEZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypothesis-driven construction of mesoscopic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.LG","authors_text":"Aiqing Zhu, Qianxiao Li, Zhuoyuan Li","submitted_at":"2026-05-15T17:26:28Z","abstract_excerpt":"Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class. Building upon a generalized Onsager principle, we introduce a unified framework encompassing both dissipative and conservative mesoscopic dynamics. We establish uniform and a priori theoretical guarantees, including "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16211","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/2605.16211/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"shingle_duplication","ran_at":"2026-05-19T17:49:44.674088Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:44.164198Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:24.819164Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T17:31:34.208026Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T17:22:06.738112Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.393951Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"919432c610d3657fb33cb4ddbe2a5aa3a9cd905f91aba05bf4607b54b0485d6f"},"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":"2026-05-20T00:01:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrNqKTQSa/O57y+WGUStWcmH+hbKjNVJR5+WBMi7JracNNuEFt/oausj3rI2CNQYYE756HufHMf0iDujJfT9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:21:44.147022Z"},"content_sha256":"f4a4b727a3da074c85a96d3e9dc607b0ad7db12d3830c302cf030ae4e6b18d27","schema_version":"1.0","event_id":"sha256:f4a4b727a3da074c85a96d3e9dc607b0ad7db12d3830c302cf030ae4e6b18d27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EM4MOEQ26JTHKVO57RIDFDCEZQ/bundle.json","state_url":"https://pith.science/pith/EM4MOEQ26JTHKVO57RIDFDCEZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EM4MOEQ26JTHKVO57RIDFDCEZQ/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":"2026-06-01T21:21:44Z","links":{"resolver":"https://pith.science/pith/EM4MOEQ26JTHKVO57RIDFDCEZQ","bundle":"https://pith.science/pith/EM4MOEQ26JTHKVO57RIDFDCEZQ/bundle.json","state":"https://pith.science/pith/EM4MOEQ26JTHKVO57RIDFDCEZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EM4MOEQ26JTHKVO57RIDFDCEZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EM4MOEQ26JTHKVO57RIDFDCEZQ","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":"0df67896596497b02fab8fca442d83f6f2a9e03387ad450a0419a681a5460421","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:26:28Z","title_canon_sha256":"f335ffa2ee29b3534de6c136317a0461a3e84f8144618bc5aa99040c043ada65"},"schema_version":"1.0","source":{"id":"2605.16211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16211","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16211v1","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16211","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"EM4MOEQ26JTH","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_16","alias_value":"EM4MOEQ26JTHKVO5","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_8","alias_value":"EM4MOEQ2","created_at":"2026-05-20T00:01:58Z"}],"graph_snapshots":[{"event_id":"sha256:f4a4b727a3da074c85a96d3e9dc607b0ad7db12d3830c302cf030ae4e6b18d27","target":"graph","created_at":"2026-05-20T00:01:58Z","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":[{"findings_count":0,"name":"shingle_duplication","ran_at":"2026-05-19T17:49:44.674088Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:44.164198Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:24.819164Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"external_links","ran_at":"2026-05-19T17:31:34.208026Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"cited_work_retraction","ran_at":"2026-05-19T17:22:06.738112Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.393951Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.16211/integrity.json","findings":[],"snapshot_sha256":"919432c610d3657fb33cb4ddbe2a5aa3a9cd905f91aba05bf4607b54b0485d6f","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class. Building upon a generalized Onsager principle, we introduce a unified framework encompassing both dissipative and conservative mesoscopic dynamics. We establish uniform and a priori theoretical guarantees, including ","authors_text":"Aiqing Zhu, Qianxiao Li, Zhuoyuan Li","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:26:28Z","title":"Hypothesis-driven construction of mesoscopic dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16211","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:e75b0a5d2ba4598c9bf05360b3e9e57369f15cc358674021acc9ccc9ffa1bdc8","target":"record","created_at":"2026-05-20T00:01:58Z","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":"0df67896596497b02fab8fca442d83f6f2a9e03387ad450a0419a681a5460421","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:26:28Z","title_canon_sha256":"f335ffa2ee29b3534de6c136317a0461a3e84f8144618bc5aa99040c043ada65"},"schema_version":"1.0","source":{"id":"2605.16211","kind":"arxiv","version":1}},"canonical_sha256":"2338c7121af2667555ddfc50328c44cc3697758da8e34325571129cc6eefcf6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2338c7121af2667555ddfc50328c44cc3697758da8e34325571129cc6eefcf6c","first_computed_at":"2026-05-20T00:01:58.247325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:58.247325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YDAeJi+oTWlcgEmrsSQEAEyd6VTJMbDsx0N91Mv2me85xeI5AU3J36jcIlIplY6GEbLobD26QrMlUWbOsIVGBQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:58.248285Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e75b0a5d2ba4598c9bf05360b3e9e57369f15cc358674021acc9ccc9ffa1bdc8","sha256:f4a4b727a3da074c85a96d3e9dc607b0ad7db12d3830c302cf030ae4e6b18d27"],"state_sha256":"90f3190721e9e60656199eddae44a009ed302a43d57322d51d4e95a0824c63a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9+st1O0qGtMeF+zXrMLOTbAkPqBFsWPvSal2vdPzw4/gU4EYZIRC0+Xtj6jyyAd+HsS6nWqmci2W0bQzx9KAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:21:44.150066Z","bundle_sha256":"14e1552050dec489b1b68266dc4b8b0cf26c29fb469db6fdb7b95dfa7b2e7636"}}