{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:HCAQQIW7KKCX25GIDVEIXQCJTD","short_pith_number":"pith:HCAQQIW7","canonical_record":{"source":{"id":"2203.06442","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-03-12T14:22:14Z","cross_cats_sorted":[],"title_canon_sha256":"725f362c739a6fc8faca6553dc04b46af3087d65faa6811e3df1992c0c992db1","abstract_canon_sha256":"ef7ee607256b9f1925743c9cb84e3536d58117bb424797b0030799bb560cfa59"},"schema_version":"1.0"},"canonical_sha256":"38810822df52857d74c81d488bc04998fd61e78c6c22c9e36101876734a91462","source":{"kind":"arxiv","id":"2203.06442","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.06442","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2203.06442v1","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.06442","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"HCAQQIW7KKCX","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"HCAQQIW7KKCX25GI","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"HCAQQIW7","created_at":"2026-07-05T04:04:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:HCAQQIW7KKCX25GIDVEIXQCJTD","target":"record","payload":{"canonical_record":{"source":{"id":"2203.06442","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-03-12T14:22:14Z","cross_cats_sorted":[],"title_canon_sha256":"725f362c739a6fc8faca6553dc04b46af3087d65faa6811e3df1992c0c992db1","abstract_canon_sha256":"ef7ee607256b9f1925743c9cb84e3536d58117bb424797b0030799bb560cfa59"},"schema_version":"1.0"},"canonical_sha256":"38810822df52857d74c81d488bc04998fd61e78c6c22c9e36101876734a91462","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:04:50.802860Z","signature_b64":"nN2+CMe1rvs6ki3MlsR/paqx6+5cvIElvZwwEskR+CkRTAMVjRT75oFSSwLU4/EtIom7NpQg3DOJMam3m4ONAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38810822df52857d74c81d488bc04998fd61e78c6c22c9e36101876734a91462","last_reissued_at":"2026-07-05T04:04:50.802335Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:04:50.802335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.06442","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":"2026-07-05T04:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M33sqp9URG1VwVtd/uWBhO1rYO5she6YDG9aZpLB2ukakO7+1cSxPR3sISSkhTQl27EzyrkUOKusDSanlT4TDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T00:25:49.386006Z"},"content_sha256":"3cd8a07381013b0cdddb0c1e9cc3a4785b07b64b2aef336d6213cd4b9791627e","schema_version":"1.0","event_id":"sha256:3cd8a07381013b0cdddb0c1e9cc3a4785b07b64b2aef336d6213cd4b9791627e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:HCAQQIW7KKCX25GIDVEIXQCJTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant Graph Mechanics Networks with Constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Fuchun Sun, Jiaqi Han, Junzhou Huang, Tingyang Xu, Wenbing Huang, Yu Rong","submitted_at":"2022-03-12T14:22:14Z","abstract_excerpt":"Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and commonly geometrically-constrained. Current methods, particularly the ones based on equivariant Graph Neural Networks (GNNs), have targeted on the first two challenges but remain immature for constrained systems. In this paper, we propose Graph Mechanics Network (GMN) which is combinatorially efficient, equivariant and constraint-aware. The core of GMN is that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.06442","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/2203.06442/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":"2026-07-05T04:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HjAZQv7R/bHQkNzEPKrS+WySogQHSpIOPGMjYOKPNgsJ0X2+QzrMZDXkzmsr+RfmZym7GI85qQFLRQYRPP2mCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T00:25:49.386517Z"},"content_sha256":"a012f4ca0699ee8ddf9d1908ef0e7a394ce0ce98117da90393d57226304907ee","schema_version":"1.0","event_id":"sha256:a012f4ca0699ee8ddf9d1908ef0e7a394ce0ce98117da90393d57226304907ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCAQQIW7KKCX25GIDVEIXQCJTD/bundle.json","state_url":"https://pith.science/pith/HCAQQIW7KKCX25GIDVEIXQCJTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCAQQIW7KKCX25GIDVEIXQCJTD/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":"2026-08-07T00:25:49Z","links":{"resolver":"https://pith.science/pith/HCAQQIW7KKCX25GIDVEIXQCJTD","bundle":"https://pith.science/pith/HCAQQIW7KKCX25GIDVEIXQCJTD/bundle.json","state":"https://pith.science/pith/HCAQQIW7KKCX25GIDVEIXQCJTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCAQQIW7KKCX25GIDVEIXQCJTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:HCAQQIW7KKCX25GIDVEIXQCJTD","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":"ef7ee607256b9f1925743c9cb84e3536d58117bb424797b0030799bb560cfa59","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-03-12T14:22:14Z","title_canon_sha256":"725f362c739a6fc8faca6553dc04b46af3087d65faa6811e3df1992c0c992db1"},"schema_version":"1.0","source":{"id":"2203.06442","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.06442","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2203.06442v1","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.06442","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"HCAQQIW7KKCX","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"HCAQQIW7KKCX25GI","created_at":"2026-07-05T04:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"HCAQQIW7","created_at":"2026-07-05T04:04:50Z"}],"graph_snapshots":[{"event_id":"sha256:a012f4ca0699ee8ddf9d1908ef0e7a394ce0ce98117da90393d57226304907ee","target":"graph","created_at":"2026-07-05T04:04:50Z","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/2203.06442/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and commonly geometrically-constrained. Current methods, particularly the ones based on equivariant Graph Neural Networks (GNNs), have targeted on the first two challenges but remain immature for constrained systems. In this paper, we propose Graph Mechanics Network (GMN) which is combinatorially efficient, equivariant and constraint-aware. The core of GMN is that ","authors_text":"Fuchun Sun, Jiaqi Han, Junzhou Huang, Tingyang Xu, Wenbing Huang, Yu Rong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-03-12T14:22:14Z","title":"Equivariant Graph Mechanics Networks with Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.06442","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":"sha256:3cd8a07381013b0cdddb0c1e9cc3a4785b07b64b2aef336d6213cd4b9791627e","target":"record","created_at":"2026-07-05T04:04:50Z","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":"ef7ee607256b9f1925743c9cb84e3536d58117bb424797b0030799bb560cfa59","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-03-12T14:22:14Z","title_canon_sha256":"725f362c739a6fc8faca6553dc04b46af3087d65faa6811e3df1992c0c992db1"},"schema_version":"1.0","source":{"id":"2203.06442","kind":"arxiv","version":1}},"canonical_sha256":"38810822df52857d74c81d488bc04998fd61e78c6c22c9e36101876734a91462","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38810822df52857d74c81d488bc04998fd61e78c6c22c9e36101876734a91462","first_computed_at":"2026-07-05T04:04:50.802335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:04:50.802335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nN2+CMe1rvs6ki3MlsR/paqx6+5cvIElvZwwEskR+CkRTAMVjRT75oFSSwLU4/EtIom7NpQg3DOJMam3m4ONAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:04:50.802860Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.06442","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cd8a07381013b0cdddb0c1e9cc3a4785b07b64b2aef336d6213cd4b9791627e","sha256:a012f4ca0699ee8ddf9d1908ef0e7a394ce0ce98117da90393d57226304907ee"],"state_sha256":"1224d4f9dc6f8dec304a5f8eb13bf0faf26d486cc246031b105eef4041d67a6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awYKxUoIadB2EzOpTZJrSEMDigqo7lMT9B5Mkr0bo1Z04S1tOW4xsBNtEqQPL8lmuYQXglboBvJ89NlCZa5VCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T00:25:49.391308Z","bundle_sha256":"6144f6c117ea95b259c1894c7f31f4f2d13f70497aa4b2b2a39cfe8caf398a17"}}