{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:62KG24UIERAC2WXQMXNVOGCI6I","short_pith_number":"pith:62KG24UI","canonical_record":{"source":{"id":"2006.04780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-06-08T17:54:43Z","cross_cats_sorted":["cs.LG","hep-ex","physics.comp-ph","stat.ML"],"title_canon_sha256":"7289eae181a8a0e827ebcf4718412a266908b01a7453b50a26effd7a66f5f83f","abstract_canon_sha256":"ae1357d47f74072f05426a2283ddb04f7183cd0b65575e6cd5dc71b1bee0961e"},"schema_version":"1.0"},"canonical_sha256":"f6946d728824402d5af065db571848f22b7b57c49c7e6d8795dbf398871d4d7f","source":{"kind":"arxiv","id":"2006.04780","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.04780","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"arxiv_version","alias_value":"2006.04780v1","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.04780","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"pith_short_12","alias_value":"62KG24UIERAC","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"pith_short_16","alias_value":"62KG24UIERAC2WXQ","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"pith_short_8","alias_value":"62KG24UI","created_at":"2026-07-05T01:08:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:62KG24UIERAC2WXQMXNVOGCI6I","target":"record","payload":{"canonical_record":{"source":{"id":"2006.04780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-06-08T17:54:43Z","cross_cats_sorted":["cs.LG","hep-ex","physics.comp-ph","stat.ML"],"title_canon_sha256":"7289eae181a8a0e827ebcf4718412a266908b01a7453b50a26effd7a66f5f83f","abstract_canon_sha256":"ae1357d47f74072f05426a2283ddb04f7183cd0b65575e6cd5dc71b1bee0961e"},"schema_version":"1.0"},"canonical_sha256":"f6946d728824402d5af065db571848f22b7b57c49c7e6d8795dbf398871d4d7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:08:48.635210Z","signature_b64":"cTTOe1browu8IxPQ0BS3X4jmJTuw4Ix59MQeMg74zU5IN6Zx0lPEnxt3957MP+G/kV6oPmUtlxqF9Ou7sP4yDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6946d728824402d5af065db571848f22b7b57c49c7e6d8795dbf398871d4d7f","last_reissued_at":"2026-07-05T01:08:48.634784Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:08:48.634784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.04780","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":"2026-07-05T01:08:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VjlDuxMxIGVstPPeLGtWFHjZrhRN4wmLf3WwHhdm/qAnlTTFG0ldlAbdYbdUzzhObJpdMtt4yc/u23HPoj/1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T15:06:21.317336Z"},"content_sha256":"808f16955738e3d4f5e6a6e9fdc47eacd26814b806e5ea35ad00a5a3098fbf12","schema_version":"1.0","event_id":"sha256:808f16955738e3d4f5e6a6e9fdc47eacd26814b806e5ea35ad00a5a3098fbf12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:62KG24UIERAC2WXQMXNVOGCI6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lorentz Group Equivariant Neural Network for Particle Physics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","hep-ex","physics.comp-ph","stat.ML"],"primary_cat":"hep-ph","authors_text":"Alexander Bogatskiy, Brandon Anderson, David W. Miller, Jan T. Offermann, Marwah Roussi, Risi Kondor","submitted_at":"2020-06-08T17:54:43Z","abstract_excerpt":"We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the finite-dimensional representations of the Lorentz group and the equivariant nonlinearity involves the tensor product. For classification tasks in particle physics, we demonstrate that such an equivariant architecture leads to drastically simpler models that have relatively few learnable parameters and are much more physically interpretable than leading approaches that use C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.04780","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/2006.04780/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":"2026-07-05T01:08:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qKnj5Z7f5x4wt+byqtEnu8FRfezWLvbL+w9rHi0afmga/dfyoSDCaIqmqGWQSK9eZPqkvcKlz+IGcvXlIfKcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T15:06:21.318134Z"},"content_sha256":"5ad24d5185993386db5132e176aea7ffd71a3fa86ff72d5e6e59d77746aec1b7","schema_version":"1.0","event_id":"sha256:5ad24d5185993386db5132e176aea7ffd71a3fa86ff72d5e6e59d77746aec1b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62KG24UIERAC2WXQMXNVOGCI6I/bundle.json","state_url":"https://pith.science/pith/62KG24UIERAC2WXQMXNVOGCI6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62KG24UIERAC2WXQMXNVOGCI6I/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":"2026-08-17T15:06:21Z","links":{"resolver":"https://pith.science/pith/62KG24UIERAC2WXQMXNVOGCI6I","bundle":"https://pith.science/pith/62KG24UIERAC2WXQMXNVOGCI6I/bundle.json","state":"https://pith.science/pith/62KG24UIERAC2WXQMXNVOGCI6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62KG24UIERAC2WXQMXNVOGCI6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:62KG24UIERAC2WXQMXNVOGCI6I","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":"ae1357d47f74072f05426a2283ddb04f7183cd0b65575e6cd5dc71b1bee0961e","cross_cats_sorted":["cs.LG","hep-ex","physics.comp-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-06-08T17:54:43Z","title_canon_sha256":"7289eae181a8a0e827ebcf4718412a266908b01a7453b50a26effd7a66f5f83f"},"schema_version":"1.0","source":{"id":"2006.04780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.04780","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"arxiv_version","alias_value":"2006.04780v1","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.04780","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"pith_short_12","alias_value":"62KG24UIERAC","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"pith_short_16","alias_value":"62KG24UIERAC2WXQ","created_at":"2026-07-05T01:08:48Z"},{"alias_kind":"pith_short_8","alias_value":"62KG24UI","created_at":"2026-07-05T01:08:48Z"}],"graph_snapshots":[{"event_id":"sha256:5ad24d5185993386db5132e176aea7ffd71a3fa86ff72d5e6e59d77746aec1b7","target":"graph","created_at":"2026-07-05T01:08:48Z","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/2006.04780/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the finite-dimensional representations of the Lorentz group and the equivariant nonlinearity involves the tensor product. For classification tasks in particle physics, we demonstrate that such an equivariant architecture leads to drastically simpler models that have relatively few learnable parameters and are much more physically interpretable than leading approaches that use C","authors_text":"Alexander Bogatskiy, Brandon Anderson, David W. Miller, Jan T. Offermann, Marwah Roussi, Risi Kondor","cross_cats":["cs.LG","hep-ex","physics.comp-ph","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-06-08T17:54:43Z","title":"Lorentz Group Equivariant Neural Network for Particle Physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.04780","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":"sha256:808f16955738e3d4f5e6a6e9fdc47eacd26814b806e5ea35ad00a5a3098fbf12","target":"record","created_at":"2026-07-05T01:08:48Z","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":"ae1357d47f74072f05426a2283ddb04f7183cd0b65575e6cd5dc71b1bee0961e","cross_cats_sorted":["cs.LG","hep-ex","physics.comp-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-06-08T17:54:43Z","title_canon_sha256":"7289eae181a8a0e827ebcf4718412a266908b01a7453b50a26effd7a66f5f83f"},"schema_version":"1.0","source":{"id":"2006.04780","kind":"arxiv","version":1}},"canonical_sha256":"f6946d728824402d5af065db571848f22b7b57c49c7e6d8795dbf398871d4d7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6946d728824402d5af065db571848f22b7b57c49c7e6d8795dbf398871d4d7f","first_computed_at":"2026-07-05T01:08:48.634784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:08:48.634784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cTTOe1browu8IxPQ0BS3X4jmJTuw4Ix59MQeMg74zU5IN6Zx0lPEnxt3957MP+G/kV6oPmUtlxqF9Ou7sP4yDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:08:48.635210Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.04780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:808f16955738e3d4f5e6a6e9fdc47eacd26814b806e5ea35ad00a5a3098fbf12","sha256:5ad24d5185993386db5132e176aea7ffd71a3fa86ff72d5e6e59d77746aec1b7"],"state_sha256":"f659a08533fb72a05a04adc9f66162a7b88029e179ad317775565eb326ceb27c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QaUw7CQXH7qe4sG0rrPuyVMhET0z804npqQzbp/K0BZ/H1TkRPYNPhaa9GO9gchg/9r7vRK6ZstbBmwXM8DSDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T15:06:21.326341Z","bundle_sha256":"c44c664115d0c5552288592782b07bc8369c22e0cd26a4cd0dfcb31ddbca9a24"}}