{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:IHDFI2YPXK5PB4LPFAJEM7XYLL","short_pith_number":"pith:IHDFI2YP","canonical_record":{"source":{"id":"2502.15376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-21T11:00:34Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"d20520e6f4837de3d53699da42fa4864f0eec0771a7b4f225873980bda5eea18","abstract_canon_sha256":"d700466b93dd4231786337c50aa59f3b5cef8c721cb4d72ba0bd2249a6d71526"},"schema_version":"1.0"},"canonical_sha256":"41c6546b0fbabaf0f16f2812467ef85ad506e64860c1c9fef85418902057db59","source":{"kind":"arxiv","id":"2502.15376","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.15376","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"2502.15376v1","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.15376","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"IHDFI2YPXK5P","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_16","alias_value":"IHDFI2YPXK5PB4LP","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_8","alias_value":"IHDFI2YP","created_at":"2026-06-19T16:11:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:IHDFI2YPXK5PB4LPFAJEM7XYLL","target":"record","payload":{"canonical_record":{"source":{"id":"2502.15376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-21T11:00:34Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"d20520e6f4837de3d53699da42fa4864f0eec0771a7b4f225873980bda5eea18","abstract_canon_sha256":"d700466b93dd4231786337c50aa59f3b5cef8c721cb4d72ba0bd2249a6d71526"},"schema_version":"1.0"},"canonical_sha256":"41c6546b0fbabaf0f16f2812467ef85ad506e64860c1c9fef85418902057db59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:10.090916Z","signature_b64":"v8TR2g+/Yq3nXj/SQJGDdkCeRHBCjm043jcq7YNciIN+97H/Te/wqGBS61HZuBYQkffQ6xOYS6x4FF1rQduABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41c6546b0fbabaf0f16f2812467ef85ad506e64860c1c9fef85418902057db59","last_reissued_at":"2026-06-19T16:11:10.090442Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:10.090442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.15376","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":"2026-06-19T16:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VgBVV3N9TW9KlfRbB0JdALwaeCLVIlIm9QRFCsDuOIH3HUlZA7kao20OC7FXZOHVb4zhcE5FQnXhVRPeyIxmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:33:59.433342Z"},"content_sha256":"9cfe80050bfe047d801beeb5560ea81eb6ff0c17a10ae29318c297ae00989cc8","schema_version":"1.0","event_id":"sha256:9cfe80050bfe047d801beeb5560ea81eb6ff0c17a10ae29318c297ae00989cc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:IHDFI2YPXK5PB4LPFAJEM7XYLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cs.LG","authors_text":"Daniel Persson, Hampus Linander, Jan E. Gerken, Longde Huang, Mats Granath, Oleksandr Balabanov","submitted_at":"2025-02-21T11:00:34Z","abstract_excerpt":"Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying space is transformed with the same group element, as opposed to a local ``gauge'' symmetry, where each point is transformed with a different group element, exponentially enlarging the size of the symmetry group. Gauge equivariant networks have so far mainly been applied to problems in quantum chromodynamics. Here, we introduce a novel application domain for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.15376","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/2502.15376/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":"2026-06-19T16:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ck16y/Tvi1NJ+2SBM/I7XVNEoOcPOnnN5Kjf7iwS+y1spVuemEqL+hDkJ9EowwID4THMU/10RzubNVGdiL7QDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:33:59.433710Z"},"content_sha256":"4447d7c51814bde0921936b8f7f7553130ea4c084eb8d7edbbae8ade31d22558","schema_version":"1.0","event_id":"sha256:4447d7c51814bde0921936b8f7f7553130ea4c084eb8d7edbbae8ade31d22558"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHDFI2YPXK5PB4LPFAJEM7XYLL/bundle.json","state_url":"https://pith.science/pith/IHDFI2YPXK5PB4LPFAJEM7XYLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHDFI2YPXK5PB4LPFAJEM7XYLL/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":"2026-06-30T03:33:59Z","links":{"resolver":"https://pith.science/pith/IHDFI2YPXK5PB4LPFAJEM7XYLL","bundle":"https://pith.science/pith/IHDFI2YPXK5PB4LPFAJEM7XYLL/bundle.json","state":"https://pith.science/pith/IHDFI2YPXK5PB4LPFAJEM7XYLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHDFI2YPXK5PB4LPFAJEM7XYLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IHDFI2YPXK5PB4LPFAJEM7XYLL","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":"d700466b93dd4231786337c50aa59f3b5cef8c721cb4d72ba0bd2249a6d71526","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-21T11:00:34Z","title_canon_sha256":"d20520e6f4837de3d53699da42fa4864f0eec0771a7b4f225873980bda5eea18"},"schema_version":"1.0","source":{"id":"2502.15376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.15376","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"2502.15376v1","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.15376","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"IHDFI2YPXK5P","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_16","alias_value":"IHDFI2YPXK5PB4LP","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_8","alias_value":"IHDFI2YP","created_at":"2026-06-19T16:11:10Z"}],"graph_snapshots":[{"event_id":"sha256:4447d7c51814bde0921936b8f7f7553130ea4c084eb8d7edbbae8ade31d22558","target":"graph","created_at":"2026-06-19T16:11:10Z","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/2502.15376/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying space is transformed with the same group element, as opposed to a local ``gauge'' symmetry, where each point is transformed with a different group element, exponentially enlarging the size of the symmetry group. Gauge equivariant networks have so far mainly been applied to problems in quantum chromodynamics. Here, we introduce a novel application domain for ","authors_text":"Daniel Persson, Hampus Linander, Jan E. Gerken, Longde Huang, Mats Granath, Oleksandr Balabanov","cross_cats":["cond-mat.mes-hall"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-21T11:00:34Z","title":"Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.15376","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":"sha256:9cfe80050bfe047d801beeb5560ea81eb6ff0c17a10ae29318c297ae00989cc8","target":"record","created_at":"2026-06-19T16:11:10Z","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":"d700466b93dd4231786337c50aa59f3b5cef8c721cb4d72ba0bd2249a6d71526","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-21T11:00:34Z","title_canon_sha256":"d20520e6f4837de3d53699da42fa4864f0eec0771a7b4f225873980bda5eea18"},"schema_version":"1.0","source":{"id":"2502.15376","kind":"arxiv","version":1}},"canonical_sha256":"41c6546b0fbabaf0f16f2812467ef85ad506e64860c1c9fef85418902057db59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41c6546b0fbabaf0f16f2812467ef85ad506e64860c1c9fef85418902057db59","first_computed_at":"2026-06-19T16:11:10.090442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:10.090442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v8TR2g+/Yq3nXj/SQJGDdkCeRHBCjm043jcq7YNciIN+97H/Te/wqGBS61HZuBYQkffQ6xOYS6x4FF1rQduABA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:10.090916Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.15376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cfe80050bfe047d801beeb5560ea81eb6ff0c17a10ae29318c297ae00989cc8","sha256:4447d7c51814bde0921936b8f7f7553130ea4c084eb8d7edbbae8ade31d22558"],"state_sha256":"88af997d0dcd9434ed650097fc4bb9655381100ae620d3c097eaf973f37102b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3n92lu7aVLh7CgrAxO5xyapMHuLgbWmN9TEdidnhEfZbIctBSIbDLma4ipai6lwL3WTWoFdgpEPtpgJxLu0yDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T03:33:59.436162Z","bundle_sha256":"aa40163061bd2ada9c211e420e1f00063e31db4f93c374bad211c37547b8e4e1"}}