{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ELRIE4Y4IOO4OJP2KZZSUTFLOF","short_pith_number":"pith:ELRIE4Y4","canonical_record":{"source":{"id":"2505.16766","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2025-05-22T15:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"adeefd4117bb6d97175e4818b147f3443aeea22b9dfde245b15af608997ef733","abstract_canon_sha256":"b6a232cab8bb8837a3ed30db84d5b366efb8d5bef79d7c41ded5cd4d9b11960c"},"schema_version":"1.0"},"canonical_sha256":"22e282731c439dc725fa56732a4cab7155e8d5976fb48750070a25d3d5303da0","source":{"kind":"arxiv","id":"2505.16766","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.16766","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"2505.16766v2","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.16766","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"ELRIE4Y4IOO4","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"pith_short_16","alias_value":"ELRIE4Y4IOO4OJP2","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"pith_short_8","alias_value":"ELRIE4Y4","created_at":"2026-07-05T11:52:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ELRIE4Y4IOO4OJP2KZZSUTFLOF","target":"record","payload":{"canonical_record":{"source":{"id":"2505.16766","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2025-05-22T15:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"adeefd4117bb6d97175e4818b147f3443aeea22b9dfde245b15af608997ef733","abstract_canon_sha256":"b6a232cab8bb8837a3ed30db84d5b366efb8d5bef79d7c41ded5cd4d9b11960c"},"schema_version":"1.0"},"canonical_sha256":"22e282731c439dc725fa56732a4cab7155e8d5976fb48750070a25d3d5303da0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:52:02.353936Z","signature_b64":"zU1JJOO0LQfYbK6rcYkkPT6EReyR6uqRYa8t07Suj9LPA4ifBXYF4yTZRiZ5JY2gJ3zUSF+Gjyfk2x0Y/E6+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22e282731c439dc725fa56732a4cab7155e8d5976fb48750070a25d3d5303da0","last_reissued_at":"2026-07-05T11:52:02.353456Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:52:02.353456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.16766","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OyuIbmeMDFql2+sfTkNWANr94I0R5ba1RvRczSwy+vJxaYysTq0T/vbj2mJCL4/ks0eiasKc5Nncc2PYf5DPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:53:47.067605Z"},"content_sha256":"610c2edbf73664eeef939150e58dfebc715a48fe19ea2eed91c50df6fef87235","schema_version":"1.0","event_id":"sha256:610c2edbf73664eeef939150e58dfebc715a48fe19ea2eed91c50df6fef87235"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ELRIE4Y4IOO4OJP2KZZSUTFLOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Dongzhe Zheng","submitted_at":"2025-05-22T15:07:59Z","abstract_excerpt":"This paper introduces a geometric mechanics framework for constrained systems on principal bundles through \\emph{compatible pairs} $(\\mathcal{D}, \\lambda)$, addressing fundamental challenges in gauge-constrained physical systems. We characterize the strong transversality condition by pairing constraint distributions $\\mathcal{D}$ with Lie algebra dual functions $\\lambda: P \\to \\mathfrak{g}^*$ satisfying compatibility $\\mathcal{D}_p = \\{v : \\langle\\lambda(p), \\omega(v)\\rangle = 0\\}$ and differential consistency $d\\lambda + \\mathrm{ad}^*_\\omega \\lambda = 0$. This framework proves equivalent to $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16766","kind":"arxiv","version":2},"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/2505.16766/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":"2026-07-05T11:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exI2+4pXtIjCct7641MPMFrmcQFc9fPfNsxOi5/FcX9wqcLcCwVfqfQ+obvt4D876gxuJVMi8smT0G/RXY8mDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:53:47.068100Z"},"content_sha256":"8cd93ebc56d47253bea1ec5d8fc231533a0dbb79bd58f53858e4f7ecb399213a","schema_version":"1.0","event_id":"sha256:8cd93ebc56d47253bea1ec5d8fc231533a0dbb79bd58f53858e4f7ecb399213a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELRIE4Y4IOO4OJP2KZZSUTFLOF/bundle.json","state_url":"https://pith.science/pith/ELRIE4Y4IOO4OJP2KZZSUTFLOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELRIE4Y4IOO4OJP2KZZSUTFLOF/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":"2026-08-08T08:53:47Z","links":{"resolver":"https://pith.science/pith/ELRIE4Y4IOO4OJP2KZZSUTFLOF","bundle":"https://pith.science/pith/ELRIE4Y4IOO4OJP2KZZSUTFLOF/bundle.json","state":"https://pith.science/pith/ELRIE4Y4IOO4OJP2KZZSUTFLOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELRIE4Y4IOO4OJP2KZZSUTFLOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ELRIE4Y4IOO4OJP2KZZSUTFLOF","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":"b6a232cab8bb8837a3ed30db84d5b366efb8d5bef79d7c41ded5cd4d9b11960c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2025-05-22T15:07:59Z","title_canon_sha256":"adeefd4117bb6d97175e4818b147f3443aeea22b9dfde245b15af608997ef733"},"schema_version":"1.0","source":{"id":"2505.16766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.16766","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"2505.16766v2","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.16766","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"ELRIE4Y4IOO4","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"pith_short_16","alias_value":"ELRIE4Y4IOO4OJP2","created_at":"2026-07-05T11:52:02Z"},{"alias_kind":"pith_short_8","alias_value":"ELRIE4Y4","created_at":"2026-07-05T11:52:02Z"}],"graph_snapshots":[{"event_id":"sha256:8cd93ebc56d47253bea1ec5d8fc231533a0dbb79bd58f53858e4f7ecb399213a","target":"graph","created_at":"2026-07-05T11:52:02Z","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/2505.16766/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a geometric mechanics framework for constrained systems on principal bundles through \\emph{compatible pairs} $(\\mathcal{D}, \\lambda)$, addressing fundamental challenges in gauge-constrained physical systems. We characterize the strong transversality condition by pairing constraint distributions $\\mathcal{D}$ with Lie algebra dual functions $\\lambda: P \\to \\mathfrak{g}^*$ satisfying compatibility $\\mathcal{D}_p = \\{v : \\langle\\lambda(p), \\omega(v)\\rangle = 0\\}$ and differential consistency $d\\lambda + \\mathrm{ad}^*_\\omega \\lambda = 0$. This framework proves equivalent to $","authors_text":"Dongzhe Zheng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2025-05-22T15:07:59Z","title":"Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16766","kind":"arxiv","version":2},"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":"sha256:610c2edbf73664eeef939150e58dfebc715a48fe19ea2eed91c50df6fef87235","target":"record","created_at":"2026-07-05T11:52:02Z","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":"b6a232cab8bb8837a3ed30db84d5b366efb8d5bef79d7c41ded5cd4d9b11960c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2025-05-22T15:07:59Z","title_canon_sha256":"adeefd4117bb6d97175e4818b147f3443aeea22b9dfde245b15af608997ef733"},"schema_version":"1.0","source":{"id":"2505.16766","kind":"arxiv","version":2}},"canonical_sha256":"22e282731c439dc725fa56732a4cab7155e8d5976fb48750070a25d3d5303da0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22e282731c439dc725fa56732a4cab7155e8d5976fb48750070a25d3d5303da0","first_computed_at":"2026-07-05T11:52:02.353456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:52:02.353456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zU1JJOO0LQfYbK6rcYkkPT6EReyR6uqRYa8t07Suj9LPA4ifBXYF4yTZRiZ5JY2gJ3zUSF+Gjyfk2x0Y/E6+AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:52:02.353936Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.16766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:610c2edbf73664eeef939150e58dfebc715a48fe19ea2eed91c50df6fef87235","sha256:8cd93ebc56d47253bea1ec5d8fc231533a0dbb79bd58f53858e4f7ecb399213a"],"state_sha256":"c35e1beaa2a7cb8e53f6c37319cbb0bf8c70eb3d2129f4ab035607911bb93026"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HtTAlsbULmAUmottagv/ZEHtaSoWPnvsFON695g8rxqPsvQgMe7x+584DdnrJB8gpSeSUeadRjdcwss6tm37Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T08:53:47.072909Z","bundle_sha256":"7cd3a054b3103c7264901905f86f01ad69d89b1905723d3d5d660389e10f301f"}}