{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VFV7BOHV7IUUCO63CWOZIZTFLT","short_pith_number":"pith:VFV7BOHV","canonical_record":{"source":{"id":"2605.31570","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-29T17:38:03Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4f93a3361672c14f8b8170d88bb13254988c005de145429c56d0bbe893286fee","abstract_canon_sha256":"f5b6b90c6b3da34fe0d8dd9940e6425a42779ca30ff3cf7528a3f7729a456315"},"schema_version":"1.0"},"canonical_sha256":"a96bf0b8f5fa29413bdb159d9466655ceccda51d4fc8020c9d90dffacefcf03d","source":{"kind":"arxiv","id":"2605.31570","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31570","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31570v1","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31570","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"VFV7BOHV7IUU","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"pith_short_16","alias_value":"VFV7BOHV7IUUCO63","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"pith_short_8","alias_value":"VFV7BOHV","created_at":"2026-06-01T02:04:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VFV7BOHV7IUUCO63CWOZIZTFLT","target":"record","payload":{"canonical_record":{"source":{"id":"2605.31570","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-29T17:38:03Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4f93a3361672c14f8b8170d88bb13254988c005de145429c56d0bbe893286fee","abstract_canon_sha256":"f5b6b90c6b3da34fe0d8dd9940e6425a42779ca30ff3cf7528a3f7729a456315"},"schema_version":"1.0"},"canonical_sha256":"a96bf0b8f5fa29413bdb159d9466655ceccda51d4fc8020c9d90dffacefcf03d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T02:04:13.579922Z","signature_b64":"sFv/NKtRgBDilGoGCdFsMpVl2KYHMBM8FeIanZtqpQlkTcciUpjC0QO0Vpu+/rUWKbov5CP72kyYvgtFAtDfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a96bf0b8f5fa29413bdb159d9466655ceccda51d4fc8020c9d90dffacefcf03d","last_reissued_at":"2026-06-01T02:04:13.579077Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T02:04:13.579077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.31570","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":"2026-06-01T02:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tlwq4zDUOEAezxvCil039uJHUMbGik46vLKu3xMLaTSzcbZPDXTInyTk9I0BD0mdP87pRbvARBrm71nFLC9UDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T00:50:50.158396Z"},"content_sha256":"f0e2c654b8aba530d53f75ec60be5744cb2336a05b13a4a883df9a07cc26ca26","schema_version":"1.0","event_id":"sha256:f0e2c654b8aba530d53f75ec60be5744cb2336a05b13a4a883df9a07cc26ca26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VFV7BOHV7IUUCO63CWOZIZTFLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational theory of Cosserat arches and affine tensors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G\\'ery de Saxc\\'e","submitted_at":"2026-05-29T17:38:03Z","abstract_excerpt":"Our purpose is to revisit the screw theory in light of the affine tensor formalism, introducing the co-momentum and momentum tensors. Our target-applications of the Euler-Poincar\\'e equation are problems of mechanics such as the motion of the rigid body or the statics and the dynamics of Cosserat arches, in relation to the concept of momentum tensor. Using the framework of Ehresmann connections on the principal bundle of affine frames, we show that the Euler-Poincar\\'e equation means that the momentum tensor is parallel-transported."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31570","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/2605.31570/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":"2026-06-01T02:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oBHYHAir/jrbOUb8fX8LqJjtuNGSoxOIgBzSzeeGHfPQCDOSkR/ihBcgNMOCvBbxSmazgVtkMDI9vuK2WuJADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T00:50:50.158764Z"},"content_sha256":"a0e01968e83ca6f33b4b00025bd6066280cd4f6a4dbf3f1b0ce95f4edb6f4dab","schema_version":"1.0","event_id":"sha256:a0e01968e83ca6f33b4b00025bd6066280cd4f6a4dbf3f1b0ce95f4edb6f4dab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFV7BOHV7IUUCO63CWOZIZTFLT/bundle.json","state_url":"https://pith.science/pith/VFV7BOHV7IUUCO63CWOZIZTFLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFV7BOHV7IUUCO63CWOZIZTFLT/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":"2026-07-05T00:50:50Z","links":{"resolver":"https://pith.science/pith/VFV7BOHV7IUUCO63CWOZIZTFLT","bundle":"https://pith.science/pith/VFV7BOHV7IUUCO63CWOZIZTFLT/bundle.json","state":"https://pith.science/pith/VFV7BOHV7IUUCO63CWOZIZTFLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFV7BOHV7IUUCO63CWOZIZTFLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VFV7BOHV7IUUCO63CWOZIZTFLT","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":"f5b6b90c6b3da34fe0d8dd9940e6425a42779ca30ff3cf7528a3f7729a456315","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-29T17:38:03Z","title_canon_sha256":"4f93a3361672c14f8b8170d88bb13254988c005de145429c56d0bbe893286fee"},"schema_version":"1.0","source":{"id":"2605.31570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31570","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31570v1","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31570","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"VFV7BOHV7IUU","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"pith_short_16","alias_value":"VFV7BOHV7IUUCO63","created_at":"2026-06-01T02:04:13Z"},{"alias_kind":"pith_short_8","alias_value":"VFV7BOHV","created_at":"2026-06-01T02:04:13Z"}],"graph_snapshots":[{"event_id":"sha256:a0e01968e83ca6f33b4b00025bd6066280cd4f6a4dbf3f1b0ce95f4edb6f4dab","target":"graph","created_at":"2026-06-01T02:04:13Z","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/2605.31570/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Our purpose is to revisit the screw theory in light of the affine tensor formalism, introducing the co-momentum and momentum tensors. Our target-applications of the Euler-Poincar\\'e equation are problems of mechanics such as the motion of the rigid body or the statics and the dynamics of Cosserat arches, in relation to the concept of momentum tensor. Using the framework of Ehresmann connections on the principal bundle of affine frames, we show that the Euler-Poincar\\'e equation means that the momentum tensor is parallel-transported.","authors_text":"G\\'ery de Saxc\\'e","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-29T17:38:03Z","title":"Variational theory of Cosserat arches and affine tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31570","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:f0e2c654b8aba530d53f75ec60be5744cb2336a05b13a4a883df9a07cc26ca26","target":"record","created_at":"2026-06-01T02:04:13Z","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":"f5b6b90c6b3da34fe0d8dd9940e6425a42779ca30ff3cf7528a3f7729a456315","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-29T17:38:03Z","title_canon_sha256":"4f93a3361672c14f8b8170d88bb13254988c005de145429c56d0bbe893286fee"},"schema_version":"1.0","source":{"id":"2605.31570","kind":"arxiv","version":1}},"canonical_sha256":"a96bf0b8f5fa29413bdb159d9466655ceccda51d4fc8020c9d90dffacefcf03d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a96bf0b8f5fa29413bdb159d9466655ceccda51d4fc8020c9d90dffacefcf03d","first_computed_at":"2026-06-01T02:04:13.579077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T02:04:13.579077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sFv/NKtRgBDilGoGCdFsMpVl2KYHMBM8FeIanZtqpQlkTcciUpjC0QO0Vpu+/rUWKbov5CP72kyYvgtFAtDfAQ==","signature_status":"signed_v1","signed_at":"2026-06-01T02:04:13.579922Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.31570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0e2c654b8aba530d53f75ec60be5744cb2336a05b13a4a883df9a07cc26ca26","sha256:a0e01968e83ca6f33b4b00025bd6066280cd4f6a4dbf3f1b0ce95f4edb6f4dab"],"state_sha256":"925b521675c481491cf5e4bb2ed2e9f97ccc059e63e5e25133edd916f713e676"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AUO5Gy+zNTFYpUY7K2f9L9nf9gmchr1kdr4DG0ic2lHcnAUJJCcmGoXzG1rBJwbWv8wV5v9qAYB1M3Dp/ieHDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T00:50:50.160827Z","bundle_sha256":"56c799e584004cc29cf8418bdd85ca55f792ae1cf7196b6ae0ecd4f10169e4c4"}}