{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:S5NAMZRFACI2XJUGRWIL7HKAFT","short_pith_number":"pith:S5NAMZRF","canonical_record":{"source":{"id":"1604.02074","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-07T16:45:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7f683fda2496fbc278b5272c0b893ebfd8287d82cf16050c8218941c74b06ece","abstract_canon_sha256":"83458058c2bcede3339c414f4725d6c90ca0bbd6774be35c9263b9d19b46551b"},"schema_version":"1.0"},"canonical_sha256":"975a0666250091aba6868d90bf9d402cecb19f65b6e1a3b484d4993bf82a6ff7","source":{"kind":"arxiv","id":"1604.02074","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02074","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02074v2","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02074","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"S5NAMZRFACI2","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S5NAMZRFACI2XJUG","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S5NAMZRF","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:S5NAMZRFACI2XJUGRWIL7HKAFT","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02074","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-07T16:45:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7f683fda2496fbc278b5272c0b893ebfd8287d82cf16050c8218941c74b06ece","abstract_canon_sha256":"83458058c2bcede3339c414f4725d6c90ca0bbd6774be35c9263b9d19b46551b"},"schema_version":"1.0"},"canonical_sha256":"975a0666250091aba6868d90bf9d402cecb19f65b6e1a3b484d4993bf82a6ff7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:10.099517Z","signature_b64":"i694zKjh9BWaJT1amZNa5gbGr2YKl+my6mKSDvbIBnUCWU9hFQDvizPoZGIsnQCfYz1q9Hj5wkxNJqZFyKtsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"975a0666250091aba6868d90bf9d402cecb19f65b6e1a3b484d4993bf82a6ff7","last_reissued_at":"2026-05-18T00:27:10.099034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:10.099034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02074","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":"2026-05-18T00:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ei6BKzd71sB+EVVgrD/LGq4gWOsf8ss105MhXv8SGCmU337Swkm1/77I91lDINJiWMCghbWDf/cNlMFWV7OsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:47:28.729979Z"},"content_sha256":"3924035325b59be5b6abcf92cae0ded8efeb8cf16bdaedc2cb1b3f839a959196","schema_version":"1.0","event_id":"sha256:3924035325b59be5b6abcf92cae0ded8efeb8cf16bdaedc2cb1b3f839a959196"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:S5NAMZRFACI2XJUGRWIL7HKAFT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order reduction, projectability and constraints of second-order field theories and higher-order mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jordi Gaset, Narciso Rom\\'an-Roy","submitted_at":"2016-04-07T16:45:46Z","abstract_excerpt":"The projectability of Poincar\\'e-Cartan forms in a third-order jet bundle $J^3\\pi$ onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint algorithm for the associated Euler-Lagrange equations in $J^3\\pi$. The results are applied to study the Hilbert Lagrangian for the Einstein equations (in vacuum) from a multisymplectic point of view. Thus we show how these equations are a consequence of the application of the constraint algorithm to the geometric field equations, meanwhile the other constraints ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02074","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":""},"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":"2026-05-18T00:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0dDQ/AHfbvhuTqP8M0MtBHcd3yoQYNbBnEiH/KZezv8WVOPg1tiup3aJ4+3WhN9Qib/GiYAq4ysJG87qq+pCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:47:28.730658Z"},"content_sha256":"f66c4909f687d3ed0584aeda35d53f616b6aa7379467a8ffdc593f425322e7d2","schema_version":"1.0","event_id":"sha256:f66c4909f687d3ed0584aeda35d53f616b6aa7379467a8ffdc593f425322e7d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5NAMZRFACI2XJUGRWIL7HKAFT/bundle.json","state_url":"https://pith.science/pith/S5NAMZRFACI2XJUGRWIL7HKAFT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5NAMZRFACI2XJUGRWIL7HKAFT/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":"2026-05-27T05:47:28Z","links":{"resolver":"https://pith.science/pith/S5NAMZRFACI2XJUGRWIL7HKAFT","bundle":"https://pith.science/pith/S5NAMZRFACI2XJUGRWIL7HKAFT/bundle.json","state":"https://pith.science/pith/S5NAMZRFACI2XJUGRWIL7HKAFT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5NAMZRFACI2XJUGRWIL7HKAFT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S5NAMZRFACI2XJUGRWIL7HKAFT","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":"83458058c2bcede3339c414f4725d6c90ca0bbd6774be35c9263b9d19b46551b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-07T16:45:46Z","title_canon_sha256":"7f683fda2496fbc278b5272c0b893ebfd8287d82cf16050c8218941c74b06ece"},"schema_version":"1.0","source":{"id":"1604.02074","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02074","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02074v2","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02074","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"S5NAMZRFACI2","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S5NAMZRFACI2XJUG","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S5NAMZRF","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f66c4909f687d3ed0584aeda35d53f616b6aa7379467a8ffdc593f425322e7d2","target":"graph","created_at":"2026-05-18T00:27:10Z","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"},"paper":{"abstract_excerpt":"The projectability of Poincar\\'e-Cartan forms in a third-order jet bundle $J^3\\pi$ onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint algorithm for the associated Euler-Lagrange equations in $J^3\\pi$. The results are applied to study the Hilbert Lagrangian for the Einstein equations (in vacuum) from a multisymplectic point of view. Thus we show how these equations are a consequence of the application of the constraint algorithm to the geometric field equations, meanwhile the other constraints ar","authors_text":"Jordi Gaset, Narciso Rom\\'an-Roy","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-07T16:45:46Z","title":"Order reduction, projectability and constraints of second-order field theories and higher-order mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02074","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":"sha256:3924035325b59be5b6abcf92cae0ded8efeb8cf16bdaedc2cb1b3f839a959196","target":"record","created_at":"2026-05-18T00:27:10Z","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":"83458058c2bcede3339c414f4725d6c90ca0bbd6774be35c9263b9d19b46551b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-07T16:45:46Z","title_canon_sha256":"7f683fda2496fbc278b5272c0b893ebfd8287d82cf16050c8218941c74b06ece"},"schema_version":"1.0","source":{"id":"1604.02074","kind":"arxiv","version":2}},"canonical_sha256":"975a0666250091aba6868d90bf9d402cecb19f65b6e1a3b484d4993bf82a6ff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"975a0666250091aba6868d90bf9d402cecb19f65b6e1a3b484d4993bf82a6ff7","first_computed_at":"2026-05-18T00:27:10.099034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:10.099034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i694zKjh9BWaJT1amZNa5gbGr2YKl+my6mKSDvbIBnUCWU9hFQDvizPoZGIsnQCfYz1q9Hj5wkxNJqZFyKtsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:10.099517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02074","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3924035325b59be5b6abcf92cae0ded8efeb8cf16bdaedc2cb1b3f839a959196","sha256:f66c4909f687d3ed0584aeda35d53f616b6aa7379467a8ffdc593f425322e7d2"],"state_sha256":"c41eba75f3ae6c33a0ae9a4425363d907fe0ba65330b7f2b889a2937d0b84dfd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eW68QIkBksAetaUh3aATEMoLe+8bzszf3KuR7eFB3Y3Y8dA91c9OzbUrDTsFmlpek2iB8ekpn5E9nTQ185rHAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:47:28.734678Z","bundle_sha256":"88c710a004680cd47c283e8cb8a66549fc6d8e728204d30c66eaee335c3db6a6"}}