{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:AI7WWF5B5VZXKBMYKU44OVDXKY","short_pith_number":"pith:AI7WWF5B","schema_version":"1.0","canonical_sha256":"023f6b17a1ed737505985539c754775613e80f9ae26b2199539036643ffea562","source":{"kind":"arxiv","id":"1012.1903","version":2},"attestation_state":"computed","paper":{"title":"Parent formulation at the Lagrangian level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Maxim Grigoriev","submitted_at":"2010-12-09T00:41:55Z","abstract_excerpt":"The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.1903","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-09T00:41:55Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"156b1108e4f9ec91016af711ad1e7a282ed54c85beee62fd9dd14ab2c3da1820","abstract_canon_sha256":"99354d82a741e819384576102f7784846e535ecf1816ec8dfbbb20fdddfed248"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:51.536778Z","signature_b64":"ZLcnSHiqT8NwTHGtciFAfgQmM30+pKbVCKhhvEVqtRekT7ON6d9pmQje5XZFYGfxsPOHhB88F6RLQway2YdDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"023f6b17a1ed737505985539c754775613e80f9ae26b2199539036643ffea562","last_reissued_at":"2026-05-18T04:16:51.536198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:51.536198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parent formulation at the Lagrangian level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Maxim Grigoriev","submitted_at":"2010-12-09T00:41:55Z","abstract_excerpt":"The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1903","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.1903","created_at":"2026-05-18T04:16:51.536284+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.1903v2","created_at":"2026-05-18T04:16:51.536284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1903","created_at":"2026-05-18T04:16:51.536284+00:00"},{"alias_kind":"pith_short_12","alias_value":"AI7WWF5B5VZX","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AI7WWF5B5VZXKBMY","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AI7WWF5B","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.29587","citing_title":"Asymptotic boundary structure of Lagrangian gauge theories","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY","json":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY.json","graph_json":"https://pith.science/api/pith-number/AI7WWF5B5VZXKBMYKU44OVDXKY/graph.json","events_json":"https://pith.science/api/pith-number/AI7WWF5B5VZXKBMYKU44OVDXKY/events.json","paper":"https://pith.science/paper/AI7WWF5B"},"agent_actions":{"view_html":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY","download_json":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY.json","view_paper":"https://pith.science/paper/AI7WWF5B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.1903&json=true","fetch_graph":"https://pith.science/api/pith-number/AI7WWF5B5VZXKBMYKU44OVDXKY/graph.json","fetch_events":"https://pith.science/api/pith-number/AI7WWF5B5VZXKBMYKU44OVDXKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY/action/storage_attestation","attest_author":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY/action/author_attestation","sign_citation":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY/action/citation_signature","submit_replication":"https://pith.science/pith/AI7WWF5B5VZXKBMYKU44OVDXKY/action/replication_record"}},"created_at":"2026-05-18T04:16:51.536284+00:00","updated_at":"2026-05-18T04:16:51.536284+00:00"}