{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:2ADSZT3RD2JV5VMYU3PXO7F5DC","short_pith_number":"pith:2ADSZT3R","schema_version":"1.0","canonical_sha256":"d0072ccf711e935ed598a6df777cbd1881d9afe757d396b2a25dccfadf6c6c46","source":{"kind":"arxiv","id":"hep-th/0609219","version":1},"attestation_state":"computed","paper":{"title":"A Canonical Analysis of the Einstein-Hilbert Action in First Order Form","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"D. G. C. McKeon, N. Kiriushcheva, S. V. Kuzmin","submitted_at":"2006-09-29T14:50:29Z","abstract_excerpt":"Using the Dirac constraint formalism, we examine the canonical structure of the Einstein-Hilbert action $S_d = \\frac{1}{16\\pi G} \\int d^dx \\sqrt{-g} R$, treating the metric $g_{\\alpha\\beta}$ and the symmetric affine connection $\\Gamma_{\\mu\\nu}^\\lambda$ as independent variables. For $d > 2$ tertiary constraints naturally arise; if these are all first class, there are $d(d-3)$ independent variables in phase space, the same number that a symmetric tensor gauge field $\\phi_{\\mu\\nu}$ possesses. If $d = 2$, the Hamiltonian becomes a linear combination of first class constraints obeying an SO(2,1) al"},"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":"hep-th/0609219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-09-29T14:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"f5fafa05a8cbcb83b05555f57c397035e37e61985e3ca996677c6b3ed3022bc8","abstract_canon_sha256":"a885d0dc065d312e02832ac3c864c85df23af0f633fee56eee8f8753de83b938"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:26:08.105366Z","signature_b64":"wTgZUFl8Gdo1uhVIA1Koplp+sCUNi6NfxAQoM5XAjfWyF45IUS+8hx3MWH8yEazpH8vreNTxshp+ykB6QjubCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0072ccf711e935ed598a6df777cbd1881d9afe757d396b2a25dccfadf6c6c46","last_reissued_at":"2026-07-04T15:26:08.104942Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:26:08.104942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Canonical Analysis of the Einstein-Hilbert Action in First Order Form","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"D. G. C. McKeon, N. Kiriushcheva, S. V. Kuzmin","submitted_at":"2006-09-29T14:50:29Z","abstract_excerpt":"Using the Dirac constraint formalism, we examine the canonical structure of the Einstein-Hilbert action $S_d = \\frac{1}{16\\pi G} \\int d^dx \\sqrt{-g} R$, treating the metric $g_{\\alpha\\beta}$ and the symmetric affine connection $\\Gamma_{\\mu\\nu}^\\lambda$ as independent variables. For $d > 2$ tertiary constraints naturally arise; if these are all first class, there are $d(d-3)$ independent variables in phase space, the same number that a symmetric tensor gauge field $\\phi_{\\mu\\nu}$ possesses. If $d = 2$, the Hamiltonian becomes a linear combination of first class constraints obeying an SO(2,1) al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0609219","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/hep-th/0609219/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0609219","created_at":"2026-07-04T15:26:08.105007+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0609219v1","created_at":"2026-07-04T15:26:08.105007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0609219","created_at":"2026-07-04T15:26:08.105007+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ADSZT3RD2JV","created_at":"2026-07-04T15:26:08.105007+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ADSZT3RD2JV5VMY","created_at":"2026-07-04T15:26:08.105007+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ADSZT3R","created_at":"2026-07-04T15:26:08.105007+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2604.25117","citing_title":"Covariant quantization of the Einstein-Hilbert theory in first-order form","ref_index":50,"is_internal_anchor":true},{"citing_arxiv_id":"2604.25117","citing_title":"Covariant quantization of the Einstein-Hilbert theory in first-order form","ref_index":50,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC","json":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC.json","graph_json":"https://pith.science/api/pith-number/2ADSZT3RD2JV5VMYU3PXO7F5DC/graph.json","events_json":"https://pith.science/api/pith-number/2ADSZT3RD2JV5VMYU3PXO7F5DC/events.json","paper":"https://pith.science/paper/2ADSZT3R"},"agent_actions":{"view_html":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC","download_json":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC.json","view_paper":"https://pith.science/paper/2ADSZT3R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0609219&json=true","fetch_graph":"https://pith.science/api/pith-number/2ADSZT3RD2JV5VMYU3PXO7F5DC/graph.json","fetch_events":"https://pith.science/api/pith-number/2ADSZT3RD2JV5VMYU3PXO7F5DC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC/action/storage_attestation","attest_author":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC/action/author_attestation","sign_citation":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC/action/citation_signature","submit_replication":"https://pith.science/pith/2ADSZT3RD2JV5VMYU3PXO7F5DC/action/replication_record"}},"created_at":"2026-07-04T15:26:08.105007+00:00","updated_at":"2026-07-04T15:26:08.105007+00:00"}