{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PJRUSU5JMS5LPCEJT34SES2NOQ","short_pith_number":"pith:PJRUSU5J","schema_version":"1.0","canonical_sha256":"7a634953a964bab788899ef9224b4d741bbe78da8ea0d48cd713ba56aeada683","source":{"kind":"arxiv","id":"1512.06820","version":1},"attestation_state":"computed","paper":{"title":"Hamiltonian analysis of higher derivative scalar-tensor theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"David Langlois, Karim Noui","submitted_at":"2015-12-21T20:45:30Z","abstract_excerpt":"We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degene"},"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":"1512.06820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-21T20:45:30Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"7633817237c698cae8db50cfbdba2dd12f30d830386d15f1711b6145bbe06e99","abstract_canon_sha256":"3d4776aefa512def8b9a7c10b814b0055e2c370ad3b9ed398443fc5c6f24a936"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:51.646383Z","signature_b64":"O0xvG2+5k/GpxFtEUOZ2qKfcwKyoQiYlc5AsSSRIz08NxnJvd6+Zjgl0/7u7BeCt8HH8hlnAMONSe5tHqAfvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a634953a964bab788899ef9224b4d741bbe78da8ea0d48cd713ba56aeada683","last_reissued_at":"2026-05-18T01:10:51.645695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:51.645695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian analysis of higher derivative scalar-tensor theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"David Langlois, Karim Noui","submitted_at":"2015-12-21T20:45:30Z","abstract_excerpt":"We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06820","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":""},"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":"1512.06820","created_at":"2026-05-18T01:10:51.645809+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06820v1","created_at":"2026-05-18T01:10:51.645809+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06820","created_at":"2026-05-18T01:10:51.645809+00:00"},{"alias_kind":"pith_short_12","alias_value":"PJRUSU5JMS5L","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PJRUSU5JMS5LPCEJ","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PJRUSU5J","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2508.19106","citing_title":"Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2512.08972","citing_title":"Degenerate higher-order scalar-tensor theories in metric-affine gravity","ref_index":35,"is_internal_anchor":true},{"citing_arxiv_id":"2602.16237","citing_title":"Rotating Black Holes with Primary Scalar Hair: Shadow Signatures in Beyond Horndeski Gravity","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ","json":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ.json","graph_json":"https://pith.science/api/pith-number/PJRUSU5JMS5LPCEJT34SES2NOQ/graph.json","events_json":"https://pith.science/api/pith-number/PJRUSU5JMS5LPCEJT34SES2NOQ/events.json","paper":"https://pith.science/paper/PJRUSU5J"},"agent_actions":{"view_html":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ","download_json":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ.json","view_paper":"https://pith.science/paper/PJRUSU5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06820&json=true","fetch_graph":"https://pith.science/api/pith-number/PJRUSU5JMS5LPCEJT34SES2NOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PJRUSU5JMS5LPCEJT34SES2NOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ/action/storage_attestation","attest_author":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ/action/author_attestation","sign_citation":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ/action/citation_signature","submit_replication":"https://pith.science/pith/PJRUSU5JMS5LPCEJT34SES2NOQ/action/replication_record"}},"created_at":"2026-05-18T01:10:51.645809+00:00","updated_at":"2026-05-18T01:10:51.645809+00:00"}