{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7WQMGSPFDBYHFVRDOLAL5QH4ZA","short_pith_number":"pith:7WQMGSPF","schema_version":"1.0","canonical_sha256":"fda0c349e5187072d62372c0bec0fcc81ac1f09d264b80d9eebc5012bb91fd55","source":{"kind":"arxiv","id":"1808.08154","version":1},"attestation_state":"computed","paper":{"title":"On the equivalence of Jordan and Einstein frames in scale-invariant gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Massimiliano Rinaldi","submitted_at":"2018-08-24T14:23:08Z","abstract_excerpt":"In this note we consider the issue of the classical equivalence of scale-invariant gravity in the Einstein and in the Jordan frames. We first consider the simplest example $f(R)=R^{2}$ and show explicitly that the equivalence breaks down when dealing with Ricci-flat solutions. We discuss the link with the fact that flat solutions in quadratic gravity have zero energy. We also consider the case of scale-invariant tensor-scalar gravity and general $f(R)$ theories. We argue that all scale-invariant gravity models have Ricci flat solutions in the Jordan frame that cannot be mapped into the Einstei"},"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":"1808.08154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-08-24T14:23:08Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"b68ea621457e4752fa0dac73c482e7e9482810e2f3080a1976367d0fbce7473e","abstract_canon_sha256":"1c3f9968bccd5c1356da0c80e17fa7ebc54ca2e86d6b9f43b463c327470aec05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:55.452638Z","signature_b64":"v+JyjHPvPhEthiJ7mzmLfzZd+fLz4jZu7oCvaZFnNAQH0tGfKkU1XZjOlw6PvMqMoE/hb8fA5m666k3RR2KQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fda0c349e5187072d62372c0bec0fcc81ac1f09d264b80d9eebc5012bb91fd55","last_reissued_at":"2026-05-18T00:03:55.452237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:55.452237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the equivalence of Jordan and Einstein frames in scale-invariant gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Massimiliano Rinaldi","submitted_at":"2018-08-24T14:23:08Z","abstract_excerpt":"In this note we consider the issue of the classical equivalence of scale-invariant gravity in the Einstein and in the Jordan frames. We first consider the simplest example $f(R)=R^{2}$ and show explicitly that the equivalence breaks down when dealing with Ricci-flat solutions. We discuss the link with the fact that flat solutions in quadratic gravity have zero energy. We also consider the case of scale-invariant tensor-scalar gravity and general $f(R)$ theories. We argue that all scale-invariant gravity models have Ricci flat solutions in the Jordan frame that cannot be mapped into the Einstei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08154","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":"1808.08154","created_at":"2026-05-18T00:03:55.452292+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.08154v1","created_at":"2026-05-18T00:03:55.452292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08154","created_at":"2026-05-18T00:03:55.452292+00:00"},{"alias_kind":"pith_short_12","alias_value":"7WQMGSPFDBYH","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7WQMGSPFDBYHFVRD","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7WQMGSPF","created_at":"2026-05-18T12:32:11.075285+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2503.12826","citing_title":"The Unknown Face of Scalar-Tensor Gravitational Theories","ref_index":35,"is_internal_anchor":true},{"citing_arxiv_id":"2510.08201","citing_title":"Spectrum of pure $R^2$ gravity: full Hamiltonian analysis","ref_index":19,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA","json":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA.json","graph_json":"https://pith.science/api/pith-number/7WQMGSPFDBYHFVRDOLAL5QH4ZA/graph.json","events_json":"https://pith.science/api/pith-number/7WQMGSPFDBYHFVRDOLAL5QH4ZA/events.json","paper":"https://pith.science/paper/7WQMGSPF"},"agent_actions":{"view_html":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA","download_json":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA.json","view_paper":"https://pith.science/paper/7WQMGSPF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.08154&json=true","fetch_graph":"https://pith.science/api/pith-number/7WQMGSPFDBYHFVRDOLAL5QH4ZA/graph.json","fetch_events":"https://pith.science/api/pith-number/7WQMGSPFDBYHFVRDOLAL5QH4ZA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA/action/storage_attestation","attest_author":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA/action/author_attestation","sign_citation":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA/action/citation_signature","submit_replication":"https://pith.science/pith/7WQMGSPFDBYHFVRDOLAL5QH4ZA/action/replication_record"}},"created_at":"2026-05-18T00:03:55.452292+00:00","updated_at":"2026-05-18T00:03:55.452292+00:00"}