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Let $R^\\gamma(M)$ be the space of smooth Riemannian metrics $g$ on $M$ for which the generalized conformal Laplace operator $-\\gamma\\Delta_g+\\mathrm{R}_g$ is strictly positive.\n  We prove that if $n=2$ and $\\gamma\\ge0$, or if $n\\ge3$ and $0\\leq \\gamma \\leq 4(n-1)/(n-2)$, the inclusion $R^0(M)\\hookrightarrow R^\\gamma(M)$ is a homotopy equivalence, thus generalizing, to all dimensions and in the maximal range, the results of Botvinnik--Rosenberg and Li--Mantoulidis. 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Let $R^\\gamma(M)$ be the space of smooth Riemannian metrics $g$ on $M$ for which the generalized conformal Laplace operator $-\\gamma\\Delta_g+\\mathrm{R}_g$ is strictly positive.\n  We prove that if $n=2$ and $\\gamma\\ge0$, or if $n\\ge3$ and $0\\leq \\gamma \\leq 4(n-1)/(n-2)$, the inclusion $R^0(M)\\hookrightarrow R^\\gamma(M)$ is a homotopy equivalence, thus generalizing, to all dimensions and in the maximal range, the results of Botvinnik--Rosenberg and Li--Mantoulidis. Then, we prove that if $n\\ge3$ and $\\gamma>4(n-1)/(n-2)$, the spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28467","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/2607.28467/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":"2607.28467","created_at":"2026-07-31T01:37:50.233048+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.28467v1","created_at":"2026-07-31T01:37:50.233048+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28467","created_at":"2026-07-31T01:37:50.233048+00:00"},{"alias_kind":"pith_short_12","alias_value":"TP7MQ3P5CUTY","created_at":"2026-07-31T01:37:50.233048+00:00"},{"alias_kind":"pith_short_16","alias_value":"TP7MQ3P5CUTYA6IW","created_at":"2026-07-31T01:37:50.233048+00:00"},{"alias_kind":"pith_short_8","alias_value":"TP7MQ3P5","created_at":"2026-07-31T01:37:50.233048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR","json":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR.json","graph_json":"https://pith.science/api/pith-number/TP7MQ3P5CUTYA6IW7H2QP2PERR/graph.json","events_json":"https://pith.science/api/pith-number/TP7MQ3P5CUTYA6IW7H2QP2PERR/events.json","paper":"https://pith.science/paper/TP7MQ3P5"},"agent_actions":{"view_html":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR","download_json":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR.json","view_paper":"https://pith.science/paper/TP7MQ3P5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.28467&json=true","fetch_graph":"https://pith.science/api/pith-number/TP7MQ3P5CUTYA6IW7H2QP2PERR/graph.json","fetch_events":"https://pith.science/api/pith-number/TP7MQ3P5CUTYA6IW7H2QP2PERR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR/action/storage_attestation","attest_author":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR/action/author_attestation","sign_citation":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR/action/citation_signature","submit_replication":"https://pith.science/pith/TP7MQ3P5CUTYA6IW7H2QP2PERR/action/replication_record"}},"created_at":"2026-07-31T01:37:50.233048+00:00","updated_at":"2026-07-31T01:37:50.233048+00:00"}