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It reads sum_p r_p.F_p=-(2/3)(Ga0)^{1/2}[(\\sum_p m_p)^{3/2}-\\sum_p m_p^{3/2}]; a0 is the MOND acceleration constant. Here I show that this relation holds in the nonrelativistic limit of any modified-gravity MOND theory. It follows from only the basic tenets of MOND (as applied to such theories): departure from standard dynamics at accelerations below a0, and space-time scale invariance"},"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":"1311.2579","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-11-11T20:58:59Z","cross_cats_sorted":["astro-ph.CO","hep-ph"],"title_canon_sha256":"b5e62ac68bff8a9c36588a382226fdd9914bbb7763b9ba6618a8aebe2fe50941","abstract_canon_sha256":"748c991f98c574fa2edeffdc152860540b01de47582bf75972ec035ab466bbf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:58.065305Z","signature_b64":"9SPoETtMHaRCNtKGUe6vTkzoM1UAB55i9Fi4b0fUPR9iYzAMHr1Ww+IGtsfCyIrzpuX9909EmzMnc6JMZqEtCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a44c9794fd011ec010150a53bc7ed9362b04bf8f882602b35054ac6380dd664","last_reissued_at":"2026-05-18T03:01:58.064571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:58.064571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General virial theorem for modified-gravity MOND","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph"],"primary_cat":"gr-qc","authors_text":"Mordehai Milgrom (Weizmann Institute)","submitted_at":"2013-11-11T20:58:59Z","abstract_excerpt":"An important and useful relation is known to hold in two specific MOND theories. 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