{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BFOOXQKY7N6R5A3VDUG7JLH2JA","short_pith_number":"pith:BFOOXQKY","schema_version":"1.0","canonical_sha256":"095cebc158fb7d1e83751d0df4acfa4805288f0ed08f4ae650775348fcf35abf","source":{"kind":"arxiv","id":"1412.1662","version":1},"attestation_state":"computed","paper":{"title":"The Schr\\\"odinger-Newton equations beyond Newton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"gr-qc","authors_text":"Giovanni Manfredi","submitted_at":"2014-12-04T13:37:42Z","abstract_excerpt":"The scope of this paper is twofold. First, we derive rigorously a low-velocity and Galilei-covariant limit of the gravitoelectromagnetic (GEM) equations. Subsequently, these reduced GEM equations are coupled to the Schr\\\"odinger equation with gravitoelectric and gravitomagnetic potentials. The resulting extended Schr\\\"odinger-Newton equations constitute a minimal model where the three fundamental constants of nature ($G$, $\\hbar$, and $c$) appear naturally. We show that the relativistic correction coming from the gravitomagnetic potential scales as the ratio of the mass of the system to the Pl"},"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":"1412.1662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-12-04T13:37:42Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"7b94ae9b8e82d965db3eb987f692bc5acbf5b6f7c41cf8db81753ca2fe71648e","abstract_canon_sha256":"7999ea1b16761d9fc2b21187c9df724003546e131eb209901db77a6409274189"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:23.287654Z","signature_b64":"FUGyAuuRuuNBXaoVrzj6Jk/lWOHdJbzDeXIHtoeyAaR0axZAx+Ea7yAtGsaolSNFI3N5+6SevqX0oRE9xMpWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"095cebc158fb7d1e83751d0df4acfa4805288f0ed08f4ae650775348fcf35abf","last_reissued_at":"2026-05-18T01:41:23.287157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:23.287157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Schr\\\"odinger-Newton equations beyond Newton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"gr-qc","authors_text":"Giovanni Manfredi","submitted_at":"2014-12-04T13:37:42Z","abstract_excerpt":"The scope of this paper is twofold. First, we derive rigorously a low-velocity and Galilei-covariant limit of the gravitoelectromagnetic (GEM) equations. Subsequently, these reduced GEM equations are coupled to the Schr\\\"odinger equation with gravitoelectric and gravitomagnetic potentials. The resulting extended Schr\\\"odinger-Newton equations constitute a minimal model where the three fundamental constants of nature ($G$, $\\hbar$, and $c$) appear naturally. We show that the relativistic correction coming from the gravitomagnetic potential scales as the ratio of the mass of the system to the Pl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1662","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":"1412.1662","created_at":"2026-05-18T01:41:23.287231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1662v1","created_at":"2026-05-18T01:41:23.287231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1662","created_at":"2026-05-18T01:41:23.287231+00:00"},{"alias_kind":"pith_short_12","alias_value":"BFOOXQKY7N6R","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BFOOXQKY7N6R5A3V","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BFOOXQKY","created_at":"2026-05-18T12:28:22.404517+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/BFOOXQKY7N6R5A3VDUG7JLH2JA","json":"https://pith.science/pith/BFOOXQKY7N6R5A3VDUG7JLH2JA.json","graph_json":"https://pith.science/api/pith-number/BFOOXQKY7N6R5A3VDUG7JLH2JA/graph.json","events_json":"https://pith.science/api/pith-number/BFOOXQKY7N6R5A3VDUG7JLH2JA/events.json","paper":"https://pith.science/paper/BFOOXQKY"},"agent_actions":{"view_html":"https://pith.science/pith/BFOOXQKY7N6R5A3VDUG7JLH2JA","download_json":"https://pith.science/pith/BFOOXQKY7N6R5A3VDUG7JLH2JA.json","view_paper":"https://pith.science/paper/BFOOXQKY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1662&json=true","fetch_graph":"https://pith.science/api/pith-number/BFOOXQKY7N6R5A3VDUG7JLH2JA/graph.json","fetch_events":"https://pith.science/api/pith-number/BFOOXQKY7N6R5A3VDUG7JLH2JA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BFOOXQKY7N6R5A3VDUG7JLH2JA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BFOOXQKY7N6R5A3VDUG7JLH2JA/action/storage_attestation","attest_author":"https://pith.science/pith/BFOOXQKY7N6R5A3VDUG7JLH2JA/action/author_attestation","sign_citation":"https://pith.science/pith/BFOOXQKY7N6R5A3VDUG7JLH2JA/action/citation_signature","submit_replication":"https://pith.science/pith/BFOOXQKY7N6R5A3VDUG7JLH2JA/action/replication_record"}},"created_at":"2026-05-18T01:41:23.287231+00:00","updated_at":"2026-05-18T01:41:23.287231+00:00"}