{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ASDMHL7PPXBKGM2O37WZ3BVJLW","short_pith_number":"pith:ASDMHL7P","schema_version":"1.0","canonical_sha256":"0486c3afef7dc2a3334edfed9d86a95da236291402fafd0abe10688bfce2f54d","source":{"kind":"arxiv","id":"1207.2642","version":1},"attestation_state":"computed","paper":{"title":"The twisted Spin$^c$ Dirac operator on K\\\"ahler submanifolds of the complex projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Georges Habib, Roger Nakad","submitted_at":"2012-07-11T14:00:46Z","abstract_excerpt":"In this paper, we estimate the eigenvalues of the twisted Dirac operator on K\\\"ahler submanifolds of the complex projective space $CP^m$ and we discuss the sharpness of this estimate for the embedding $CP^d \\hookrightarrow CP^m$."},"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":"1207.2642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-11T14:00:46Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"10f804c09b779c29ab40c5ba2aa028951aa26a49465b03d6181ac92da47cc9f5","abstract_canon_sha256":"3e00ddd91da0d9f8087e1dcca7e95df8469ad161de5691e87cdcce2fb2f77bf6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:14.908264Z","signature_b64":"dqzwSdFzfGRD9kGpuKou04qDZw9yW4fpSbHj+kcm1CbsatJtFaOz7Z+K1vE5DABnfVqBK/KiCbp45w5mSHdkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0486c3afef7dc2a3334edfed9d86a95da236291402fafd0abe10688bfce2f54d","last_reissued_at":"2026-05-18T03:51:14.907829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:14.907829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The twisted Spin$^c$ Dirac operator on K\\\"ahler submanifolds of the complex projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Georges Habib, Roger Nakad","submitted_at":"2012-07-11T14:00:46Z","abstract_excerpt":"In this paper, we estimate the eigenvalues of the twisted Dirac operator on K\\\"ahler submanifolds of the complex projective space $CP^m$ and we discuss the sharpness of this estimate for the embedding $CP^d \\hookrightarrow CP^m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2642","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":"1207.2642","created_at":"2026-05-18T03:51:14.907895+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.2642v1","created_at":"2026-05-18T03:51:14.907895+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2642","created_at":"2026-05-18T03:51:14.907895+00:00"},{"alias_kind":"pith_short_12","alias_value":"ASDMHL7PPXBK","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"ASDMHL7PPXBKGM2O","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"ASDMHL7P","created_at":"2026-05-18T12:26:58.693483+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/ASDMHL7PPXBKGM2O37WZ3BVJLW","json":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW.json","graph_json":"https://pith.science/api/pith-number/ASDMHL7PPXBKGM2O37WZ3BVJLW/graph.json","events_json":"https://pith.science/api/pith-number/ASDMHL7PPXBKGM2O37WZ3BVJLW/events.json","paper":"https://pith.science/paper/ASDMHL7P"},"agent_actions":{"view_html":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW","download_json":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW.json","view_paper":"https://pith.science/paper/ASDMHL7P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.2642&json=true","fetch_graph":"https://pith.science/api/pith-number/ASDMHL7PPXBKGM2O37WZ3BVJLW/graph.json","fetch_events":"https://pith.science/api/pith-number/ASDMHL7PPXBKGM2O37WZ3BVJLW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/action/storage_attestation","attest_author":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/action/author_attestation","sign_citation":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/action/citation_signature","submit_replication":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/action/replication_record"}},"created_at":"2026-05-18T03:51:14.907895+00:00","updated_at":"2026-05-18T03:51:14.907895+00:00"}