{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ASDMHL7PPXBKGM2O37WZ3BVJLW","short_pith_number":"pith:ASDMHL7P","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"},"canonical_sha256":"0486c3afef7dc2a3334edfed9d86a95da236291402fafd0abe10688bfce2f54d","source":{"kind":"arxiv","id":"1207.2642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2642","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2642v1","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2642","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"ASDMHL7PPXBK","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ASDMHL7PPXBKGM2O","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ASDMHL7P","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ASDMHL7PPXBKGM2O37WZ3BVJLW","target":"record","payload":{"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"},"canonical_sha256":"0486c3afef7dc2a3334edfed9d86a95da236291402fafd0abe10688bfce2f54d","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"},"source_kind":"arxiv","source_id":"1207.2642","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMWuh2DQY/KdFLgoPl/oScrXj0SZjCnkNs3GNj3e40JP9aUX+yXg7JaR8dnbSw2gOaKLvWJEalxuKZNi1f3qDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:25:45.401462Z"},"content_sha256":"e14606acedda799703f71e077bf6297157128f0b5a238bbe77ee03abbd78ad07","schema_version":"1.0","event_id":"sha256:e14606acedda799703f71e077bf6297157128f0b5a238bbe77ee03abbd78ad07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ASDMHL7PPXBKGM2O37WZ3BVJLW","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ai+8Mk8EF+6IJ/bAhzKlmTmiwFKzJqmsonU+W5el93E5FWJwg3X+9jry6e7QPcjTNZHs9ac37E0tYKVpBFT3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:25:45.401860Z"},"content_sha256":"93feac1956b7c3c384ab17e3d7c42b5570c2cb24f7da3ed5c422f59772fd2797","schema_version":"1.0","event_id":"sha256:93feac1956b7c3c384ab17e3d7c42b5570c2cb24f7da3ed5c422f59772fd2797"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/bundle.json","state_url":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T05:25:45Z","links":{"resolver":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW","bundle":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/bundle.json","state":"https://pith.science/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASDMHL7PPXBKGM2O37WZ3BVJLW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ASDMHL7PPXBKGM2O37WZ3BVJLW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3e00ddd91da0d9f8087e1dcca7e95df8469ad161de5691e87cdcce2fb2f77bf6","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-11T14:00:46Z","title_canon_sha256":"10f804c09b779c29ab40c5ba2aa028951aa26a49465b03d6181ac92da47cc9f5"},"schema_version":"1.0","source":{"id":"1207.2642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2642","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2642v1","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2642","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"ASDMHL7PPXBK","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ASDMHL7PPXBKGM2O","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ASDMHL7P","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:93feac1956b7c3c384ab17e3d7c42b5570c2cb24f7da3ed5c422f59772fd2797","target":"graph","created_at":"2026-05-18T03:51:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 $CP^d \\hookrightarrow CP^m$.","authors_text":"Georges Habib, Roger Nakad","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-11T14:00:46Z","title":"The twisted Spin$^c$ Dirac operator on K\\\"ahler submanifolds of the complex projective space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2642","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e14606acedda799703f71e077bf6297157128f0b5a238bbe77ee03abbd78ad07","target":"record","created_at":"2026-05-18T03:51:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3e00ddd91da0d9f8087e1dcca7e95df8469ad161de5691e87cdcce2fb2f77bf6","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-11T14:00:46Z","title_canon_sha256":"10f804c09b779c29ab40c5ba2aa028951aa26a49465b03d6181ac92da47cc9f5"},"schema_version":"1.0","source":{"id":"1207.2642","kind":"arxiv","version":1}},"canonical_sha256":"0486c3afef7dc2a3334edfed9d86a95da236291402fafd0abe10688bfce2f54d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0486c3afef7dc2a3334edfed9d86a95da236291402fafd0abe10688bfce2f54d","first_computed_at":"2026-05-18T03:51:14.907829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:14.907829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqzwSdFzfGRD9kGpuKou04qDZw9yW4fpSbHj+kcm1CbsatJtFaOz7Z+K1vE5DABnfVqBK/KiCbp45w5mSHdkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:14.908264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e14606acedda799703f71e077bf6297157128f0b5a238bbe77ee03abbd78ad07","sha256:93feac1956b7c3c384ab17e3d7c42b5570c2cb24f7da3ed5c422f59772fd2797"],"state_sha256":"cdbbb13c3dd97f554ece856031169786eef63329ea6a37748fa401658761ec49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/V1IlIbIYbfTbtIYJNA5Ne9Fjd5dXYfQRdPFha3Ul69sDoQtIXv/q3CBmyiP4kFff1htYUGBrZbr3uu82K+MCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:25:45.403859Z","bundle_sha256":"07dfffaeda04225287acb12c4815e419662e446cd4c9594759050add5c804c40"}}