{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SQDAWMSYYEYEVVGW2DS5RBCKSU","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":"91ca3632886d9d4bf9d25b3ab24e6cbe2d05ab7696417e32a4e4eb78dba31bc5","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-16T13:58:24Z","title_canon_sha256":"0e7ef0c27467bbe04b2ec598a43d5218bcf98caac0bba808ecda5d3ee089f157"},"schema_version":"1.0","source":{"id":"1009.3179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3179","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3179v1","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3179","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"SQDAWMSYYEYE","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SQDAWMSYYEYEVVGW","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SQDAWMSY","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:49953bc8dee4189e36469282d76b45a2df33178a5c2a09fec96700fcda9b21e5","target":"graph","created_at":"2026-05-18T04:40:46Z","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":"For a Dirac operator $D_{\\bar{g}}$ over a spin compact Riemannian manifold with boundary $(\\bar{X},\\bar{g})$, we give a natural construction of the Calder\\'on projector and of the associated Bergman projector on the space of harmonic spinors on $\\bar{X}$, and we analyze their Schwartz kernels. Our approach is based on the conformal covariance of $D_{\\bar{g}}$ and the scattering theory for the Dirac operator associated to the complete conformal metric $g=\\bar{g}/\\rho^2$ where $\\rho$ is a smooth function on $\\bar{X}$ which equals the distance to the boundary near $\\partial\\bar{X}$. We show that ","authors_text":"Colin Guillarmou, Jinsung Park, Sergiu Moroianu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-16T13:58:24Z","title":"Bergman and Calder\\'on projectors for Dirac operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3179","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":"sha256:9b45ccbdc1ae5d65f925077d2c7ae0a255f977bfdd995f1142493ee77dd5388b","target":"record","created_at":"2026-05-18T04:40:46Z","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":"91ca3632886d9d4bf9d25b3ab24e6cbe2d05ab7696417e32a4e4eb78dba31bc5","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-16T13:58:24Z","title_canon_sha256":"0e7ef0c27467bbe04b2ec598a43d5218bcf98caac0bba808ecda5d3ee089f157"},"schema_version":"1.0","source":{"id":"1009.3179","kind":"arxiv","version":1}},"canonical_sha256":"94060b3258c1304ad4d6d0e5d8844a952b23ea34825f957cad548678eeecb730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94060b3258c1304ad4d6d0e5d8844a952b23ea34825f957cad548678eeecb730","first_computed_at":"2026-05-18T04:40:46.813139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:46.813139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u3oL4lk6Zi7CUJjnJORC3mtF8kAJwGvKCP3QbGsKyb/Do9K8Aff84kFFoeJd8S9mXwZpaj4MfHMMDsmfIeZGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:46.813637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b45ccbdc1ae5d65f925077d2c7ae0a255f977bfdd995f1142493ee77dd5388b","sha256:49953bc8dee4189e36469282d76b45a2df33178a5c2a09fec96700fcda9b21e5"],"state_sha256":"6dfac214a30e943d27b6f005b49aa25d76fefa531e80c4f676d4501a1d7af848"}