{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:YEWBWFGBEQTIOJARMQKS3ICEAO","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":"5087cda633d62f478b4970129f33ee0443581184f48dc7eb0f3aa7db3a708af0","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2005-04-08T01:01:01Z","title_canon_sha256":"4258cc419f58bb2064bc4d8bda2e3d87bebf4d73701314bc47992fa21e5acd3d"},"schema_version":"1.0","source":{"id":"math/0504161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504161","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504161v1","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504161","created_at":"2026-05-18T04:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"YEWBWFGBEQTI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"YEWBWFGBEQTIOJAR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"YEWBWFGB","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:a46448d42d70130ed911436cca48d47640f25088539afd1f666b4f016eefbe7a","target":"graph","created_at":"2026-05-18T04:32:20Z","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":"After analyzing renormalization schemes on a Poincar\\'e-Einstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is well-known, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior under a variation of the Poincar\\'e-Einstein structure, and obtain, from the renormalized integral of the Pfaffian, an extension of the Gauss-Bonnet theorem.","authors_text":"Pierre Albin","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2005-04-08T01:01:01Z","title":"Renormalizing Curvature Integrals on Poincare-Einstein Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504161","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":"sha256:86281f78edbe03783a9290fc6271dec8b8a5c7b61a00a6dbe91eeee1a7dcf84f","target":"record","created_at":"2026-05-18T04:32:20Z","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":"5087cda633d62f478b4970129f33ee0443581184f48dc7eb0f3aa7db3a708af0","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2005-04-08T01:01:01Z","title_canon_sha256":"4258cc419f58bb2064bc4d8bda2e3d87bebf4d73701314bc47992fa21e5acd3d"},"schema_version":"1.0","source":{"id":"math/0504161","kind":"arxiv","version":1}},"canonical_sha256":"c12c1b14c1242687241164152da04403b605c6f2abbed36217e30707de7bb1c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c12c1b14c1242687241164152da04403b605c6f2abbed36217e30707de7bb1c5","first_computed_at":"2026-05-18T04:32:20.607693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:20.607693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EZOOre5tO1Czul+rQufgoc9NdJYIitr7CVhSOXidqDtGBdggOKp5kuMOXCvAAsgKxXaBzeTnlNQbKEWTCLvWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:20.608287Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86281f78edbe03783a9290fc6271dec8b8a5c7b61a00a6dbe91eeee1a7dcf84f","sha256:a46448d42d70130ed911436cca48d47640f25088539afd1f666b4f016eefbe7a"],"state_sha256":"71281988462af5c61182f9637d456cd22b433a018fd3c35e88a18038da2418b7"}