{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q3JUZKOT6Z2CNVNGDAHDI7E6AR","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":"f6e4c775064b0c7e4966d5c9d2458b91a9fef748c2850571b00d71b810a668fd","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-11-03T20:57:47Z","title_canon_sha256":"549824df9ef36852049828bbf3ff7567707f84ab840158319c1cea56a8a09020"},"schema_version":"1.0","source":{"id":"1411.0658","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0658","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0658v3","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0658","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"Q3JUZKOT6Z2C","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3JUZKOT6Z2CNVNG","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3JUZKOT","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:5c01e2000f3ffdc289e4d801e7cd5c95710a4c131205edcd24861ee2bdbb2ae3","target":"graph","created_at":"2026-05-18T01:23:45Z","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":"Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {\\lambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with frequency at most {\\lambda}. A corollary is that, when rescaled around a non self-focal point, the kernel of the spectral projector onto the frequency interval (\\lambda, \\lambda + 1] has a universal scaling limit as {\\lambda} goes to infinity (depending only on the dimension of M). Our results also imply that if M has no conjugate points, then immersions of","authors_text":"Boris Hanin, Yaiza Canzani","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-11-03T20:57:47Z","title":"Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0658","kind":"arxiv","version":3},"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":"sha256:12a6135c2c5055d23eb4adc5b2b412c66bea32a8241ff6da889b1312b6fa6a32","target":"record","created_at":"2026-05-18T01:23:45Z","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":"f6e4c775064b0c7e4966d5c9d2458b91a9fef748c2850571b00d71b810a668fd","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-11-03T20:57:47Z","title_canon_sha256":"549824df9ef36852049828bbf3ff7567707f84ab840158319c1cea56a8a09020"},"schema_version":"1.0","source":{"id":"1411.0658","kind":"arxiv","version":3}},"canonical_sha256":"86d34ca9d3f67426d5a6180e347c9e045037f88ceca2d33ded7122b066b02a22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86d34ca9d3f67426d5a6180e347c9e045037f88ceca2d33ded7122b066b02a22","first_computed_at":"2026-05-18T01:23:45.288240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:45.288240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r2NdP19Ok+HudUc0JAXHey/+Wlr65Q8fDff5AvscgYQURNFwC7zpjuFnYSEALLpxfnUWngs8HSzrSwkdRc3pCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:45.288889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0658","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12a6135c2c5055d23eb4adc5b2b412c66bea32a8241ff6da889b1312b6fa6a32","sha256:5c01e2000f3ffdc289e4d801e7cd5c95710a4c131205edcd24861ee2bdbb2ae3"],"state_sha256":"597e022ed8a889efeb146e848532658bcc56733a9f759b983c1786ecb3c4a5f9"}