{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OB2BXJ3WHUHMHVSVAVUKVNGMQN","short_pith_number":"pith:OB2BXJ3W","canonical_record":{"source":{"id":"1809.08677","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-23T20:56:18Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4cf807f33338d62a5371c42be70475aaa98dcde832f38121700d31d30d1cfd0c","abstract_canon_sha256":"0a9f87db75340e8e057fca75529e89ac29d113353e6c728a277448010c6c8845"},"schema_version":"1.0"},"canonical_sha256":"70741ba7763d0ec3d6550568aab4cc8371ec9bf62152d8a7a6ec49b23eff9c46","source":{"kind":"arxiv","id":"1809.08677","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08677","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08677v2","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08677","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"OB2BXJ3WHUHM","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OB2BXJ3WHUHMHVSV","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OB2BXJ3W","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OB2BXJ3WHUHMHVSVAVUKVNGMQN","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08677","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-23T20:56:18Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4cf807f33338d62a5371c42be70475aaa98dcde832f38121700d31d30d1cfd0c","abstract_canon_sha256":"0a9f87db75340e8e057fca75529e89ac29d113353e6c728a277448010c6c8845"},"schema_version":"1.0"},"canonical_sha256":"70741ba7763d0ec3d6550568aab4cc8371ec9bf62152d8a7a6ec49b23eff9c46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:33.518047Z","signature_b64":"IuS8QC4eQXAX3V6gULWnBtvWrFARor5WV5qXg+6qIz15EWiaWQLCTVSIHQRA+QFqf5seI5acVixa3n0f3t4SDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70741ba7763d0ec3d6550568aab4cc8371ec9bf62152d8a7a6ec49b23eff9c46","last_reissued_at":"2026-05-17T23:56:33.517451Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:33.517451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08677","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8W0aVwmT9o34aWFJ8PgJr6BH37cTPbz7MnKdESIyt0ffLefuMpD3g4Kvhq+jJ924ATGBQV/wO7HaWNdSdB6RCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:49:42.760697Z"},"content_sha256":"a4be8c701c1e2ad459f46f9dfde9a2d5683111aae7937ce4dd6d7904f84c3de6","schema_version":"1.0","event_id":"sha256:a4be8c701c1e2ad459f46f9dfde9a2d5683111aae7937ce4dd6d7904f84c3de6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OB2BXJ3WHUHMHVSVAVUKVNGMQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A microlocal approach to eigenfunction concentration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Jeffrey Galkowski","submitted_at":"2018-09-23T20:56:18Z","abstract_excerpt":"We describe a new approach to understanding averages of high energy Laplace eigenfunctions, $u_h$, over submanifolds, $$ \\Big|\\int _H u_hd\\sigma_H\\Big| $$ where $H\\subset M$ is a submanifold and $\\sigma_H$ the induced by the Riemannian metric on $M$. This approach can be applied uniformly to submanifolds of codimension $1\\leq k\\leq n$ and in particular, gives a new approach to understanding $\\|u_h\\|_{L^\\infty(M)}$. The method, developed in the author's recent work together with Y. Canzani and J. Toth, relies on estimating averages by the behavior of $u_h$ microlocally near the conormal bundle "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08677","kind":"arxiv","version":2},"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":"2026-05-17T23:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sXt3Tmi012PLnwq2uXHru+se+UcOG24+RFBhZGa64ZxEzqUz++wAfdYHQyhXVWNumMeLfPI1AzFB+lrCXMlYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:49:42.761051Z"},"content_sha256":"5c668d9cce6c3874af0bd5bd66c4b8b5e550980307f68819fb40fadd17bb4de7","schema_version":"1.0","event_id":"sha256:5c668d9cce6c3874af0bd5bd66c4b8b5e550980307f68819fb40fadd17bb4de7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OB2BXJ3WHUHMHVSVAVUKVNGMQN/bundle.json","state_url":"https://pith.science/pith/OB2BXJ3WHUHMHVSVAVUKVNGMQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OB2BXJ3WHUHMHVSVAVUKVNGMQN/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":"2026-06-03T14:49:42Z","links":{"resolver":"https://pith.science/pith/OB2BXJ3WHUHMHVSVAVUKVNGMQN","bundle":"https://pith.science/pith/OB2BXJ3WHUHMHVSVAVUKVNGMQN/bundle.json","state":"https://pith.science/pith/OB2BXJ3WHUHMHVSVAVUKVNGMQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OB2BXJ3WHUHMHVSVAVUKVNGMQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OB2BXJ3WHUHMHVSVAVUKVNGMQN","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":"0a9f87db75340e8e057fca75529e89ac29d113353e6c728a277448010c6c8845","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-23T20:56:18Z","title_canon_sha256":"4cf807f33338d62a5371c42be70475aaa98dcde832f38121700d31d30d1cfd0c"},"schema_version":"1.0","source":{"id":"1809.08677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08677","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08677v2","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08677","created_at":"2026-05-17T23:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"OB2BXJ3WHUHM","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OB2BXJ3WHUHMHVSV","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OB2BXJ3W","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:5c668d9cce6c3874af0bd5bd66c4b8b5e550980307f68819fb40fadd17bb4de7","target":"graph","created_at":"2026-05-17T23:56:33Z","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":"We describe a new approach to understanding averages of high energy Laplace eigenfunctions, $u_h$, over submanifolds, $$ \\Big|\\int _H u_hd\\sigma_H\\Big| $$ where $H\\subset M$ is a submanifold and $\\sigma_H$ the induced by the Riemannian metric on $M$. This approach can be applied uniformly to submanifolds of codimension $1\\leq k\\leq n$ and in particular, gives a new approach to understanding $\\|u_h\\|_{L^\\infty(M)}$. The method, developed in the author's recent work together with Y. Canzani and J. Toth, relies on estimating averages by the behavior of $u_h$ microlocally near the conormal bundle ","authors_text":"Jeffrey Galkowski","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-23T20:56:18Z","title":"A microlocal approach to eigenfunction concentration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08677","kind":"arxiv","version":2},"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:a4be8c701c1e2ad459f46f9dfde9a2d5683111aae7937ce4dd6d7904f84c3de6","target":"record","created_at":"2026-05-17T23:56:33Z","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":"0a9f87db75340e8e057fca75529e89ac29d113353e6c728a277448010c6c8845","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-23T20:56:18Z","title_canon_sha256":"4cf807f33338d62a5371c42be70475aaa98dcde832f38121700d31d30d1cfd0c"},"schema_version":"1.0","source":{"id":"1809.08677","kind":"arxiv","version":2}},"canonical_sha256":"70741ba7763d0ec3d6550568aab4cc8371ec9bf62152d8a7a6ec49b23eff9c46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70741ba7763d0ec3d6550568aab4cc8371ec9bf62152d8a7a6ec49b23eff9c46","first_computed_at":"2026-05-17T23:56:33.517451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:33.517451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IuS8QC4eQXAX3V6gULWnBtvWrFARor5WV5qXg+6qIz15EWiaWQLCTVSIHQRA+QFqf5seI5acVixa3n0f3t4SDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:33.518047Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4be8c701c1e2ad459f46f9dfde9a2d5683111aae7937ce4dd6d7904f84c3de6","sha256:5c668d9cce6c3874af0bd5bd66c4b8b5e550980307f68819fb40fadd17bb4de7"],"state_sha256":"cfae41dd2a54cc03a61ec89e26e92a0e8bf8be0673f2e90abdba2c26b1cc07eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BscQvFDqfsYhgmEPggxIqLC4NwjyuxNqviakVjWBPbQjz5dUsSR/7A+LTz8oNIBYydssTjpPFb7L/TJRoVW0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:49:42.763045Z","bundle_sha256":"b7033eb37116ee3d39d72ee986eb4a867c69e124dba59be876fa3092199d3cba"}}