{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZEHWXFMXZDERN6Q5TWWG4XDKTG","short_pith_number":"pith:ZEHWXFMX","canonical_record":{"source":{"id":"1504.00554","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T13:39:13Z","cross_cats_sorted":[],"title_canon_sha256":"53b4cbcdabc204f27356aad13feb6c40f6cbc1d81aeaf8126f0275af26b2322f","abstract_canon_sha256":"cc76ee8001867ab5fbb6589974c9880dfff94a85d396efbf864eb76e808a7689"},"schema_version":"1.0"},"canonical_sha256":"c90f6b9597c8c916fa1d9dac6e5c6a99ad33fbe8592076d555c02e42cb1b2a28","source":{"kind":"arxiv","id":"1504.00554","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00554","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00554v3","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00554","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"ZEHWXFMXZDER","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZEHWXFMXZDERN6Q5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZEHWXFMX","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZEHWXFMXZDERN6Q5TWWG4XDKTG","target":"record","payload":{"canonical_record":{"source":{"id":"1504.00554","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T13:39:13Z","cross_cats_sorted":[],"title_canon_sha256":"53b4cbcdabc204f27356aad13feb6c40f6cbc1d81aeaf8126f0275af26b2322f","abstract_canon_sha256":"cc76ee8001867ab5fbb6589974c9880dfff94a85d396efbf864eb76e808a7689"},"schema_version":"1.0"},"canonical_sha256":"c90f6b9597c8c916fa1d9dac6e5c6a99ad33fbe8592076d555c02e42cb1b2a28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:42.211886Z","signature_b64":"xOnqlh4G3o075BVs+RYT/yH8aj3RI7J2ZwP9jFh6OtOJqhQyxw9ASVtcIDL1V6iba6+GVoaQuat57rifGg8mBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c90f6b9597c8c916fa1d9dac6e5c6a99ad33fbe8592076d555c02e42cb1b2a28","last_reissued_at":"2026-05-18T00:04:42.211174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:42.211174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.00554","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9SImWWdCLxQYr46IsmOiYZyXb8BcplMw3NfPo1kMeKWfI3vo2BKCDJrgd8IHad56Lu/vNRis4QU+tPPK47MxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:08:55.971057Z"},"content_sha256":"bf2c3dc806edebd3d29e8a4aac3ed60e4762ed3ca2d99ab811bc934042d1d0b3","schema_version":"1.0","event_id":"sha256:bf2c3dc806edebd3d29e8a4aac3ed60e4762ed3ca2d99ab811bc934042d1d0b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZEHWXFMXZDERN6Q5TWWG4XDKTG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sampling inequality for $L^2$-norms of eigenfunctions, spectral projectors, and Weyl sequences of Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ivan Veseli\\'c, Martin Tautenhahn","submitted_at":"2015-04-02T13:39:13Z","abstract_excerpt":"We consider a Schr\\\"odinger operator with bounded, measurable potential in multidimensional Euclidean space. We prove for every $L^2$-eigenfunction a quantitative equidistribution estimate. It compares the total $L^2$-norm with the $L^2$-norm over an equidistributed collection of balls. Our estimate is explicit with respect to the radius of the balls, norm of the potential and the energy of the eigenfunction. Similar estimates also hold for Weyl sequences and for linear combinations of eigenfunctions, as long as the associated eigenvalues are sufficiently close."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00554","kind":"arxiv","version":3},"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":"2026-05-18T00:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWyzRNHBT9UEsWJxVORj2Oc53Mt8e9TP75uqZeXf/s1VmF8OWxLVhege03cBrsEnQ/lUBuvFPQUo1ObtWHYTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:08:55.971418Z"},"content_sha256":"130f53610eb29ae67095b85fc6f96d4741c0010a3dda7c51450d4e027fab3bc3","schema_version":"1.0","event_id":"sha256:130f53610eb29ae67095b85fc6f96d4741c0010a3dda7c51450d4e027fab3bc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZEHWXFMXZDERN6Q5TWWG4XDKTG/bundle.json","state_url":"https://pith.science/pith/ZEHWXFMXZDERN6Q5TWWG4XDKTG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZEHWXFMXZDERN6Q5TWWG4XDKTG/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":"2026-06-26T16:08:55Z","links":{"resolver":"https://pith.science/pith/ZEHWXFMXZDERN6Q5TWWG4XDKTG","bundle":"https://pith.science/pith/ZEHWXFMXZDERN6Q5TWWG4XDKTG/bundle.json","state":"https://pith.science/pith/ZEHWXFMXZDERN6Q5TWWG4XDKTG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZEHWXFMXZDERN6Q5TWWG4XDKTG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZEHWXFMXZDERN6Q5TWWG4XDKTG","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":"cc76ee8001867ab5fbb6589974c9880dfff94a85d396efbf864eb76e808a7689","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T13:39:13Z","title_canon_sha256":"53b4cbcdabc204f27356aad13feb6c40f6cbc1d81aeaf8126f0275af26b2322f"},"schema_version":"1.0","source":{"id":"1504.00554","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00554","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00554v3","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00554","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"ZEHWXFMXZDER","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZEHWXFMXZDERN6Q5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZEHWXFMX","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:130f53610eb29ae67095b85fc6f96d4741c0010a3dda7c51450d4e027fab3bc3","target":"graph","created_at":"2026-05-18T00:04:42Z","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 consider a Schr\\\"odinger operator with bounded, measurable potential in multidimensional Euclidean space. We prove for every $L^2$-eigenfunction a quantitative equidistribution estimate. It compares the total $L^2$-norm with the $L^2$-norm over an equidistributed collection of balls. Our estimate is explicit with respect to the radius of the balls, norm of the potential and the energy of the eigenfunction. Similar estimates also hold for Weyl sequences and for linear combinations of eigenfunctions, as long as the associated eigenvalues are sufficiently close.","authors_text":"Ivan Veseli\\'c, Martin Tautenhahn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T13:39:13Z","title":"Sampling inequality for $L^2$-norms of eigenfunctions, spectral projectors, and Weyl sequences of Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00554","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:bf2c3dc806edebd3d29e8a4aac3ed60e4762ed3ca2d99ab811bc934042d1d0b3","target":"record","created_at":"2026-05-18T00:04:42Z","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":"cc76ee8001867ab5fbb6589974c9880dfff94a85d396efbf864eb76e808a7689","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T13:39:13Z","title_canon_sha256":"53b4cbcdabc204f27356aad13feb6c40f6cbc1d81aeaf8126f0275af26b2322f"},"schema_version":"1.0","source":{"id":"1504.00554","kind":"arxiv","version":3}},"canonical_sha256":"c90f6b9597c8c916fa1d9dac6e5c6a99ad33fbe8592076d555c02e42cb1b2a28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c90f6b9597c8c916fa1d9dac6e5c6a99ad33fbe8592076d555c02e42cb1b2a28","first_computed_at":"2026-05-18T00:04:42.211174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:42.211174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xOnqlh4G3o075BVs+RYT/yH8aj3RI7J2ZwP9jFh6OtOJqhQyxw9ASVtcIDL1V6iba6+GVoaQuat57rifGg8mBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:42.211886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00554","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf2c3dc806edebd3d29e8a4aac3ed60e4762ed3ca2d99ab811bc934042d1d0b3","sha256:130f53610eb29ae67095b85fc6f96d4741c0010a3dda7c51450d4e027fab3bc3"],"state_sha256":"7e68d285ec1c0943ce948cbf38d7e71d1b755e329b8ba1ee0c29b465ddb6ad55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VpvNsTkqdCfy3fjAt3ihpnFOWIGwhZFHQUqrAvViD4j1nfFtkZkirQwb6ydpPepzNzz9cajxIF9qnkMK0hW+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:08:55.973427Z","bundle_sha256":"89eeb76af9c09291023ce96f5c7297d9eafd9c426605e90238569059d62e6039"}}