{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:X6XRV2HG756GYSH6Q3BYK3MBQR","short_pith_number":"pith:X6XRV2HG","canonical_record":{"source":{"id":"1707.08392","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-26T11:50:42Z","cross_cats_sorted":["math.PR","math.SP"],"title_canon_sha256":"a8690c61dc42e568477db4bc9b84888d362c04aa63fe99953bd6ae24973b8055","abstract_canon_sha256":"70f2568ed02b45d7670cc66c06de5f56aad17df9735fc602b78d346a626c650f"},"schema_version":"1.0"},"canonical_sha256":"bfaf1ae8e6ff7c6c48fe86c3856d818453685b1f63ec83b3f73e948171bc4953","source":{"kind":"arxiv","id":"1707.08392","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08392","created_at":"2026-05-18T00:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08392v3","created_at":"2026-05-18T00:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08392","created_at":"2026-05-18T00:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"X6XRV2HG756G","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X6XRV2HG756GYSH6","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X6XRV2HG","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:X6XRV2HG756GYSH6Q3BYK3MBQR","target":"record","payload":{"canonical_record":{"source":{"id":"1707.08392","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-26T11:50:42Z","cross_cats_sorted":["math.PR","math.SP"],"title_canon_sha256":"a8690c61dc42e568477db4bc9b84888d362c04aa63fe99953bd6ae24973b8055","abstract_canon_sha256":"70f2568ed02b45d7670cc66c06de5f56aad17df9735fc602b78d346a626c650f"},"schema_version":"1.0"},"canonical_sha256":"bfaf1ae8e6ff7c6c48fe86c3856d818453685b1f63ec83b3f73e948171bc4953","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:53.280693Z","signature_b64":"Yz+qcZxtc9IGdyDTxNX8bSBc3g2aWUlEsbuweCyB3jaA8WhJxWDwR1zvCF3PdFtRLPJ4eRWxYHzXWOxRRiudAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfaf1ae8e6ff7c6c48fe86c3856d818453685b1f63ec83b3f73e948171bc4953","last_reissued_at":"2026-05-18T00:28:53.280128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:53.280128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.08392","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":"2026-05-18T00:28:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5FMXmVTtQij4ABSMKKJTKqCygn+QHcF79+E+Jr3eOkSX0v/RiOZK74zDaw5D6JaxxlgurLkC3IRJSwZKjt3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:11:25.552377Z"},"content_sha256":"b2f6482523d6983342112b20ff79eef4299cbd561bb1e3d18dab59f3101394be","schema_version":"1.0","event_id":"sha256:b2f6482523d6983342112b20ff79eef4299cbd561bb1e3d18dab59f3101394be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:X6XRV2HG756GYSH6Q3BYK3MBQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Location of maximizers of eigenfunctions of fractional Schr\\\"odinger's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.SP"],"primary_cat":"math.AP","authors_text":"Anup Biswas","submitted_at":"2017-07-26T11:50:42Z","abstract_excerpt":"Eigenfunctions of the fractional Schr\\\"odinger operators in a domain $\\mathcal{D}$ are considered, and a relation between the supremum of the potential and the distance of a maximizer of the eigenfunction from $\\partial\\mathcal{D}$ is established. This, in particular, extends a recent result of Rachh and Steinerberger to the fractional Schr\\\"odinger operators. We also propose a fractional version of the Barta's inequality and also generalize a celebrated Lieb's theorem for fractional Schr\\\"odinger operators. As applications of above results we obtain a Faber-Krahn inequality for non-local Schr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08392","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":"2026-05-18T00:28:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Db2ITpDur89/dmBruK4FN+NZz3rWgPbwjFE2R7XwITGm2Zh4hl0GjY7NxzR3Z+3TDqh0rqI4YzTgZpUMSB9YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:11:25.552768Z"},"content_sha256":"657bdb6feceed8904f5d857f16ab979542de584d9e40a76dc00196c7746ceed8","schema_version":"1.0","event_id":"sha256:657bdb6feceed8904f5d857f16ab979542de584d9e40a76dc00196c7746ceed8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6XRV2HG756GYSH6Q3BYK3MBQR/bundle.json","state_url":"https://pith.science/pith/X6XRV2HG756GYSH6Q3BYK3MBQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6XRV2HG756GYSH6Q3BYK3MBQR/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":"2026-05-30T22:11:25Z","links":{"resolver":"https://pith.science/pith/X6XRV2HG756GYSH6Q3BYK3MBQR","bundle":"https://pith.science/pith/X6XRV2HG756GYSH6Q3BYK3MBQR/bundle.json","state":"https://pith.science/pith/X6XRV2HG756GYSH6Q3BYK3MBQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6XRV2HG756GYSH6Q3BYK3MBQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X6XRV2HG756GYSH6Q3BYK3MBQR","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":"70f2568ed02b45d7670cc66c06de5f56aad17df9735fc602b78d346a626c650f","cross_cats_sorted":["math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-26T11:50:42Z","title_canon_sha256":"a8690c61dc42e568477db4bc9b84888d362c04aa63fe99953bd6ae24973b8055"},"schema_version":"1.0","source":{"id":"1707.08392","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08392","created_at":"2026-05-18T00:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08392v3","created_at":"2026-05-18T00:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08392","created_at":"2026-05-18T00:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"X6XRV2HG756G","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X6XRV2HG756GYSH6","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X6XRV2HG","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:657bdb6feceed8904f5d857f16ab979542de584d9e40a76dc00196c7746ceed8","target":"graph","created_at":"2026-05-18T00:28:53Z","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":"Eigenfunctions of the fractional Schr\\\"odinger operators in a domain $\\mathcal{D}$ are considered, and a relation between the supremum of the potential and the distance of a maximizer of the eigenfunction from $\\partial\\mathcal{D}$ is established. This, in particular, extends a recent result of Rachh and Steinerberger to the fractional Schr\\\"odinger operators. We also propose a fractional version of the Barta's inequality and also generalize a celebrated Lieb's theorem for fractional Schr\\\"odinger operators. As applications of above results we obtain a Faber-Krahn inequality for non-local Schr","authors_text":"Anup Biswas","cross_cats":["math.PR","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-26T11:50:42Z","title":"Location of maximizers of eigenfunctions of fractional Schr\\\"odinger's equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08392","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:b2f6482523d6983342112b20ff79eef4299cbd561bb1e3d18dab59f3101394be","target":"record","created_at":"2026-05-18T00:28:53Z","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":"70f2568ed02b45d7670cc66c06de5f56aad17df9735fc602b78d346a626c650f","cross_cats_sorted":["math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-26T11:50:42Z","title_canon_sha256":"a8690c61dc42e568477db4bc9b84888d362c04aa63fe99953bd6ae24973b8055"},"schema_version":"1.0","source":{"id":"1707.08392","kind":"arxiv","version":3}},"canonical_sha256":"bfaf1ae8e6ff7c6c48fe86c3856d818453685b1f63ec83b3f73e948171bc4953","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfaf1ae8e6ff7c6c48fe86c3856d818453685b1f63ec83b3f73e948171bc4953","first_computed_at":"2026-05-18T00:28:53.280128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:53.280128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yz+qcZxtc9IGdyDTxNX8bSBc3g2aWUlEsbuweCyB3jaA8WhJxWDwR1zvCF3PdFtRLPJ4eRWxYHzXWOxRRiudAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:53.280693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.08392","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2f6482523d6983342112b20ff79eef4299cbd561bb1e3d18dab59f3101394be","sha256:657bdb6feceed8904f5d857f16ab979542de584d9e40a76dc00196c7746ceed8"],"state_sha256":"2ea456b0bdccab897724bf2d77cc75c609a5334ad0b668bf1b452d665d156242"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+BE71HSaQohmXSdeIytGZ56GRQevf754hqMyU70EGBn6LydvN5To4vidwy2ZWpZ+Wote7YkZCWrz06cEpP/ZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:11:25.556346Z","bundle_sha256":"382c384399572eba56a8633faa0d5440b5ebb88107e07634d78b2b55f79e01c7"}}