{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MFZKXREYA735KBS3PZIB2Q7XMK","short_pith_number":"pith:MFZKXREY","canonical_record":{"source":{"id":"1709.05611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-17T06:17:04Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1b133fb3a3116a060d2c9c80f504880c27dcbfbe1f3396148a6aae0dc74b6584","abstract_canon_sha256":"23ad7667d2e9a6a7ed74eda48762d3febd5835f7e97c41486fa957539fbc5557"},"schema_version":"1.0"},"canonical_sha256":"6172abc49807f7d5065b7e501d43f76299cbcb797bb638d19b1b6710422a9d6d","source":{"kind":"arxiv","id":"1709.05611","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05611","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05611v2","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05611","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"MFZKXREYA735","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MFZKXREYA735KBS3","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MFZKXREY","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MFZKXREYA735KBS3PZIB2Q7XMK","target":"record","payload":{"canonical_record":{"source":{"id":"1709.05611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-17T06:17:04Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1b133fb3a3116a060d2c9c80f504880c27dcbfbe1f3396148a6aae0dc74b6584","abstract_canon_sha256":"23ad7667d2e9a6a7ed74eda48762d3febd5835f7e97c41486fa957539fbc5557"},"schema_version":"1.0"},"canonical_sha256":"6172abc49807f7d5065b7e501d43f76299cbcb797bb638d19b1b6710422a9d6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:23.783683Z","signature_b64":"iPTucEkplAMT0YKqWB0uvZp0e49rq8fcyVqBQL2NNzBVTJvvdNdHFY89tNHKafhjsCpVGoZ383c/nWXiDENiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6172abc49807f7d5065b7e501d43f76299cbcb797bb638d19b1b6710422a9d6d","last_reissued_at":"2026-05-18T00:07:23.783193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:23.783193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.05611","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":"2026-05-18T00:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xdkxzXMTgsNAFLSpzEGYyf+GZeRtxAZFG637bOL1ZuuQHGg3UWxhpOi8KSAliL9BONLJb4BGUkjZS4lF/7/pAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:09:33.438572Z"},"content_sha256":"0bb18f900bd64142868c9a44c1dd0f7c143c9b8647dcd6c72e58bf54ce0f2c06","schema_version":"1.0","event_id":"sha256:0bb18f900bd64142868c9a44c1dd0f7c143c9b8647dcd6c72e58bf54ce0f2c06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MFZKXREYA735KBS3PZIB2Q7XMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp bound on the largest positive eigenvalue for one-dimensional Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Wencai Liu","submitted_at":"2017-09-17T06:17:04Z","abstract_excerpt":"Let $H=-D^2+V$ be a Schr\\\"odinger operator on $ L^2(\\mathbb{R})$, or on $ L^2(0,\\infty)$. Suppose the potential satisfies $\\limsup_{x\\to \\infty}|xV(x)|=a<\\infty$. We prove that $H$ admits no eigenvalue larger than $ \\frac{4a^2}{\\pi^2}$. For any positive $a$ and $\\lambda$ with $0<\\lambda< \\frac{4a^2}{\\pi^2}$, we construct potentials $V$ such that $\\limsup_{x\\to \\infty}|xV(x)|=a $ and the associated Sch\\\"rodinger operator $H=-D^2+V$ has eigenvalue $\\lambda$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05611","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":"2026-05-18T00:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cCAS3epaeqBXILEg30Cvi+WsrrHNINIIEhGzhPArreG2fojDeKvDqESnOD+CRLRtu9ug6pp2qdNJiLPCVt4DAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:09:33.438902Z"},"content_sha256":"3781a0932107be83b6486c401b50cea019a628e78652c819e93bc1d8d406b69d","schema_version":"1.0","event_id":"sha256:3781a0932107be83b6486c401b50cea019a628e78652c819e93bc1d8d406b69d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFZKXREYA735KBS3PZIB2Q7XMK/bundle.json","state_url":"https://pith.science/pith/MFZKXREYA735KBS3PZIB2Q7XMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFZKXREYA735KBS3PZIB2Q7XMK/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":"2026-06-27T00:09:33Z","links":{"resolver":"https://pith.science/pith/MFZKXREYA735KBS3PZIB2Q7XMK","bundle":"https://pith.science/pith/MFZKXREYA735KBS3PZIB2Q7XMK/bundle.json","state":"https://pith.science/pith/MFZKXREYA735KBS3PZIB2Q7XMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFZKXREYA735KBS3PZIB2Q7XMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MFZKXREYA735KBS3PZIB2Q7XMK","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":"23ad7667d2e9a6a7ed74eda48762d3febd5835f7e97c41486fa957539fbc5557","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-17T06:17:04Z","title_canon_sha256":"1b133fb3a3116a060d2c9c80f504880c27dcbfbe1f3396148a6aae0dc74b6584"},"schema_version":"1.0","source":{"id":"1709.05611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05611","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05611v2","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05611","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"MFZKXREYA735","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MFZKXREYA735KBS3","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MFZKXREY","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:3781a0932107be83b6486c401b50cea019a628e78652c819e93bc1d8d406b69d","target":"graph","created_at":"2026-05-18T00:07:23Z","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 $H=-D^2+V$ be a Schr\\\"odinger operator on $ L^2(\\mathbb{R})$, or on $ L^2(0,\\infty)$. Suppose the potential satisfies $\\limsup_{x\\to \\infty}|xV(x)|=a<\\infty$. We prove that $H$ admits no eigenvalue larger than $ \\frac{4a^2}{\\pi^2}$. For any positive $a$ and $\\lambda$ with $0<\\lambda< \\frac{4a^2}{\\pi^2}$, we construct potentials $V$ such that $\\limsup_{x\\to \\infty}|xV(x)|=a $ and the associated Sch\\\"rodinger operator $H=-D^2+V$ has eigenvalue $\\lambda$.","authors_text":"Wencai Liu","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-17T06:17:04Z","title":"Sharp bound on the largest positive eigenvalue for one-dimensional Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05611","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":"sha256:0bb18f900bd64142868c9a44c1dd0f7c143c9b8647dcd6c72e58bf54ce0f2c06","target":"record","created_at":"2026-05-18T00:07:23Z","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":"23ad7667d2e9a6a7ed74eda48762d3febd5835f7e97c41486fa957539fbc5557","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-17T06:17:04Z","title_canon_sha256":"1b133fb3a3116a060d2c9c80f504880c27dcbfbe1f3396148a6aae0dc74b6584"},"schema_version":"1.0","source":{"id":"1709.05611","kind":"arxiv","version":2}},"canonical_sha256":"6172abc49807f7d5065b7e501d43f76299cbcb797bb638d19b1b6710422a9d6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6172abc49807f7d5065b7e501d43f76299cbcb797bb638d19b1b6710422a9d6d","first_computed_at":"2026-05-18T00:07:23.783193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:23.783193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iPTucEkplAMT0YKqWB0uvZp0e49rq8fcyVqBQL2NNzBVTJvvdNdHFY89tNHKafhjsCpVGoZ383c/nWXiDENiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:23.783683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bb18f900bd64142868c9a44c1dd0f7c143c9b8647dcd6c72e58bf54ce0f2c06","sha256:3781a0932107be83b6486c401b50cea019a628e78652c819e93bc1d8d406b69d"],"state_sha256":"5739b78b426e50bfd4af71a0c967a024e64857a2ab4d3e49bd7f1bcf90ee573f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A70PCAMgkUKyD2hkQxdfb12YHdFKiqXC6i2Vh1Vt1ftMtC6d8iiblciHfr8igxdHUx2F11nsqhQUvotZUUrqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T00:09:33.440915Z","bundle_sha256":"5889bd8ca4d3839992c6d7d45d47d12f8c3277e66ec69ab7a1b8a971c8d59b85"}}