{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7V2CMXDDQTKGVS5BM2ALZXWL3W","short_pith_number":"pith:7V2CMXDD","canonical_record":{"source":{"id":"1412.7992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-12-26T21:19:11Z","cross_cats_sorted":[],"title_canon_sha256":"f05775418b416401b8b76d125b5e10b97ef34007ec63e7b6ef738c1d2a3611b4","abstract_canon_sha256":"5d5a02739d507abdcdd9b34a1f23dcf3bb9aac48a08db033b20ab3b009d3147c"},"schema_version":"1.0"},"canonical_sha256":"fd74265c6384d46acba16680bcdecbddb9d070d990051866ce190af048e24b39","source":{"kind":"arxiv","id":"1412.7992","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7992","created_at":"2026-05-18T02:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7992v2","created_at":"2026-05-18T02:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7992","created_at":"2026-05-18T02:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"7V2CMXDDQTKG","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7V2CMXDDQTKGVS5B","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7V2CMXDD","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7V2CMXDDQTKGVS5BM2ALZXWL3W","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-12-26T21:19:11Z","cross_cats_sorted":[],"title_canon_sha256":"f05775418b416401b8b76d125b5e10b97ef34007ec63e7b6ef738c1d2a3611b4","abstract_canon_sha256":"5d5a02739d507abdcdd9b34a1f23dcf3bb9aac48a08db033b20ab3b009d3147c"},"schema_version":"1.0"},"canonical_sha256":"fd74265c6384d46acba16680bcdecbddb9d070d990051866ce190af048e24b39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:58.895122Z","signature_b64":"zQZyB6oLlejljlkYk/HN32WfM053bapjNvfxV6qTYPOkLyNKXfwspue4JEaxmZGBkRUkCYX9f6KSJocExcxGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd74265c6384d46acba16680bcdecbddb9d070d990051866ce190af048e24b39","last_reissued_at":"2026-05-18T02:20:58.894600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:58.894600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7992","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":"2026-05-18T02:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bq0+YLtSWqByZdJ8WCAwZXHe2GK3daZb98sa8IkRwkuW8IeZJkfFtOJo/raheMwNHoIEmMzSJ9Qr1EaZ0laQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:48:05.149826Z"},"content_sha256":"2e564fa8d8a2678e86b4f966da91dc671758c0fa79b71706c87b074cdc701388","schema_version":"1.0","event_id":"sha256:2e564fa8d8a2678e86b4f966da91dc671758c0fa79b71706c87b074cdc701388"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7V2CMXDDQTKGVS5BM2ALZXWL3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On majorants of eigenvalues of Sturm-Liouville problems with potentials from balls of weighted spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A.A. Vladimirov","submitted_at":"2014-12-26T21:19:11Z","abstract_excerpt":"It is constructively proved that for class $A_{r,\\gamma}=\\{q\\in L_{1,loc}(0,1): q\\leq 0, \\int_0^1 rq^\\gamma\\,dx\\leqslant 1\\}$, where $r\\in C[0,1]$ is uniformly positive weight and $\\gamma>1$, there exists a unique potential $\\hat q\\in A_{r,\\gamma}$ such that minimal eigenvalue $\\lambda_0(\\hat q)$ of boundary problem $$-y\"+\\hat qy=\\lambda y, y(0)=y(1)=0 $$ is equal to $M_{r,\\gamma}=\\sup_{q\\in A_{r,\\gamma}}\\lambda_0(q)$. For case $\\gamma=1$ we obtain that there exists a unique potential $\\hat q\\in\\Gamma_{r,\\gamma}$ with analogous property. Here $\\Gamma_{r,\\gamma}$ is a closure of $A_{r,\\gamma}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7992","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":"2026-05-18T02:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hDFRq5HOs05Qkd8phEoIUZA2czivvpfY1bc8GratSthHWiATDCyXi0Pe1LD/yp3JlF8LRXMeq/xwLHN9V2dhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:48:05.150169Z"},"content_sha256":"78421d68f2549145e3e408c62f843aa2746d84016d2b84f82ee671db52864027","schema_version":"1.0","event_id":"sha256:78421d68f2549145e3e408c62f843aa2746d84016d2b84f82ee671db52864027"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7V2CMXDDQTKGVS5BM2ALZXWL3W/bundle.json","state_url":"https://pith.science/pith/7V2CMXDDQTKGVS5BM2ALZXWL3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7V2CMXDDQTKGVS5BM2ALZXWL3W/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":"2026-06-05T12:48:05Z","links":{"resolver":"https://pith.science/pith/7V2CMXDDQTKGVS5BM2ALZXWL3W","bundle":"https://pith.science/pith/7V2CMXDDQTKGVS5BM2ALZXWL3W/bundle.json","state":"https://pith.science/pith/7V2CMXDDQTKGVS5BM2ALZXWL3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7V2CMXDDQTKGVS5BM2ALZXWL3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7V2CMXDDQTKGVS5BM2ALZXWL3W","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":"5d5a02739d507abdcdd9b34a1f23dcf3bb9aac48a08db033b20ab3b009d3147c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-12-26T21:19:11Z","title_canon_sha256":"f05775418b416401b8b76d125b5e10b97ef34007ec63e7b6ef738c1d2a3611b4"},"schema_version":"1.0","source":{"id":"1412.7992","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7992","created_at":"2026-05-18T02:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7992v2","created_at":"2026-05-18T02:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7992","created_at":"2026-05-18T02:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"7V2CMXDDQTKG","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7V2CMXDDQTKGVS5B","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7V2CMXDD","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:78421d68f2549145e3e408c62f843aa2746d84016d2b84f82ee671db52864027","target":"graph","created_at":"2026-05-18T02:20:58Z","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":"It is constructively proved that for class $A_{r,\\gamma}=\\{q\\in L_{1,loc}(0,1): q\\leq 0, \\int_0^1 rq^\\gamma\\,dx\\leqslant 1\\}$, where $r\\in C[0,1]$ is uniformly positive weight and $\\gamma>1$, there exists a unique potential $\\hat q\\in A_{r,\\gamma}$ such that minimal eigenvalue $\\lambda_0(\\hat q)$ of boundary problem $$-y\"+\\hat qy=\\lambda y, y(0)=y(1)=0 $$ is equal to $M_{r,\\gamma}=\\sup_{q\\in A_{r,\\gamma}}\\lambda_0(q)$. For case $\\gamma=1$ we obtain that there exists a unique potential $\\hat q\\in\\Gamma_{r,\\gamma}$ with analogous property. Here $\\Gamma_{r,\\gamma}$ is a closure of $A_{r,\\gamma}$ ","authors_text":"A.A. Vladimirov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-12-26T21:19:11Z","title":"On majorants of eigenvalues of Sturm-Liouville problems with potentials from balls of weighted spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7992","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":"sha256:2e564fa8d8a2678e86b4f966da91dc671758c0fa79b71706c87b074cdc701388","target":"record","created_at":"2026-05-18T02:20:58Z","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":"5d5a02739d507abdcdd9b34a1f23dcf3bb9aac48a08db033b20ab3b009d3147c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-12-26T21:19:11Z","title_canon_sha256":"f05775418b416401b8b76d125b5e10b97ef34007ec63e7b6ef738c1d2a3611b4"},"schema_version":"1.0","source":{"id":"1412.7992","kind":"arxiv","version":2}},"canonical_sha256":"fd74265c6384d46acba16680bcdecbddb9d070d990051866ce190af048e24b39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd74265c6384d46acba16680bcdecbddb9d070d990051866ce190af048e24b39","first_computed_at":"2026-05-18T02:20:58.894600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:58.894600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zQZyB6oLlejljlkYk/HN32WfM053bapjNvfxV6qTYPOkLyNKXfwspue4JEaxmZGBkRUkCYX9f6KSJocExcxGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:58.895122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7992","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e564fa8d8a2678e86b4f966da91dc671758c0fa79b71706c87b074cdc701388","sha256:78421d68f2549145e3e408c62f843aa2746d84016d2b84f82ee671db52864027"],"state_sha256":"5aecc2a0158b863986d2d39eccba9b846f9987f2f5acfcb37ad90ae60d51dc2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ruOO8FFaMYcAmpFjhedgx0xSs15mhCxEyZ+5coQv2vwI3O+Uy3zg8pnY4PDIVJJHPuPxfdNJzgt7mGNqs1u/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:48:05.152119Z","bundle_sha256":"0a67e137507fa63dc8302bccf9ede9ca9f4cc22bdd38376ea48e0a0ae362ce17"}}