{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MQPDHWMV7WLRHEWZB3F4F46OHH","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":"00441391df7157014e6b8528a399b6a3ef0ff575c75f27c0e3007d710a91145e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-14T16:54:59Z","title_canon_sha256":"8ca434db9474acff0219c26cacd844c946f9bebfdf793ab59967ddd253bddbe4"},"schema_version":"1.0","source":{"id":"1504.03624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03624","created_at":"2026-05-18T02:18:50Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03624v1","created_at":"2026-05-18T02:18:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03624","created_at":"2026-05-18T02:18:50Z"},{"alias_kind":"pith_short_12","alias_value":"MQPDHWMV7WLR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MQPDHWMV7WLRHEWZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MQPDHWMV","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:70cc248b738a72dcce1a988ed767e6762728f59162aebd9176c6c60a6d80d081","target":"graph","created_at":"2026-05-18T02:18:50Z","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 construct new bases of real functions from $L^{2}\\left(B_{r}\\right)$ and from $L^{2}\\left(\\mathbb{Q}_{p}\\right)$. These functions are eigenfunctions of the $p$-adic pseudo-differential Vladimirov operator, which is defined on a compact set $B_{r}\\subset\\mathbb{Q}_{p}$ of the field of $p$-adic numbers $\\mathbb{Q}_{p}$ or, respectively, on the entire field $\\mathbb{Q}_{p}$. A relation between the basis of functions from $L^{2}\\left(\\mathbb{Q}_{p}\\right)$ and the basis of $p$-adic wavelets from $L^{2}\\left(\\mathbb{Q}_{p}\\right)$ is found. As an application, we consider the solution of the Cauc","authors_text":"A.Kh. Bikulov, A.P. Zubarev","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-14T16:54:59Z","title":"On one real basis for $L^2(Q_p)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03624","kind":"arxiv","version":1},"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":"sha256:0fe8e8bde99c0d74edb597150f73b260bdd4b59ffe766e224547c28fdade1cd3","target":"record","created_at":"2026-05-18T02:18:50Z","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":"00441391df7157014e6b8528a399b6a3ef0ff575c75f27c0e3007d710a91145e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-14T16:54:59Z","title_canon_sha256":"8ca434db9474acff0219c26cacd844c946f9bebfdf793ab59967ddd253bddbe4"},"schema_version":"1.0","source":{"id":"1504.03624","kind":"arxiv","version":1}},"canonical_sha256":"641e33d995fd971392d90ecbc2f3ce39eba250f3daaf7abd7851212e7721650b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"641e33d995fd971392d90ecbc2f3ce39eba250f3daaf7abd7851212e7721650b","first_computed_at":"2026-05-18T02:18:50.360192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:50.360192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nPBpaXn+Fs9/gW5a7vFwAlyB6dLKHWbOiLRHX7AvE0EI+yviL/6NwGAcw3YSgbsI6aLCmFRyp0GXEbUtQ9kvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:50.360770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fe8e8bde99c0d74edb597150f73b260bdd4b59ffe766e224547c28fdade1cd3","sha256:70cc248b738a72dcce1a988ed767e6762728f59162aebd9176c6c60a6d80d081"],"state_sha256":"63a43f28c80ed63e24fbac61f8fd889c7d89c222e7f4394a0feee53a002c055f"}