{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VSICHMZH6WJP7DDM4277K2F5XR","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":"2ab3c86d2dbeebe0d44ebcbcc26fe0ac1079baf47edbf8ebc8a1205e59e6ffa2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-24T00:44:01Z","title_canon_sha256":"47e65055583aa6f1caf7537595135e2ddcc5f310ecfd14e41e5410a05e9d4ae8"},"schema_version":"1.0","source":{"id":"1308.5268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5268","created_at":"2026-05-18T03:15:07Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5268v1","created_at":"2026-05-18T03:15:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5268","created_at":"2026-05-18T03:15:07Z"},{"alias_kind":"pith_short_12","alias_value":"VSICHMZH6WJP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VSICHMZH6WJP7DDM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VSICHMZH","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:5de5e64edd0f7a2b041773558f1854c3669beb453bf5dda54bdbe27660be336d","target":"graph","created_at":"2026-05-18T03:15:07Z","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":"In this paper we give necessary and sufficient conditions for the system of positive numbers $ M_{k_1}, M_{k_2},..., M_{k_{d}},$ $0\\leq k_1<...<k_{d} {\\leq} r$, to guarantee the existence of an $r$-monotone function defined on the negative half-line $\\RR_-$ and such that $\\|x^{(k_i)}\\|_{\\infty}=M_{k_i}, i=1,2,...,d$.","authors_text":"Oleg Kovalenko, Vladyslav Babenko, Yuliya Babenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-24T00:44:01Z","title":"Kolmogorov's Problem on the Class of Multiply Monotone Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5268","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:c19caf2940f6673251c7ae8c0d76930a554918b386f8e94e16b8b3b7b6f7a045","target":"record","created_at":"2026-05-18T03:15:07Z","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":"2ab3c86d2dbeebe0d44ebcbcc26fe0ac1079baf47edbf8ebc8a1205e59e6ffa2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-24T00:44:01Z","title_canon_sha256":"47e65055583aa6f1caf7537595135e2ddcc5f310ecfd14e41e5410a05e9d4ae8"},"schema_version":"1.0","source":{"id":"1308.5268","kind":"arxiv","version":1}},"canonical_sha256":"ac9023b327f592ff8c6ce6bff568bdbc4759c8b2d3d85be6f07bc17c8564d1c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac9023b327f592ff8c6ce6bff568bdbc4759c8b2d3d85be6f07bc17c8564d1c7","first_computed_at":"2026-05-18T03:15:07.263306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:07.263306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7GDYATfzlck6sFZeLoqqbb9O1+4dHBdrZDxknD68rXbgIcwT6pswrYFLw2jZ8xTiZpOUzZo9X1olFK86mFDYCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:07.263977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c19caf2940f6673251c7ae8c0d76930a554918b386f8e94e16b8b3b7b6f7a045","sha256:5de5e64edd0f7a2b041773558f1854c3669beb453bf5dda54bdbe27660be336d"],"state_sha256":"c75fddd7961af70031143c4ef639ce5b6f2c025ef89f41e7d937ca835a34ebb7"}