{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:24USVVFMBC7MMDFXOBGWBDBMKA","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":"f051627915d73b8c1ccb8dd50eed6b5f5a919f569a2f5c9c433e7172a3259079","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-28T07:14:00Z","title_canon_sha256":"526caf797b35c873cf2a545875b1790984ef3d8d4212c7969aadfaa637f48356"},"schema_version":"1.0","source":{"id":"1506.08369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08369","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08369v1","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08369","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"24USVVFMBC7M","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"24USVVFMBC7MMDFX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"24USVVFM","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:dc86a419a6967f0ac558fc78c6c924ed4c0efb48b865ce2cb08f70a0f22806b0","target":"graph","created_at":"2026-05-17T23:41:37Z","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":"A function $f=f_T$ is called least energy approximation to a function $B$ on the interval $[0,T]$ with penalty $Q$ if it solves the variational problem $$ \\int_0^T \\left[ f'(t)^2 + Q(f(t)-B(t)) \\right] dt \\searrow \\min. $$ For quadratic penalty the least energy approximation can be found explicitly. If $B$ is a random process with stationary increments, then on large intervals $f_T$ also is close to a process of the same class and the relation between the corresponding spectral measures can be found. We show that in a long run (when $T\\to \\infty$) the expectation of energy of optimal approxima","authors_text":"Mikhail Lifshits, Zakhar Kabluchko","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-28T07:14:00Z","title":"Least Energy Approximation for Processes with Stationary Increments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08369","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":"sha256:6f5638162d726da87de7a4b754ae804dfc5ab7d0faf25e0aa936bdf8fb03bba4","target":"record","created_at":"2026-05-17T23:41:37Z","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":"f051627915d73b8c1ccb8dd50eed6b5f5a919f569a2f5c9c433e7172a3259079","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-28T07:14:00Z","title_canon_sha256":"526caf797b35c873cf2a545875b1790984ef3d8d4212c7969aadfaa637f48356"},"schema_version":"1.0","source":{"id":"1506.08369","kind":"arxiv","version":1}},"canonical_sha256":"d7292ad4ac08bec60cb7704d608c2c5008d130e142069cc8efa0b71671efaeaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7292ad4ac08bec60cb7704d608c2c5008d130e142069cc8efa0b71671efaeaa","first_computed_at":"2026-05-17T23:41:37.636186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:37.636186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wt7q4CWBjFla67CHcrPWqT2awRj2kWVm/nGJxk1kBy43lW/Wn96JnWtBYYafMD3foT8ZTfXhSb+vo4SLnjNGDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:37.636911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f5638162d726da87de7a4b754ae804dfc5ab7d0faf25e0aa936bdf8fb03bba4","sha256:dc86a419a6967f0ac558fc78c6c924ed4c0efb48b865ce2cb08f70a0f22806b0"],"state_sha256":"5e3dda50282717cbd21171656f885c3b57f633c5c1f750901473de4e4400d12f"}