{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3RJPDEZMVETV5V77IKK2ES23N2","short_pith_number":"pith:3RJPDEZM","canonical_record":{"source":{"id":"1003.4942","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-25T16:06:44Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"8741ca1dd69c0d7c6ac34d9649cde536a482c4a3cbcb9d63726da0da55d9d799","abstract_canon_sha256":"2a4e78b86b3e2bef2258d0e1ba5f24e2e1bf9b844191f7ffc8c77ffffcbc26c3"},"schema_version":"1.0"},"canonical_sha256":"dc52f1932ca9275ed7ff4295a24b5b6ea9aaa3e1e647de2b48550c3b6abc0930","source":{"kind":"arxiv","id":"1003.4942","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4942","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4942v2","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4942","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"3RJPDEZMVETV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3RJPDEZMVETV5V77","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3RJPDEZM","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3RJPDEZMVETV5V77IKK2ES23N2","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4942","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-25T16:06:44Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"8741ca1dd69c0d7c6ac34d9649cde536a482c4a3cbcb9d63726da0da55d9d799","abstract_canon_sha256":"2a4e78b86b3e2bef2258d0e1ba5f24e2e1bf9b844191f7ffc8c77ffffcbc26c3"},"schema_version":"1.0"},"canonical_sha256":"dc52f1932ca9275ed7ff4295a24b5b6ea9aaa3e1e647de2b48550c3b6abc0930","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:26.693639Z","signature_b64":"oB9uAiTOYG6zHmCYOPyl6U72bk/K2mQf8OIyYOiL58+werzUfHpfJa5xb4fJhPRylhFZR+n98Z1vBS7DkzAiDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc52f1932ca9275ed7ff4295a24b5b6ea9aaa3e1e647de2b48550c3b6abc0930","last_reissued_at":"2026-05-18T02:24:26.692886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:26.692886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4942","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":"2026-05-18T02:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/K9a3i9EJ1ZcdpTBdVr7WHd0BGTCBnfj6tSvNEsEifRDXcPeAyhHHll7U3rgOQO4mDqaNPPS0Gnqct2osqYhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:47:07.551231Z"},"content_sha256":"c26062986c389dcec61d7b864f0c2a270f01df553146cdac6d5ababa1c2e92fc","schema_version":"1.0","event_id":"sha256:c26062986c389dcec61d7b864f0c2a270f01df553146cdac6d5ababa1c2e92fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3RJPDEZMVETV5V77IKK2ES23N2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Dynamic Programming using Halfspace Queries and Multiscale Monge decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Charalampos E. Tsourakakis, Gary L. Miller, Richard Peng, Russell Schwartz","submitted_at":"2010-03-25T16:06:44Z","abstract_excerpt":"Let $P=(P_1, P_2, \\ldots, P_n)$, $P_i \\in \\field{R}$ for all $i$, be a signal and let $C$ be a constant. In this work our goal is to find a function $F:[n]\\rightarrow \\field{R}$ which optimizes the following objective function:\n  $$ \\min_{F} \\sum_{i=1}^n (P_i-F_i)^2 + C\\times |\\{i:F_i \\neq F_{i+1} \\} | $$\n  The above optimization problem reduces to solving the following recurrence, which can be done efficiently using dynamic programming in $O(n^2)$ time:\n  $$ OPT_i = \\min_{0 \\leq j \\leq i-1} [ OPT_j + \\sum_{k=j+1}^i (P_k - (\\sum_{m=j+1}^i P_m)/(i-j) )^2 ]+ C $$\n  The above recurrence arises na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4942","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":"2026-05-18T02:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2U9JSYdOnWDUvirnxhsKOjn8C6ioLQ+4MhSx/omJJ6MXgHO/OJGzm1d9IQ97OnJBmkdYCuxbcIus4ikb67iAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:47:07.551996Z"},"content_sha256":"65994e34af17fbceb548730cfc6ff6f2645ba8bd2ec250ee22901defc6c70ad0","schema_version":"1.0","event_id":"sha256:65994e34af17fbceb548730cfc6ff6f2645ba8bd2ec250ee22901defc6c70ad0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RJPDEZMVETV5V77IKK2ES23N2/bundle.json","state_url":"https://pith.science/pith/3RJPDEZMVETV5V77IKK2ES23N2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RJPDEZMVETV5V77IKK2ES23N2/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":"2026-06-04T20:47:07Z","links":{"resolver":"https://pith.science/pith/3RJPDEZMVETV5V77IKK2ES23N2","bundle":"https://pith.science/pith/3RJPDEZMVETV5V77IKK2ES23N2/bundle.json","state":"https://pith.science/pith/3RJPDEZMVETV5V77IKK2ES23N2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RJPDEZMVETV5V77IKK2ES23N2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3RJPDEZMVETV5V77IKK2ES23N2","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":"2a4e78b86b3e2bef2258d0e1ba5f24e2e1bf9b844191f7ffc8c77ffffcbc26c3","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-25T16:06:44Z","title_canon_sha256":"8741ca1dd69c0d7c6ac34d9649cde536a482c4a3cbcb9d63726da0da55d9d799"},"schema_version":"1.0","source":{"id":"1003.4942","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4942","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4942v2","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4942","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"3RJPDEZMVETV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3RJPDEZMVETV5V77","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3RJPDEZM","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:65994e34af17fbceb548730cfc6ff6f2645ba8bd2ec250ee22901defc6c70ad0","target":"graph","created_at":"2026-05-18T02:24:26Z","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 $P=(P_1, P_2, \\ldots, P_n)$, $P_i \\in \\field{R}$ for all $i$, be a signal and let $C$ be a constant. In this work our goal is to find a function $F:[n]\\rightarrow \\field{R}$ which optimizes the following objective function:\n  $$ \\min_{F} \\sum_{i=1}^n (P_i-F_i)^2 + C\\times |\\{i:F_i \\neq F_{i+1} \\} | $$\n  The above optimization problem reduces to solving the following recurrence, which can be done efficiently using dynamic programming in $O(n^2)$ time:\n  $$ OPT_i = \\min_{0 \\leq j \\leq i-1} [ OPT_j + \\sum_{k=j+1}^i (P_k - (\\sum_{m=j+1}^i P_m)/(i-j) )^2 ]+ C $$\n  The above recurrence arises na","authors_text":"Charalampos E. Tsourakakis, Gary L. Miller, Richard Peng, Russell Schwartz","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-25T16:06:44Z","title":"Approximate Dynamic Programming using Halfspace Queries and Multiscale Monge decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4942","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:c26062986c389dcec61d7b864f0c2a270f01df553146cdac6d5ababa1c2e92fc","target":"record","created_at":"2026-05-18T02:24:26Z","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":"2a4e78b86b3e2bef2258d0e1ba5f24e2e1bf9b844191f7ffc8c77ffffcbc26c3","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-25T16:06:44Z","title_canon_sha256":"8741ca1dd69c0d7c6ac34d9649cde536a482c4a3cbcb9d63726da0da55d9d799"},"schema_version":"1.0","source":{"id":"1003.4942","kind":"arxiv","version":2}},"canonical_sha256":"dc52f1932ca9275ed7ff4295a24b5b6ea9aaa3e1e647de2b48550c3b6abc0930","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc52f1932ca9275ed7ff4295a24b5b6ea9aaa3e1e647de2b48550c3b6abc0930","first_computed_at":"2026-05-18T02:24:26.692886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:26.692886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oB9uAiTOYG6zHmCYOPyl6U72bk/K2mQf8OIyYOiL58+werzUfHpfJa5xb4fJhPRylhFZR+n98Z1vBS7DkzAiDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:26.693639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4942","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c26062986c389dcec61d7b864f0c2a270f01df553146cdac6d5ababa1c2e92fc","sha256:65994e34af17fbceb548730cfc6ff6f2645ba8bd2ec250ee22901defc6c70ad0"],"state_sha256":"a007d4dc27333d39fdd502c7f2d0b9575307b1b3773de18e064f1cbad2e0f12a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKJv7cFf1H/SRRIXEtOR3p7ZgQDL+YYoZH3DQlf/J9KWivyF9dfX6swWiRnWJWTNC7WMmI+cD//SZrgx2c8NBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:47:07.555969Z","bundle_sha256":"d33f20d2ad7e6c3f925fa672b5ca697919919d5951de2e691b3fc426b8eed1c4"}}