{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KSD76PRG7UMPJPHSVJHPMMV754","short_pith_number":"pith:KSD76PRG","canonical_record":{"source":{"id":"1603.05719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T22:53:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9a00657db3911e6717ac9e33dd7eef5a5dc5275513d7371e2eb53b14532c4a4e","abstract_canon_sha256":"3dc1b212c207614fafdc3df4d8945c4fbd5bfa00697cbe5b9aede07a10b4a508"},"schema_version":"1.0"},"canonical_sha256":"5487ff3e26fd18f4bcf2aa4ef632bfef384eec9e5395026fdec80647976289ae","source":{"kind":"arxiv","id":"1603.05719","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05719","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05719v2","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05719","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"KSD76PRG7UMP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KSD76PRG7UMPJPHS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KSD76PRG","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KSD76PRG7UMPJPHSVJHPMMV754","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T22:53:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9a00657db3911e6717ac9e33dd7eef5a5dc5275513d7371e2eb53b14532c4a4e","abstract_canon_sha256":"3dc1b212c207614fafdc3df4d8945c4fbd5bfa00697cbe5b9aede07a10b4a508"},"schema_version":"1.0"},"canonical_sha256":"5487ff3e26fd18f4bcf2aa4ef632bfef384eec9e5395026fdec80647976289ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:33.358893Z","signature_b64":"fHLDIn3hpGkg8qzZV2KQzPuvv6E19RVUKvd6G/P8EgeOo2bnyMAic65C2jLkLRTo+eZ/0Pr4mvm521RfAn2cAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5487ff3e26fd18f4bcf2aa4ef632bfef384eec9e5395026fdec80647976289ae","last_reissued_at":"2026-05-18T00:07:33.358311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:33.358311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05719","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":"2026-05-18T00:07:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zqEShxcTxv/U9oJY162EzWTRrNAclS0I++IGGrnqmmzPPbFyPl8KefmobjPaxkz09iMCGXZUG3XZrbIF+m3ZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:53:41.478043Z"},"content_sha256":"8ec29f47b3fe0d2ea5735975f7bdbc49d2836ab3f2e95e3d9a4971439c26fd86","schema_version":"1.0","event_id":"sha256:8ec29f47b3fe0d2ea5735975f7bdbc49d2836ab3f2e95e3d9a4971439c26fd86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KSD76PRG7UMPJPHSVJHPMMV754","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient evaluation of scaled proximal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.OC","authors_text":"Gabriel Goh, Michael P. Friedlander","submitted_at":"2016-03-17T22:53:22Z","abstract_excerpt":"Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex optimization. We show how an interior method can be used to efficiently compute the proximal operator of a quadratic-support function under different metrics. When the metric and the function have the right structure, the proximal map can be computed with cost nearly linear in the input size. We describe how to use this approach to implement quasi-Newton methods for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05719","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":"2026-05-18T00:07:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FR0IseRXPaHv8HGWA52KYTBSp+LeR6gQhOiqqoM9NGFFDKvUtPlKP19AHoSOTvO5uotcHQ2del8OKzVodqq9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:53:41.478712Z"},"content_sha256":"cd48a2d36ca5da10de7ae3a35de1f5c26cd73765a97e3179bcb577630b65a713","schema_version":"1.0","event_id":"sha256:cd48a2d36ca5da10de7ae3a35de1f5c26cd73765a97e3179bcb577630b65a713"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSD76PRG7UMPJPHSVJHPMMV754/bundle.json","state_url":"https://pith.science/pith/KSD76PRG7UMPJPHSVJHPMMV754/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSD76PRG7UMPJPHSVJHPMMV754/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":"2026-06-07T05:53:41Z","links":{"resolver":"https://pith.science/pith/KSD76PRG7UMPJPHSVJHPMMV754","bundle":"https://pith.science/pith/KSD76PRG7UMPJPHSVJHPMMV754/bundle.json","state":"https://pith.science/pith/KSD76PRG7UMPJPHSVJHPMMV754/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSD76PRG7UMPJPHSVJHPMMV754/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KSD76PRG7UMPJPHSVJHPMMV754","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":"3dc1b212c207614fafdc3df4d8945c4fbd5bfa00697cbe5b9aede07a10b4a508","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T22:53:22Z","title_canon_sha256":"9a00657db3911e6717ac9e33dd7eef5a5dc5275513d7371e2eb53b14532c4a4e"},"schema_version":"1.0","source":{"id":"1603.05719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05719","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05719v2","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05719","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"KSD76PRG7UMP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KSD76PRG7UMPJPHS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KSD76PRG","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:cd48a2d36ca5da10de7ae3a35de1f5c26cd73765a97e3179bcb577630b65a713","target":"graph","created_at":"2026-05-18T00:07:33Z","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":"Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex optimization. We show how an interior method can be used to efficiently compute the proximal operator of a quadratic-support function under different metrics. When the metric and the function have the right structure, the proximal map can be computed with cost nearly linear in the input size. We describe how to use this approach to implement quasi-Newton methods for ","authors_text":"Gabriel Goh, Michael P. Friedlander","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T22:53:22Z","title":"Efficient evaluation of scaled proximal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05719","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":"sha256:8ec29f47b3fe0d2ea5735975f7bdbc49d2836ab3f2e95e3d9a4971439c26fd86","target":"record","created_at":"2026-05-18T00:07:33Z","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":"3dc1b212c207614fafdc3df4d8945c4fbd5bfa00697cbe5b9aede07a10b4a508","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T22:53:22Z","title_canon_sha256":"9a00657db3911e6717ac9e33dd7eef5a5dc5275513d7371e2eb53b14532c4a4e"},"schema_version":"1.0","source":{"id":"1603.05719","kind":"arxiv","version":2}},"canonical_sha256":"5487ff3e26fd18f4bcf2aa4ef632bfef384eec9e5395026fdec80647976289ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5487ff3e26fd18f4bcf2aa4ef632bfef384eec9e5395026fdec80647976289ae","first_computed_at":"2026-05-18T00:07:33.358311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:33.358311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fHLDIn3hpGkg8qzZV2KQzPuvv6E19RVUKvd6G/P8EgeOo2bnyMAic65C2jLkLRTo+eZ/0Pr4mvm521RfAn2cAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:33.358893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ec29f47b3fe0d2ea5735975f7bdbc49d2836ab3f2e95e3d9a4971439c26fd86","sha256:cd48a2d36ca5da10de7ae3a35de1f5c26cd73765a97e3179bcb577630b65a713"],"state_sha256":"fc8bc4a466c775f0acb434929d9ba62cea9dbd8a15f5d059548e9d01e542cc39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6v5LzjMm5HTFFXZ8ZdpJIF0LctBSmqvsPHTQ9db86W2nuVsNbT+XSGHLKpJmuDuZf/R7FwP3USOLB0xUfOHgBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:53:41.482203Z","bundle_sha256":"3932398a1f659a411f61e9d65d6876493a9e6ee3476da3dbcf46123559ec1a15"}}