{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Y7QY2LGMX54EE7HMG4EXKPVVWF","short_pith_number":"pith:Y7QY2LGM","canonical_record":{"source":{"id":"1405.7741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-29T22:36:19Z","cross_cats_sorted":[],"title_canon_sha256":"922c70f00cd824f19d2e22871bb9c39465f6e11a7164b63f90f5114244c19d52","abstract_canon_sha256":"e5b30208c0d293daf04ffb072d57cdac05f5dc7116f33095860bf523011c9d7b"},"schema_version":"1.0"},"canonical_sha256":"c7e18d2cccbf78427cec3709753eb5b17f4b270adc4377c73b3b5874be22a873","source":{"kind":"arxiv","id":"1405.7741","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7741","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7741v2","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7741","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"Y7QY2LGMX54E","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y7QY2LGMX54EE7HM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y7QY2LGM","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Y7QY2LGMX54EE7HMG4EXKPVVWF","target":"record","payload":{"canonical_record":{"source":{"id":"1405.7741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-29T22:36:19Z","cross_cats_sorted":[],"title_canon_sha256":"922c70f00cd824f19d2e22871bb9c39465f6e11a7164b63f90f5114244c19d52","abstract_canon_sha256":"e5b30208c0d293daf04ffb072d57cdac05f5dc7116f33095860bf523011c9d7b"},"schema_version":"1.0"},"canonical_sha256":"c7e18d2cccbf78427cec3709753eb5b17f4b270adc4377c73b3b5874be22a873","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:45.875611Z","signature_b64":"Vd9jHdNThHkX4qkCmQpKotjySL3UUYX6B5TuhSk0CdP5uwv0+0SR/h/E2EkXHWYaB0XPmEM1OOWQKcVeRa99DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7e18d2cccbf78427cec3709753eb5b17f4b270adc4377c73b3b5874be22a873","last_reissued_at":"2026-05-18T02:48:45.874936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:45.874936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.7741","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":"2026-05-18T02:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uch85WP5RFnoivUm57xGEjB41eN2tZNX3NtriQGwo89Nz3PBq1JsFl+bsGxTVwnCaK1RSmV0wxX9Y1AcP2fHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T10:17:53.520590Z"},"content_sha256":"a04b493ef7bb574bf12610c0a62d9711197ab946152bb717d41ee0008d91262d","schema_version":"1.0","event_id":"sha256:a04b493ef7bb574bf12610c0a62d9711197ab946152bb717d41ee0008d91262d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Y7QY2LGMX54EE7HMG4EXKPVVWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Properties of Pseudocontractive Updates in Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Patrick W. Gallagher, Zhuowen Tu","submitted_at":"2014-05-29T22:36:19Z","abstract_excerpt":"Many convex optimization methods are conceived of and analyzed in a largely separate fashion. In contrast to this traditional separation, this manuscript points out and demonstrates the utility of an important but largely unremarked common thread running through many prominent optimization methods. In particular, we show that methods such as successive orthogonal projection, gradient descent, projected gradient descent, the proximal-point method, forward-backward splitting, the alternating direction method of multipliers, and under- or over-relaxed variants of the preceding all involve updates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7741","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":"2026-05-18T02:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UuY4y2te9nlLWtNF7b1Vo1pf4mx7GuiRLf7G51CuR+smQy7obYnW0Y3vhbBJ7zRFiGxHywyr9PPvOy+r9dW5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T10:17:53.521388Z"},"content_sha256":"a58ca8fd909c86d39519d423760e650c2946b117efe3e07ec8efa4c42de93ef9","schema_version":"1.0","event_id":"sha256:a58ca8fd909c86d39519d423760e650c2946b117efe3e07ec8efa4c42de93ef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y7QY2LGMX54EE7HMG4EXKPVVWF/bundle.json","state_url":"https://pith.science/pith/Y7QY2LGMX54EE7HMG4EXKPVVWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y7QY2LGMX54EE7HMG4EXKPVVWF/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":"2026-08-15T10:17:53Z","links":{"resolver":"https://pith.science/pith/Y7QY2LGMX54EE7HMG4EXKPVVWF","bundle":"https://pith.science/pith/Y7QY2LGMX54EE7HMG4EXKPVVWF/bundle.json","state":"https://pith.science/pith/Y7QY2LGMX54EE7HMG4EXKPVVWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y7QY2LGMX54EE7HMG4EXKPVVWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Y7QY2LGMX54EE7HMG4EXKPVVWF","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":"e5b30208c0d293daf04ffb072d57cdac05f5dc7116f33095860bf523011c9d7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-29T22:36:19Z","title_canon_sha256":"922c70f00cd824f19d2e22871bb9c39465f6e11a7164b63f90f5114244c19d52"},"schema_version":"1.0","source":{"id":"1405.7741","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7741","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7741v2","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7741","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"Y7QY2LGMX54E","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y7QY2LGMX54EE7HM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y7QY2LGM","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:a58ca8fd909c86d39519d423760e650c2946b117efe3e07ec8efa4c42de93ef9","target":"graph","created_at":"2026-05-18T02:48:45Z","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":"Many convex optimization methods are conceived of and analyzed in a largely separate fashion. In contrast to this traditional separation, this manuscript points out and demonstrates the utility of an important but largely unremarked common thread running through many prominent optimization methods. In particular, we show that methods such as successive orthogonal projection, gradient descent, projected gradient descent, the proximal-point method, forward-backward splitting, the alternating direction method of multipliers, and under- or over-relaxed variants of the preceding all involve updates","authors_text":"Patrick W. Gallagher, Zhuowen Tu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-29T22:36:19Z","title":"Properties of Pseudocontractive Updates in Convex Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7741","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:a04b493ef7bb574bf12610c0a62d9711197ab946152bb717d41ee0008d91262d","target":"record","created_at":"2026-05-18T02:48:45Z","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":"e5b30208c0d293daf04ffb072d57cdac05f5dc7116f33095860bf523011c9d7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-29T22:36:19Z","title_canon_sha256":"922c70f00cd824f19d2e22871bb9c39465f6e11a7164b63f90f5114244c19d52"},"schema_version":"1.0","source":{"id":"1405.7741","kind":"arxiv","version":2}},"canonical_sha256":"c7e18d2cccbf78427cec3709753eb5b17f4b270adc4377c73b3b5874be22a873","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7e18d2cccbf78427cec3709753eb5b17f4b270adc4377c73b3b5874be22a873","first_computed_at":"2026-05-18T02:48:45.874936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:45.874936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vd9jHdNThHkX4qkCmQpKotjySL3UUYX6B5TuhSk0CdP5uwv0+0SR/h/E2EkXHWYaB0XPmEM1OOWQKcVeRa99DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:45.875611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7741","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a04b493ef7bb574bf12610c0a62d9711197ab946152bb717d41ee0008d91262d","sha256:a58ca8fd909c86d39519d423760e650c2946b117efe3e07ec8efa4c42de93ef9"],"state_sha256":"03c8752e43a10c25ca10221d9f6a1e077180eca37ab0a040189e908c017b4087"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WobPgeKBe9Hi1z80+HowXMMhKZ6HU2zpZxCYKPxHsdzEstsCWCIiYrJPhmfwOucCPQ/uLLt+Cx01Ff65ZwQTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T10:17:53.528280Z","bundle_sha256":"ab8b658b1d5933962ad61f7603d294627ee8f028498dc3397e7e163b7d759fc8"}}