{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KEKVRLN2O3B5O6U2R4JIUNKG3M","short_pith_number":"pith:KEKVRLN2","canonical_record":{"source":{"id":"2607.08035","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-09T01:25:30Z","cross_cats_sorted":[],"title_canon_sha256":"ec38eeaf67ffb465a881e531bb3753170e2cb92a2a394aa47cc0a00ebcff6e15","abstract_canon_sha256":"c1e035d501fd824bd99ae1c5bf5284049b9017031d119eea79a23cfb8e82586b"},"schema_version":"1.0"},"canonical_sha256":"511558adba76c3d77a9a8f128a3546db118f3bbf6b3675ddf1362ae4cd74b122","source":{"kind":"arxiv","id":"2607.08035","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08035","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08035v1","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08035","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"pith_short_12","alias_value":"KEKVRLN2O3B5","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"pith_short_16","alias_value":"KEKVRLN2O3B5O6U2","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"pith_short_8","alias_value":"KEKVRLN2","created_at":"2026-07-10T00:19:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KEKVRLN2O3B5O6U2R4JIUNKG3M","target":"record","payload":{"canonical_record":{"source":{"id":"2607.08035","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-09T01:25:30Z","cross_cats_sorted":[],"title_canon_sha256":"ec38eeaf67ffb465a881e531bb3753170e2cb92a2a394aa47cc0a00ebcff6e15","abstract_canon_sha256":"c1e035d501fd824bd99ae1c5bf5284049b9017031d119eea79a23cfb8e82586b"},"schema_version":"1.0"},"canonical_sha256":"511558adba76c3d77a9a8f128a3546db118f3bbf6b3675ddf1362ae4cd74b122","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T00:19:08.186954Z","signature_b64":"XtRtiQEJo/6lyPAtLXL4uz59H3+lAaLVvykeYU4l4gZAXk7qMxd6P+/TLrlufDa3G/ITw78aK0hy7NSxwcs7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"511558adba76c3d77a9a8f128a3546db118f3bbf6b3675ddf1362ae4cd74b122","last_reissued_at":"2026-07-10T00:19:08.186564Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T00:19:08.186564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.08035","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-10T00:19:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNhg8zqMe5ecIUgdMjnYOPmBX6Lncyy+/P3SZvrK8m+jzHG9iMzwOd2ZsWbn6wtS0B5sDRgDeKqvIvEWZh9nBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:42:14.109792Z"},"content_sha256":"19e5b755b12f1f1e9560c1178ff546e249a687fad79a3d2fff5483967702c88d","schema_version":"1.0","event_id":"sha256:19e5b755b12f1f1e9560c1178ff546e249a687fad79a3d2fff5483967702c88d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KEKVRLN2O3B5O6U2R4JIUNKG3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Linear Convergence of the Primal-Dual Hybrid Gradient Method for Semidefinite Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xin Jiang","submitted_at":"2026-07-09T01:25:30Z","abstract_excerpt":"Primal-dual first-order methods are widely used for large-scale semidefinite programming (SDP), but their ability to compute highly accurate solutions is not well explained by global convergence theory alone. We study the local convergence of the primal-dual hybrid gradient (PDHG) method applied to a standard primal--dual SDP pair. We show that PDHG converges eventually (R-)linearly whenever the limiting KKT point satisfies either strict complementarity or primal--dual nondegeneracy. The proof views PDHG as a preconditioned proximal point method for the KKT inclusion and combines its descent i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08035","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08035/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-10T00:19:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YB4Z3I7JcIcfcL6VDNXphzrNL8GpzWsakrWHKRWCmac22Rhl6MeF7HB5fA7yY0yAi7aSoQXTZR6xTPUvSg2rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:42:14.110708Z"},"content_sha256":"d0d5e325663edd4b8b1d78a6487e4dd222340341ed170f6bc632570711b1653b","schema_version":"1.0","event_id":"sha256:d0d5e325663edd4b8b1d78a6487e4dd222340341ed170f6bc632570711b1653b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEKVRLN2O3B5O6U2R4JIUNKG3M/bundle.json","state_url":"https://pith.science/pith/KEKVRLN2O3B5O6U2R4JIUNKG3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEKVRLN2O3B5O6U2R4JIUNKG3M/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":"2026-08-10T12:42:14Z","links":{"resolver":"https://pith.science/pith/KEKVRLN2O3B5O6U2R4JIUNKG3M","bundle":"https://pith.science/pith/KEKVRLN2O3B5O6U2R4JIUNKG3M/bundle.json","state":"https://pith.science/pith/KEKVRLN2O3B5O6U2R4JIUNKG3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEKVRLN2O3B5O6U2R4JIUNKG3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KEKVRLN2O3B5O6U2R4JIUNKG3M","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":"c1e035d501fd824bd99ae1c5bf5284049b9017031d119eea79a23cfb8e82586b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-09T01:25:30Z","title_canon_sha256":"ec38eeaf67ffb465a881e531bb3753170e2cb92a2a394aa47cc0a00ebcff6e15"},"schema_version":"1.0","source":{"id":"2607.08035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08035","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08035v1","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08035","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"pith_short_12","alias_value":"KEKVRLN2O3B5","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"pith_short_16","alias_value":"KEKVRLN2O3B5O6U2","created_at":"2026-07-10T00:19:08Z"},{"alias_kind":"pith_short_8","alias_value":"KEKVRLN2","created_at":"2026-07-10T00:19:08Z"}],"graph_snapshots":[{"event_id":"sha256:d0d5e325663edd4b8b1d78a6487e4dd222340341ed170f6bc632570711b1653b","target":"graph","created_at":"2026-07-10T00:19:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.08035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Primal-dual first-order methods are widely used for large-scale semidefinite programming (SDP), but their ability to compute highly accurate solutions is not well explained by global convergence theory alone. We study the local convergence of the primal-dual hybrid gradient (PDHG) method applied to a standard primal--dual SDP pair. We show that PDHG converges eventually (R-)linearly whenever the limiting KKT point satisfies either strict complementarity or primal--dual nondegeneracy. The proof views PDHG as a preconditioned proximal point method for the KKT inclusion and combines its descent i","authors_text":"Xin Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-09T01:25:30Z","title":"Local Linear Convergence of the Primal-Dual Hybrid Gradient Method for Semidefinite Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08035","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":"sha256:19e5b755b12f1f1e9560c1178ff546e249a687fad79a3d2fff5483967702c88d","target":"record","created_at":"2026-07-10T00:19:08Z","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":"c1e035d501fd824bd99ae1c5bf5284049b9017031d119eea79a23cfb8e82586b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-09T01:25:30Z","title_canon_sha256":"ec38eeaf67ffb465a881e531bb3753170e2cb92a2a394aa47cc0a00ebcff6e15"},"schema_version":"1.0","source":{"id":"2607.08035","kind":"arxiv","version":1}},"canonical_sha256":"511558adba76c3d77a9a8f128a3546db118f3bbf6b3675ddf1362ae4cd74b122","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"511558adba76c3d77a9a8f128a3546db118f3bbf6b3675ddf1362ae4cd74b122","first_computed_at":"2026-07-10T00:19:08.186564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T00:19:08.186564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XtRtiQEJo/6lyPAtLXL4uz59H3+lAaLVvykeYU4l4gZAXk7qMxd6P+/TLrlufDa3G/ITw78aK0hy7NSxwcs7Cw==","signature_status":"signed_v1","signed_at":"2026-07-10T00:19:08.186954Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.08035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19e5b755b12f1f1e9560c1178ff546e249a687fad79a3d2fff5483967702c88d","sha256:d0d5e325663edd4b8b1d78a6487e4dd222340341ed170f6bc632570711b1653b"],"state_sha256":"3cee692e7f1a308b8e0da4d66e2e81270f6abb4a40320acb3b281a19d9d6077c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xMVN9htucatFNG+/7/J1fmmc9mVowoW+jVsztz2nmDraXITjt7PNqAlp+SYGt8aLb5ymNel1XntB8dvgBizNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T12:42:14.118218Z","bundle_sha256":"203650abe725b69d72e4d4954e3bdae59dbaa0ecb781b33c75fb59055750b703"}}