{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BXP2VCK4HH5YWMHJKQL2M5BXYB","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":"5128cc420a1c3229e906fdb1a26b5edf4b33408e9a65b08f34fb52481c526c66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-07-13T06:21:01Z","title_canon_sha256":"3c2a2863ee65c68945bf3f8608a20183f592596cbd3014173e8431400d17a9f9"},"schema_version":"1.0","source":{"id":"1507.03331","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03331","created_at":"2026-05-18T00:56:46Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03331v7","created_at":"2026-05-18T00:56:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03331","created_at":"2026-05-18T00:56:46Z"},{"alias_kind":"pith_short_12","alias_value":"BXP2VCK4HH5Y","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BXP2VCK4HH5YWMHJ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BXP2VCK4","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:e27bd3e3cb129b5590d7fa087e7a6849316e2b4ab1f65e536aad6a544c0cb3a7","target":"graph","created_at":"2026-05-18T00:56:46Z","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":"Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs or custom hardware implementations. This problem becomes challenging when the program does not employ solely linear operations, and non-linearities are inherent to many interesting computational problems in real-world applications.\n  Existing solutions to reasoning possibly lead to either inaccurate bounds or high analysis time in the presence of nonlinear c","authors_text":"Alastair Donaldson, George Constantinides, Victor Magron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-07-13T06:21:01Z","title":"Certified Roundoff Error Bounds Using Semidefinite Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03331","kind":"arxiv","version":7},"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":"sha256:48cbf4a6ae9982c1e22f39a69e4ac26855851a8627842530979e21e7da934bb2","target":"record","created_at":"2026-05-18T00:56:46Z","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":"5128cc420a1c3229e906fdb1a26b5edf4b33408e9a65b08f34fb52481c526c66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-07-13T06:21:01Z","title_canon_sha256":"3c2a2863ee65c68945bf3f8608a20183f592596cbd3014173e8431400d17a9f9"},"schema_version":"1.0","source":{"id":"1507.03331","kind":"arxiv","version":7}},"canonical_sha256":"0ddfaa895c39fb8b30e95417a67437c05d4de60e22dbd926c166404d75b96369","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ddfaa895c39fb8b30e95417a67437c05d4de60e22dbd926c166404d75b96369","first_computed_at":"2026-05-18T00:56:46.732236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:46.732236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7y2FgXFV3sKmRqVF9JlquOMtPkiLZCPsWBx+eIOesluzPLSnaSET4CfPOnQTWKFZrnAmqSNVxMEZp5k6yDvoAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:46.732796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03331","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48cbf4a6ae9982c1e22f39a69e4ac26855851a8627842530979e21e7da934bb2","sha256:e27bd3e3cb129b5590d7fa087e7a6849316e2b4ab1f65e536aad6a544c0cb3a7"],"state_sha256":"2a9db7eb53c923f7750392cbfefb2b10003193451abc71f0cf21e19d8952e5e3"}