{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X6636MU3EBV4NQJJIS7GAXHKWH","short_pith_number":"pith:X6636MU3","canonical_record":{"source":{"id":"1409.4824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T22:31:11Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"b9fe805b60a7145e1264f02cd689737e32f057a3fba8b4539697080c977aa46b","abstract_canon_sha256":"1267340dfd51b1cf62c8bc864ee91f5fd2c055f07d61d63d6a6eaaadab3ec74a"},"schema_version":"1.0"},"canonical_sha256":"bfbdbf329b206bc6c12944be605ceab1f0680aa0f667c6d9d9eab8cd93e9c8c6","source":{"kind":"arxiv","id":"1409.4824","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4824","created_at":"2026-05-18T02:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4824v1","created_at":"2026-05-18T02:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4824","created_at":"2026-05-18T02:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"X6636MU3EBV4","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X6636MU3EBV4NQJJ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X6636MU3","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X6636MU3EBV4NQJJIS7GAXHKWH","target":"record","payload":{"canonical_record":{"source":{"id":"1409.4824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T22:31:11Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"b9fe805b60a7145e1264f02cd689737e32f057a3fba8b4539697080c977aa46b","abstract_canon_sha256":"1267340dfd51b1cf62c8bc864ee91f5fd2c055f07d61d63d6a6eaaadab3ec74a"},"schema_version":"1.0"},"canonical_sha256":"bfbdbf329b206bc6c12944be605ceab1f0680aa0f667c6d9d9eab8cd93e9c8c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:38.601740Z","signature_b64":"LEQAVZDvgPz+aWf7XkqpYnSVEVU4Z9z8jPns15mYKiUyhcsssrPoYhEE6eBq9q+eNSmd4Lr9n5vO59De9MnJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfbdbf329b206bc6c12944be605ceab1f0680aa0f667c6d9d9eab8cd93e9c8c6","last_reissued_at":"2026-05-18T02:42:38.601069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:38.601069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.4824","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":"2026-05-18T02:42:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fM2P24UylhcGdHc57XceX5yFrg5BKNos9iIpFNkPU3S9vjRFCUZ5QnhMx/lPMYHMDv6W54ygYLg6Rnl5GV6FBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:42:35.979937Z"},"content_sha256":"cc215ba9e64ba3abde55b24f2eb66e23322268770801bb41a30a58e42c7ac01a","schema_version":"1.0","event_id":"sha256:cc215ba9e64ba3abde55b24f2eb66e23322268770801bb41a30a58e42c7ac01a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X6636MU3EBV4NQJJIS7GAXHKWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uncertainty Quantification for Integrated Circuits: Stochastic Spectral Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.CE","authors_text":"Ibrahim (Abe) M. Elfadel, Luca Daniel, Zheng Zhang","submitted_at":"2014-09-16T22:31:11Z","abstract_excerpt":"Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently developed stochastic testing and the appl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4824","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":""},"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":"2026-05-18T02:42:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f351rF6z14/qclDSG032nBDk1WFOIxwfPLwCzYqBGozZOHk0tz0jvhZXH/ybPmFzPyXQbEMcoD1MKBFbaPtTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:42:35.980281Z"},"content_sha256":"4d7098c30fc9e41cc443a84a6d89c15e31ae1743e866b7173748a2ebc668d91b","schema_version":"1.0","event_id":"sha256:4d7098c30fc9e41cc443a84a6d89c15e31ae1743e866b7173748a2ebc668d91b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6636MU3EBV4NQJJIS7GAXHKWH/bundle.json","state_url":"https://pith.science/pith/X6636MU3EBV4NQJJIS7GAXHKWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6636MU3EBV4NQJJIS7GAXHKWH/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":"2026-06-29T19:42:35Z","links":{"resolver":"https://pith.science/pith/X6636MU3EBV4NQJJIS7GAXHKWH","bundle":"https://pith.science/pith/X6636MU3EBV4NQJJIS7GAXHKWH/bundle.json","state":"https://pith.science/pith/X6636MU3EBV4NQJJIS7GAXHKWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6636MU3EBV4NQJJIS7GAXHKWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X6636MU3EBV4NQJJIS7GAXHKWH","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":"1267340dfd51b1cf62c8bc864ee91f5fd2c055f07d61d63d6a6eaaadab3ec74a","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T22:31:11Z","title_canon_sha256":"b9fe805b60a7145e1264f02cd689737e32f057a3fba8b4539697080c977aa46b"},"schema_version":"1.0","source":{"id":"1409.4824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4824","created_at":"2026-05-18T02:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4824v1","created_at":"2026-05-18T02:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4824","created_at":"2026-05-18T02:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"X6636MU3EBV4","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X6636MU3EBV4NQJJ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X6636MU3","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:4d7098c30fc9e41cc443a84a6d89c15e31ae1743e866b7173748a2ebc668d91b","target":"graph","created_at":"2026-05-18T02:42:38Z","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":"Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently developed stochastic testing and the appl","authors_text":"Ibrahim (Abe) M. Elfadel, Luca Daniel, Zheng Zhang","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T22:31:11Z","title":"Uncertainty Quantification for Integrated Circuits: Stochastic Spectral Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4824","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:cc215ba9e64ba3abde55b24f2eb66e23322268770801bb41a30a58e42c7ac01a","target":"record","created_at":"2026-05-18T02:42:38Z","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":"1267340dfd51b1cf62c8bc864ee91f5fd2c055f07d61d63d6a6eaaadab3ec74a","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2014-09-16T22:31:11Z","title_canon_sha256":"b9fe805b60a7145e1264f02cd689737e32f057a3fba8b4539697080c977aa46b"},"schema_version":"1.0","source":{"id":"1409.4824","kind":"arxiv","version":1}},"canonical_sha256":"bfbdbf329b206bc6c12944be605ceab1f0680aa0f667c6d9d9eab8cd93e9c8c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfbdbf329b206bc6c12944be605ceab1f0680aa0f667c6d9d9eab8cd93e9c8c6","first_computed_at":"2026-05-18T02:42:38.601069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:38.601069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LEQAVZDvgPz+aWf7XkqpYnSVEVU4Z9z8jPns15mYKiUyhcsssrPoYhEE6eBq9q+eNSmd4Lr9n5vO59De9MnJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:38.601740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc215ba9e64ba3abde55b24f2eb66e23322268770801bb41a30a58e42c7ac01a","sha256:4d7098c30fc9e41cc443a84a6d89c15e31ae1743e866b7173748a2ebc668d91b"],"state_sha256":"ba2f0a063e468f5aff94db98ab8dada396c90371b8ca05c464cee1ca974088d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wITsJ6pP2PkaZAbMPHwr8RQsY+lgDtW7p5crtG0/MvvMjM87m5CVFHDhzkgiD1TYrQXXlUayuwqVQnZEpL5HCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:42:35.982175Z","bundle_sha256":"ea2dcc5f29e2c95dd6b4471a95efc5de0c4b25cad2da04ffef8a2671cd114b91"}}