{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VSP56OBP7UWEPTK223PGCN2EBQ","short_pith_number":"pith:VSP56OBP","canonical_record":{"source":{"id":"1202.6483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-29T08:47:53Z","cross_cats_sorted":[],"title_canon_sha256":"2bf3a18eba62998bbdf09297caa79e7f3bf048a927625a07fa316d793d7cd0c0","abstract_canon_sha256":"995f134313243d0fecfeef256d81ad1004b3cb59d4520372aaa6bffe5a113d7c"},"schema_version":"1.0"},"canonical_sha256":"ac9fdf382ffd2c47cd5ad6de6137440c1cc3a8dec594561d4d807013edab8e5d","source":{"kind":"arxiv","id":"1202.6483","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6483","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6483v2","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6483","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"VSP56OBP7UWE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VSP56OBP7UWEPTK2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VSP56OBP","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VSP56OBP7UWEPTK223PGCN2EBQ","target":"record","payload":{"canonical_record":{"source":{"id":"1202.6483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-29T08:47:53Z","cross_cats_sorted":[],"title_canon_sha256":"2bf3a18eba62998bbdf09297caa79e7f3bf048a927625a07fa316d793d7cd0c0","abstract_canon_sha256":"995f134313243d0fecfeef256d81ad1004b3cb59d4520372aaa6bffe5a113d7c"},"schema_version":"1.0"},"canonical_sha256":"ac9fdf382ffd2c47cd5ad6de6137440c1cc3a8dec594561d4d807013edab8e5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:28.849119Z","signature_b64":"NPJiqm/HB1Oi1dNjTKMvYXrsIuIKcN0GK9ZO/747UZNSZP92Ev2pRNg66JMlNpDlgyhpVfrb5nv/PML6b+UYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac9fdf382ffd2c47cd5ad6de6137440c1cc3a8dec594561d4d807013edab8e5d","last_reissued_at":"2026-05-18T03:59:28.848298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:28.848298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.6483","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":"2026-05-18T03:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u9+b67qeuqCNIPoG7WK86sasq/pPMRIwYWPsQFX0KA021YGy8Wj9kuNrN2VWWtRLZLUSE0EppaznUqsqXyARCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:22:25.823378Z"},"content_sha256":"d5d34fdedd99ccbc9f8b33ca33b185c44d69b49032ad2216057d7bcfd4ba7582","schema_version":"1.0","event_id":"sha256:d5d34fdedd99ccbc9f8b33ca33b185c44d69b49032ad2216057d7bcfd4ba7582"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VSP56OBP7UWEPTK223PGCN2EBQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Chernoff-type Lower Bound for the Gaussian Q-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fran\\c{c}ois D. C\\^ot\\'e, Ioannis N. Psaromiligkos, Warren J. Gross","submitted_at":"2012-02-29T08:47:53Z","abstract_excerpt":"A lower bound for the Gaussian Q-function is presented in the form of a single exponential function with parametric order and weight. We prove the lower bound by introducing two functions, one related to the Q-function and the other similarly related to the exponential function, and by obtaining inequalities that indicate the sign of the difference of the two functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6483","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":"2026-05-18T03:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HW3LVa/icjxktFe7NtbtaisuVNDIgC16dAEyJWHYewNT74y0aHM4llHTDiEkqVTaVz6un+sMO29KiVr7W+q2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:22:25.823826Z"},"content_sha256":"067b855010918c7bb63af3366196671fb458ea701ede02abd550540db38d013b","schema_version":"1.0","event_id":"sha256:067b855010918c7bb63af3366196671fb458ea701ede02abd550540db38d013b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSP56OBP7UWEPTK223PGCN2EBQ/bundle.json","state_url":"https://pith.science/pith/VSP56OBP7UWEPTK223PGCN2EBQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSP56OBP7UWEPTK223PGCN2EBQ/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":"2026-05-27T19:22:25Z","links":{"resolver":"https://pith.science/pith/VSP56OBP7UWEPTK223PGCN2EBQ","bundle":"https://pith.science/pith/VSP56OBP7UWEPTK223PGCN2EBQ/bundle.json","state":"https://pith.science/pith/VSP56OBP7UWEPTK223PGCN2EBQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSP56OBP7UWEPTK223PGCN2EBQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VSP56OBP7UWEPTK223PGCN2EBQ","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":"995f134313243d0fecfeef256d81ad1004b3cb59d4520372aaa6bffe5a113d7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-29T08:47:53Z","title_canon_sha256":"2bf3a18eba62998bbdf09297caa79e7f3bf048a927625a07fa316d793d7cd0c0"},"schema_version":"1.0","source":{"id":"1202.6483","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6483","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6483v2","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6483","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"VSP56OBP7UWE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VSP56OBP7UWEPTK2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VSP56OBP","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:067b855010918c7bb63af3366196671fb458ea701ede02abd550540db38d013b","target":"graph","created_at":"2026-05-18T03:59:28Z","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":"A lower bound for the Gaussian Q-function is presented in the form of a single exponential function with parametric order and weight. We prove the lower bound by introducing two functions, one related to the Q-function and the other similarly related to the exponential function, and by obtaining inequalities that indicate the sign of the difference of the two functions.","authors_text":"Fran\\c{c}ois D. C\\^ot\\'e, Ioannis N. Psaromiligkos, Warren J. Gross","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-29T08:47:53Z","title":"A Chernoff-type Lower Bound for the Gaussian Q-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6483","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:d5d34fdedd99ccbc9f8b33ca33b185c44d69b49032ad2216057d7bcfd4ba7582","target":"record","created_at":"2026-05-18T03:59:28Z","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":"995f134313243d0fecfeef256d81ad1004b3cb59d4520372aaa6bffe5a113d7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-29T08:47:53Z","title_canon_sha256":"2bf3a18eba62998bbdf09297caa79e7f3bf048a927625a07fa316d793d7cd0c0"},"schema_version":"1.0","source":{"id":"1202.6483","kind":"arxiv","version":2}},"canonical_sha256":"ac9fdf382ffd2c47cd5ad6de6137440c1cc3a8dec594561d4d807013edab8e5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac9fdf382ffd2c47cd5ad6de6137440c1cc3a8dec594561d4d807013edab8e5d","first_computed_at":"2026-05-18T03:59:28.848298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:28.848298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NPJiqm/HB1Oi1dNjTKMvYXrsIuIKcN0GK9ZO/747UZNSZP92Ev2pRNg66JMlNpDlgyhpVfrb5nv/PML6b+UYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:28.849119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6483","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5d34fdedd99ccbc9f8b33ca33b185c44d69b49032ad2216057d7bcfd4ba7582","sha256:067b855010918c7bb63af3366196671fb458ea701ede02abd550540db38d013b"],"state_sha256":"61f55c4f5ff08f2fafd0022a348e6cc5d2c219cda299165edf6f6a402d4a6795"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3gxT+h3OsteneLhJy54LD6BQ2PqcdpPeiuzWOrkdRlzxOkzfvMU17I+oD3wy0sP6YIBXA1GzbsecN3pKtVwxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:22:25.826376Z","bundle_sha256":"ad852b4cc0cbb893699149d7d49d2550688d3a4ece1df50e0d18f977559339d6"}}