{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2M7QZUPA5R3F7DBSIKRLPN2K4V","short_pith_number":"pith:2M7QZUPA","canonical_record":{"source":{"id":"2404.19186","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-04-30T01:22:55Z","cross_cats_sorted":["cs.CR","math.IT","math.MG","math.NT"],"title_canon_sha256":"cd4ff6db68ad881dc6af875ce343ebe1ebca3b6f25062765e14725aeed8ceab8","abstract_canon_sha256":"06622db3e789844f857ee4cdeed3736519170ddc979795b3c439e5f050690bd2"},"schema_version":"1.0"},"canonical_sha256":"d33f0cd1e0ec765f8c3242a2b7b74ae546c885feae4093f3e41df089ed85299e","source":{"kind":"arxiv","id":"2404.19186","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19186","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19186v1","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19186","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"2M7QZUPA5R3F","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"pith_short_16","alias_value":"2M7QZUPA5R3F7DBS","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"pith_short_8","alias_value":"2M7QZUPA","created_at":"2026-07-05T08:13:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2M7QZUPA5R3F7DBSIKRLPN2K4V","target":"record","payload":{"canonical_record":{"source":{"id":"2404.19186","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-04-30T01:22:55Z","cross_cats_sorted":["cs.CR","math.IT","math.MG","math.NT"],"title_canon_sha256":"cd4ff6db68ad881dc6af875ce343ebe1ebca3b6f25062765e14725aeed8ceab8","abstract_canon_sha256":"06622db3e789844f857ee4cdeed3736519170ddc979795b3c439e5f050690bd2"},"schema_version":"1.0"},"canonical_sha256":"d33f0cd1e0ec765f8c3242a2b7b74ae546c885feae4093f3e41df089ed85299e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:13:39.556190Z","signature_b64":"dT43oIELGxAmeq71B2R2tZw7UPSpCPU0pU7SpJTz5KP8Va51m57b74CAuhfnyq7ybNUNI/y24kVxn/7Xl5RxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d33f0cd1e0ec765f8c3242a2b7b74ae546c885feae4093f3e41df089ed85299e","last_reissued_at":"2026-07-05T08:13:39.555684Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:13:39.555684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.19186","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":"2026-07-05T08:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47XzmR3jLfgNm0+uohKo/czY0zAIzvZTZZ1rUAd2r4t1dp2Uf0ZIH4voeWF8l0FJ5+Q/6hkWNB14BcG0eThzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:22:07.321604Z"},"content_sha256":"5634f7c7c6fe330e948882ee83564e37fc2d8e8961d9431f4559bca5f6f732b5","schema_version":"1.0","event_id":"sha256:5634f7c7c6fe330e948882ee83564e37fc2d8e8961d9431f4559bca5f6f732b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2M7QZUPA5R3F7DBSIKRLPN2K4V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Mathematical Foundation of Post-Quantum Cryptography","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","math.IT","math.MG","math.NT"],"primary_cat":"cs.IT","authors_text":"Chuanming Zong","submitted_at":"2024-04-30T01:22:55Z","abstract_excerpt":"On July 5, 2022, the National Institute of Standards and Technology announced four possible post-quantum cryptography standards, three of them are based on lattice theory and the other one is based on Hash function. It is well-known that the security of the lattice cryptography relies on the hardness of the shortest vector problem (SVP) and the closest vector problem (CVP). In fact, the SVP is a sphere packing problem and the CVP is a sphere covering problem. Furthermore, both SVP and CVP are equivalent to arithmetic problems of positive definite quadratic forms. This paper will briefly introd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19186","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/2404.19186/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":"2026-07-05T08:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TRSvebGrkDiibSstAcDR8CC+aoCFfrPgx0387oVuMsl7uPHGktCpwgfjv2MUVLgyJZsmsu6r/4Rph0QqOdlQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:22:07.321994Z"},"content_sha256":"ce784a0251a278c489c236bcdd9d4a8b3e2c9247b9247c40ab5c3a71291f54ca","schema_version":"1.0","event_id":"sha256:ce784a0251a278c489c236bcdd9d4a8b3e2c9247b9247c40ab5c3a71291f54ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2M7QZUPA5R3F7DBSIKRLPN2K4V/bundle.json","state_url":"https://pith.science/pith/2M7QZUPA5R3F7DBSIKRLPN2K4V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2M7QZUPA5R3F7DBSIKRLPN2K4V/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":"2026-08-13T12:22:07Z","links":{"resolver":"https://pith.science/pith/2M7QZUPA5R3F7DBSIKRLPN2K4V","bundle":"https://pith.science/pith/2M7QZUPA5R3F7DBSIKRLPN2K4V/bundle.json","state":"https://pith.science/pith/2M7QZUPA5R3F7DBSIKRLPN2K4V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2M7QZUPA5R3F7DBSIKRLPN2K4V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2M7QZUPA5R3F7DBSIKRLPN2K4V","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":"06622db3e789844f857ee4cdeed3736519170ddc979795b3c439e5f050690bd2","cross_cats_sorted":["cs.CR","math.IT","math.MG","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-04-30T01:22:55Z","title_canon_sha256":"cd4ff6db68ad881dc6af875ce343ebe1ebca3b6f25062765e14725aeed8ceab8"},"schema_version":"1.0","source":{"id":"2404.19186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19186","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19186v1","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19186","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"2M7QZUPA5R3F","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"pith_short_16","alias_value":"2M7QZUPA5R3F7DBS","created_at":"2026-07-05T08:13:39Z"},{"alias_kind":"pith_short_8","alias_value":"2M7QZUPA","created_at":"2026-07-05T08:13:39Z"}],"graph_snapshots":[{"event_id":"sha256:ce784a0251a278c489c236bcdd9d4a8b3e2c9247b9247c40ab5c3a71291f54ca","target":"graph","created_at":"2026-07-05T08:13:39Z","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/2404.19186/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"On July 5, 2022, the National Institute of Standards and Technology announced four possible post-quantum cryptography standards, three of them are based on lattice theory and the other one is based on Hash function. It is well-known that the security of the lattice cryptography relies on the hardness of the shortest vector problem (SVP) and the closest vector problem (CVP). In fact, the SVP is a sphere packing problem and the CVP is a sphere covering problem. Furthermore, both SVP and CVP are equivalent to arithmetic problems of positive definite quadratic forms. This paper will briefly introd","authors_text":"Chuanming Zong","cross_cats":["cs.CR","math.IT","math.MG","math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-04-30T01:22:55Z","title":"The Mathematical Foundation of Post-Quantum Cryptography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19186","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":"sha256:5634f7c7c6fe330e948882ee83564e37fc2d8e8961d9431f4559bca5f6f732b5","target":"record","created_at":"2026-07-05T08:13:39Z","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":"06622db3e789844f857ee4cdeed3736519170ddc979795b3c439e5f050690bd2","cross_cats_sorted":["cs.CR","math.IT","math.MG","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-04-30T01:22:55Z","title_canon_sha256":"cd4ff6db68ad881dc6af875ce343ebe1ebca3b6f25062765e14725aeed8ceab8"},"schema_version":"1.0","source":{"id":"2404.19186","kind":"arxiv","version":1}},"canonical_sha256":"d33f0cd1e0ec765f8c3242a2b7b74ae546c885feae4093f3e41df089ed85299e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d33f0cd1e0ec765f8c3242a2b7b74ae546c885feae4093f3e41df089ed85299e","first_computed_at":"2026-07-05T08:13:39.555684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:13:39.555684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dT43oIELGxAmeq71B2R2tZw7UPSpCPU0pU7SpJTz5KP8Va51m57b74CAuhfnyq7ybNUNI/y24kVxn/7Xl5RxCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:13:39.556190Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.19186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5634f7c7c6fe330e948882ee83564e37fc2d8e8961d9431f4559bca5f6f732b5","sha256:ce784a0251a278c489c236bcdd9d4a8b3e2c9247b9247c40ab5c3a71291f54ca"],"state_sha256":"91c5e37737e5fa9e01ff6baf18b9370123bf3937a12efd72260deea125a2368c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9IOQrNpMrcU2HymarQT4lSXWE1L5uT/Vy0jMlhzabgAanDvUb2XUgQaiTFItMQPbvYfYsQsZLGByuZ5t9VutDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T12:22:07.325126Z","bundle_sha256":"e224be931bd3741019bd51a9b49fa479118138a8291c9f693e2f90be93e8969f"}}