{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FZWJ4TTJ7O77REAW7GIMWE66AF","short_pith_number":"pith:FZWJ4TTJ","canonical_record":{"source":{"id":"1512.00943","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T04:28:17Z","cross_cats_sorted":[],"title_canon_sha256":"ccaa59950e33144c351f1112110fe94411d04b358b54806e7ba9c33ae861e500","abstract_canon_sha256":"dc4ff7d418de50e9d316399b6ed4a98bed4538ff6f3bf573c19b0c4fc60cb719"},"schema_version":"1.0"},"canonical_sha256":"2e6c9e4e69fbbff89016f990cb13de016ac3ab814ce1714b7e3a12c23b946cb1","source":{"kind":"arxiv","id":"1512.00943","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00943","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00943v1","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00943","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"FZWJ4TTJ7O77","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FZWJ4TTJ7O77REAW","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FZWJ4TTJ","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FZWJ4TTJ7O77REAW7GIMWE66AF","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00943","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T04:28:17Z","cross_cats_sorted":[],"title_canon_sha256":"ccaa59950e33144c351f1112110fe94411d04b358b54806e7ba9c33ae861e500","abstract_canon_sha256":"dc4ff7d418de50e9d316399b6ed4a98bed4538ff6f3bf573c19b0c4fc60cb719"},"schema_version":"1.0"},"canonical_sha256":"2e6c9e4e69fbbff89016f990cb13de016ac3ab814ce1714b7e3a12c23b946cb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:23.776976Z","signature_b64":"hN/v3aJgFZDP+6dsuEz+jqiF7kjDMLtAt8nhHfFpY2QPoLTuOcnE5s60CkdQqoMFAYCCiEEHPQzmhThjvXPlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e6c9e4e69fbbff89016f990cb13de016ac3ab814ce1714b7e3a12c23b946cb1","last_reissued_at":"2026-05-18T01:25:23.776589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:23.776589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00943","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":"2026-05-18T01:25:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fWCqQFR1TTL1x5UovhAnW/E1nALlbNncyanSowPu6kORBNgcq7IWLVgdtbZyY5ISFbN6dQptR3F6O72dtL/nDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:55:07.037394Z"},"content_sha256":"64c5f6062db0fd485468e719174013f4b527eafc04fa9b8bc542a5be16d156e6","schema_version":"1.0","event_id":"sha256:64c5f6062db0fd485468e719174013f4b527eafc04fa9b8bc542a5be16d156e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FZWJ4TTJ7O77REAW7GIMWE66AF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Combinatorial Problem Related to Sparse Systems of Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Igor Semaev, Peter Horak, Zsolt Tuza","submitted_at":"2015-12-03T04:28:17Z","abstract_excerpt":"Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext. Raddum and Semaev proposed new methods for solving such sparse systems. It turns out that a combinatorial MaxMinMax problem provides bounds on the average computational complexity of sparse systems. In this paper we initiate a study of a linear algebra variation of this MaxMinMax problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00943","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":"2026-05-18T01:25:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G1Ld9czBuLFcX0kJA8Kkm7RiYhFUvAYV7M7MvLimyukoFTn6lq+8IK+IarYEimvzuXTSh8aFhcuAlWBMGTWYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:55:07.037724Z"},"content_sha256":"76d8700e4609b97e986b5e37e1bac22d7607327de8a11e873eda0227455a3842","schema_version":"1.0","event_id":"sha256:76d8700e4609b97e986b5e37e1bac22d7607327de8a11e873eda0227455a3842"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZWJ4TTJ7O77REAW7GIMWE66AF/bundle.json","state_url":"https://pith.science/pith/FZWJ4TTJ7O77REAW7GIMWE66AF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZWJ4TTJ7O77REAW7GIMWE66AF/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":"2026-06-20T05:55:07Z","links":{"resolver":"https://pith.science/pith/FZWJ4TTJ7O77REAW7GIMWE66AF","bundle":"https://pith.science/pith/FZWJ4TTJ7O77REAW7GIMWE66AF/bundle.json","state":"https://pith.science/pith/FZWJ4TTJ7O77REAW7GIMWE66AF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZWJ4TTJ7O77REAW7GIMWE66AF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FZWJ4TTJ7O77REAW7GIMWE66AF","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":"dc4ff7d418de50e9d316399b6ed4a98bed4538ff6f3bf573c19b0c4fc60cb719","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T04:28:17Z","title_canon_sha256":"ccaa59950e33144c351f1112110fe94411d04b358b54806e7ba9c33ae861e500"},"schema_version":"1.0","source":{"id":"1512.00943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00943","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00943v1","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00943","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"FZWJ4TTJ7O77","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FZWJ4TTJ7O77REAW","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FZWJ4TTJ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:76d8700e4609b97e986b5e37e1bac22d7607327de8a11e873eda0227455a3842","target":"graph","created_at":"2026-05-18T01:25:23Z","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":"Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext. Raddum and Semaev proposed new methods for solving such sparse systems. It turns out that a combinatorial MaxMinMax problem provides bounds on the average computational complexity of sparse systems. In this paper we initiate a study of a linear algebra variation of this MaxMinMax problem.","authors_text":"Igor Semaev, Peter Horak, Zsolt Tuza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T04:28:17Z","title":"A Combinatorial Problem Related to Sparse Systems of Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00943","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":"sha256:64c5f6062db0fd485468e719174013f4b527eafc04fa9b8bc542a5be16d156e6","target":"record","created_at":"2026-05-18T01:25:23Z","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":"dc4ff7d418de50e9d316399b6ed4a98bed4538ff6f3bf573c19b0c4fc60cb719","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T04:28:17Z","title_canon_sha256":"ccaa59950e33144c351f1112110fe94411d04b358b54806e7ba9c33ae861e500"},"schema_version":"1.0","source":{"id":"1512.00943","kind":"arxiv","version":1}},"canonical_sha256":"2e6c9e4e69fbbff89016f990cb13de016ac3ab814ce1714b7e3a12c23b946cb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e6c9e4e69fbbff89016f990cb13de016ac3ab814ce1714b7e3a12c23b946cb1","first_computed_at":"2026-05-18T01:25:23.776589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:23.776589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hN/v3aJgFZDP+6dsuEz+jqiF7kjDMLtAt8nhHfFpY2QPoLTuOcnE5s60CkdQqoMFAYCCiEEHPQzmhThjvXPlCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:23.776976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64c5f6062db0fd485468e719174013f4b527eafc04fa9b8bc542a5be16d156e6","sha256:76d8700e4609b97e986b5e37e1bac22d7607327de8a11e873eda0227455a3842"],"state_sha256":"d567c2fff984ffd4ca01d68f5a3c2fc2ff5fc2810aa2a39a03e5a331bb326d2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+VqKTao5bDXR0jHp0ti5w9s6P8ECfk0FAwQa6LvoTJzJOErmFCOLIVZTaRNnOq4PfAUF6j/n822Ethdyl0UeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:55:07.039483Z","bundle_sha256":"b600a28601edbbcfc3fa7d5ea1fbc994eed1b809324583f3d8519e0633899ffb"}}