{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:G3Z3MWOJDJRAQ4F7WHULZQPXER","short_pith_number":"pith:G3Z3MWOJ","canonical_record":{"source":{"id":"1403.5355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-03-21T03:45:08Z","cross_cats_sorted":["cs.MS","nlin.CD"],"title_canon_sha256":"18824ed65f97a96f36b586b18b5cb44d2f3d77b894cf6a1c55509f5ffe10739c","abstract_canon_sha256":"4f8c57c8350105f54b25bf3a6e9b2180275ba185adbde8e3c7db09317286102f"},"schema_version":"1.0"},"canonical_sha256":"36f3b659c91a620870bfb1e8bcc1f72469ecfa43e534ecbf78ef8c8c1e9946b1","source":{"kind":"arxiv","id":"1403.5355","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5355","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5355v2","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5355","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"G3Z3MWOJDJRA","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G3Z3MWOJDJRAQ4F7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G3Z3MWOJ","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:G3Z3MWOJDJRAQ4F7WHULZQPXER","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-03-21T03:45:08Z","cross_cats_sorted":["cs.MS","nlin.CD"],"title_canon_sha256":"18824ed65f97a96f36b586b18b5cb44d2f3d77b894cf6a1c55509f5ffe10739c","abstract_canon_sha256":"4f8c57c8350105f54b25bf3a6e9b2180275ba185adbde8e3c7db09317286102f"},"schema_version":"1.0"},"canonical_sha256":"36f3b659c91a620870bfb1e8bcc1f72469ecfa43e534ecbf78ef8c8c1e9946b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:47.286690Z","signature_b64":"VGFSKiBlvFobs6CPceRyyc8fyoLQUNoydDzL42JNhHEOb/vU45dsoSkyOcPUen6RHz0+blZuuXZ9qFFvPb0KBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36f3b659c91a620870bfb1e8bcc1f72469ecfa43e534ecbf78ef8c8c1e9946b1","last_reissued_at":"2026-05-18T01:15:47.285396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:47.285396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5355","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bSNVv//ee8oRXXlNLjfpw8HDJqNn14Cq0g2MzyN04YjGV7Z8P4YZ9CWC/WMr/eaBwE2syo7NxSAVp+Xz7y1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:22:59.664391Z"},"content_sha256":"8ea74ddc631772be6282c3063565af574121984672d8a13224990c460c57b9a6","schema_version":"1.0","event_id":"sha256:8ea74ddc631772be6282c3063565af574121984672d8a13224990c460c57b9a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:G3Z3MWOJDJRAQ4F7WHULZQPXER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The MIXMAX random number generator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","nlin.CD"],"primary_cat":"hep-lat","authors_text":"Konstantin G. Savvidy","submitted_at":"2014-03-21T03:45:08Z","abstract_excerpt":"In this note, we give a practical solution to the problem of determining the maximal period of matrix generators of pseudo-random numbers which are based on an integer-valued unimodular matrix of size NxN known as MIXMAX and arithmetic defined on a Galois field GF[p] with large prime modulus p. The existing theory of Galois finite fields is adapted to the present case, and necessary and sufficient condition to attain the maximum period is formulated. Three efficient algorithms are presented. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to rec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5355","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HKrkZavkanev4AaIQ5KczPIIq1lziFXXppuh5tLz3XRZCJac1cCXRSZ5s6dWyosNEGFCUkY06v1uUzlF0c9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:22:59.665134Z"},"content_sha256":"861fda5c551eaea84b3aa21fa1af1ea500aec3d90b5cd2a80905a41c82140367","schema_version":"1.0","event_id":"sha256:861fda5c551eaea84b3aa21fa1af1ea500aec3d90b5cd2a80905a41c82140367"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3Z3MWOJDJRAQ4F7WHULZQPXER/bundle.json","state_url":"https://pith.science/pith/G3Z3MWOJDJRAQ4F7WHULZQPXER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3Z3MWOJDJRAQ4F7WHULZQPXER/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":"2026-06-11T22:22:59Z","links":{"resolver":"https://pith.science/pith/G3Z3MWOJDJRAQ4F7WHULZQPXER","bundle":"https://pith.science/pith/G3Z3MWOJDJRAQ4F7WHULZQPXER/bundle.json","state":"https://pith.science/pith/G3Z3MWOJDJRAQ4F7WHULZQPXER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3Z3MWOJDJRAQ4F7WHULZQPXER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G3Z3MWOJDJRAQ4F7WHULZQPXER","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":"4f8c57c8350105f54b25bf3a6e9b2180275ba185adbde8e3c7db09317286102f","cross_cats_sorted":["cs.MS","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-03-21T03:45:08Z","title_canon_sha256":"18824ed65f97a96f36b586b18b5cb44d2f3d77b894cf6a1c55509f5ffe10739c"},"schema_version":"1.0","source":{"id":"1403.5355","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5355","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5355v2","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5355","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"G3Z3MWOJDJRA","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G3Z3MWOJDJRAQ4F7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G3Z3MWOJ","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:861fda5c551eaea84b3aa21fa1af1ea500aec3d90b5cd2a80905a41c82140367","target":"graph","created_at":"2026-05-18T01:15:47Z","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":"In this note, we give a practical solution to the problem of determining the maximal period of matrix generators of pseudo-random numbers which are based on an integer-valued unimodular matrix of size NxN known as MIXMAX and arithmetic defined on a Galois field GF[p] with large prime modulus p. The existing theory of Galois finite fields is adapted to the present case, and necessary and sufficient condition to attain the maximum period is formulated. Three efficient algorithms are presented. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to rec","authors_text":"Konstantin G. Savvidy","cross_cats":["cs.MS","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-03-21T03:45:08Z","title":"The MIXMAX random number generator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5355","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":"sha256:8ea74ddc631772be6282c3063565af574121984672d8a13224990c460c57b9a6","target":"record","created_at":"2026-05-18T01:15:47Z","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":"4f8c57c8350105f54b25bf3a6e9b2180275ba185adbde8e3c7db09317286102f","cross_cats_sorted":["cs.MS","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-03-21T03:45:08Z","title_canon_sha256":"18824ed65f97a96f36b586b18b5cb44d2f3d77b894cf6a1c55509f5ffe10739c"},"schema_version":"1.0","source":{"id":"1403.5355","kind":"arxiv","version":2}},"canonical_sha256":"36f3b659c91a620870bfb1e8bcc1f72469ecfa43e534ecbf78ef8c8c1e9946b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36f3b659c91a620870bfb1e8bcc1f72469ecfa43e534ecbf78ef8c8c1e9946b1","first_computed_at":"2026-05-18T01:15:47.285396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:47.285396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VGFSKiBlvFobs6CPceRyyc8fyoLQUNoydDzL42JNhHEOb/vU45dsoSkyOcPUen6RHz0+blZuuXZ9qFFvPb0KBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:47.286690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5355","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ea74ddc631772be6282c3063565af574121984672d8a13224990c460c57b9a6","sha256:861fda5c551eaea84b3aa21fa1af1ea500aec3d90b5cd2a80905a41c82140367"],"state_sha256":"5d6fa07298f350079eced25ce321a88511380801a605e3a935a932abcf3002f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzgMEN2V7a+GeF7dYiws3DSxhEh3thgo8j1e+t2P75U2BHHHLBWZ51KBNhh2LVTkXCPdKy4zyrksmFAge0KkDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:22:59.669618Z","bundle_sha256":"648d8b0c6cef4a073daf649f8519cad1435efa480b508190c065fe5b7f90bb8b"}}