{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZJEYXQTKGPJDT27MAN4OWVC4RM","short_pith_number":"pith:ZJEYXQTK","canonical_record":{"source":{"id":"1608.01551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-04T14:34:35Z","cross_cats_sorted":[],"title_canon_sha256":"88349939619107759300d2c184df7acd2b2a834b477bc5f4d258337364cbb289","abstract_canon_sha256":"e8335e1e4855703c5f0c04794a240025c49dcd48ccbb635ec85a7f7fec356f2a"},"schema_version":"1.0"},"canonical_sha256":"ca498bc26a33d239ebec0378eb545c8b0729c2b2ffe053a5e4a093300b7a8e4b","source":{"kind":"arxiv","id":"1608.01551","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01551","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01551v1","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01551","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZJEYXQTKGPJD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZJEYXQTKGPJDT27M","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZJEYXQTK","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZJEYXQTKGPJDT27MAN4OWVC4RM","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-04T14:34:35Z","cross_cats_sorted":[],"title_canon_sha256":"88349939619107759300d2c184df7acd2b2a834b477bc5f4d258337364cbb289","abstract_canon_sha256":"e8335e1e4855703c5f0c04794a240025c49dcd48ccbb635ec85a7f7fec356f2a"},"schema_version":"1.0"},"canonical_sha256":"ca498bc26a33d239ebec0378eb545c8b0729c2b2ffe053a5e4a093300b7a8e4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:52.143535Z","signature_b64":"gAdv1BVmXAHTpzuWw1rB3OeTA7KJDymd/T+08z+65V8P9Bev/uXdZwG1wojIqmPDNnM++2mWzUhrl1BIPBwNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca498bc26a33d239ebec0378eb545c8b0729c2b2ffe053a5e4a093300b7a8e4b","last_reissued_at":"2026-05-18T01:09:52.142901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:52.142901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01551","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":"2026-05-18T01:09:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GpNqBI2tW9zuNqMG2VlQutbfXHfuoZEmAA0HOHqn1aeRmlr0vIt48THdhdD1swQpo8/QbHaBuWV4905ECFjFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T09:47:51.235931Z"},"content_sha256":"29d891cf3d0f379123afe56f58d9a89f47ab58f1488c1e77f2d25c91270dff1d","schema_version":"1.0","event_id":"sha256:29d891cf3d0f379123afe56f58d9a89f47ab58f1488c1e77f2d25c91270dff1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZJEYXQTKGPJDT27MAN4OWVC4RM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal degrees of invariants of (super)groups - a connection to cryptology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexandr N. Zubkov, Frantisek Marko","submitted_at":"2016-08-04T14:34:35Z","abstract_excerpt":"We investigate questions related to the minimal degree of invariants of finitely generated diagonalizable groups. These questions were raised in connection to security of a public key cryptosystem based on invariants of diagonalizable groups. We derive results for minimal degrees of invariants of finite groups, abelian groups and algebraic groups. For algebraic groups we relate the minimal degree of the group to the minimal degrees of its tori. Finally, we investigate invariants of certain supergroups that are superanalogs of tori. It is interesting to note that a basis of these invariants is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01551","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":"2026-05-18T01:09:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lZfCNoy+T5hxdG1p4GQ8TILDSRH4lqvYj5Nl+s+RNhjGryZcKNSuH2fNKveMcI01RrZYT8rRb+buoWrop9FXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T09:47:51.236272Z"},"content_sha256":"7671458f5942b8e8fd5a83eaf49ad51a754f8354fe55531da8aa8af8fa5d8d05","schema_version":"1.0","event_id":"sha256:7671458f5942b8e8fd5a83eaf49ad51a754f8354fe55531da8aa8af8fa5d8d05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJEYXQTKGPJDT27MAN4OWVC4RM/bundle.json","state_url":"https://pith.science/pith/ZJEYXQTKGPJDT27MAN4OWVC4RM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJEYXQTKGPJDT27MAN4OWVC4RM/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":"2026-06-30T09:47:51Z","links":{"resolver":"https://pith.science/pith/ZJEYXQTKGPJDT27MAN4OWVC4RM","bundle":"https://pith.science/pith/ZJEYXQTKGPJDT27MAN4OWVC4RM/bundle.json","state":"https://pith.science/pith/ZJEYXQTKGPJDT27MAN4OWVC4RM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJEYXQTKGPJDT27MAN4OWVC4RM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZJEYXQTKGPJDT27MAN4OWVC4RM","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":"e8335e1e4855703c5f0c04794a240025c49dcd48ccbb635ec85a7f7fec356f2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-04T14:34:35Z","title_canon_sha256":"88349939619107759300d2c184df7acd2b2a834b477bc5f4d258337364cbb289"},"schema_version":"1.0","source":{"id":"1608.01551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01551","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01551v1","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01551","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZJEYXQTKGPJD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZJEYXQTKGPJDT27M","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZJEYXQTK","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:7671458f5942b8e8fd5a83eaf49ad51a754f8354fe55531da8aa8af8fa5d8d05","target":"graph","created_at":"2026-05-18T01:09:52Z","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":"We investigate questions related to the minimal degree of invariants of finitely generated diagonalizable groups. These questions were raised in connection to security of a public key cryptosystem based on invariants of diagonalizable groups. We derive results for minimal degrees of invariants of finite groups, abelian groups and algebraic groups. For algebraic groups we relate the minimal degree of the group to the minimal degrees of its tori. Finally, we investigate invariants of certain supergroups that are superanalogs of tori. It is interesting to note that a basis of these invariants is ","authors_text":"Alexandr N. Zubkov, Frantisek Marko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-04T14:34:35Z","title":"Minimal degrees of invariants of (super)groups - a connection to cryptology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01551","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":"sha256:29d891cf3d0f379123afe56f58d9a89f47ab58f1488c1e77f2d25c91270dff1d","target":"record","created_at":"2026-05-18T01:09:52Z","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":"e8335e1e4855703c5f0c04794a240025c49dcd48ccbb635ec85a7f7fec356f2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-04T14:34:35Z","title_canon_sha256":"88349939619107759300d2c184df7acd2b2a834b477bc5f4d258337364cbb289"},"schema_version":"1.0","source":{"id":"1608.01551","kind":"arxiv","version":1}},"canonical_sha256":"ca498bc26a33d239ebec0378eb545c8b0729c2b2ffe053a5e4a093300b7a8e4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca498bc26a33d239ebec0378eb545c8b0729c2b2ffe053a5e4a093300b7a8e4b","first_computed_at":"2026-05-18T01:09:52.142901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:52.142901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gAdv1BVmXAHTpzuWw1rB3OeTA7KJDymd/T+08z+65V8P9Bev/uXdZwG1wojIqmPDNnM++2mWzUhrl1BIPBwNCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:52.143535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29d891cf3d0f379123afe56f58d9a89f47ab58f1488c1e77f2d25c91270dff1d","sha256:7671458f5942b8e8fd5a83eaf49ad51a754f8354fe55531da8aa8af8fa5d8d05"],"state_sha256":"6ab46106d6aeab79d47212f212907263b3da07d37bbc90ea4af2918979f999e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RZWAat5wS0XugwqeCFYKH6ViYOIjnA6AeurrhyjMyqrZN6l06HfRaGkNB4PaY2SlYgggRA9RU0I/US05DapwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T09:47:51.238125Z","bundle_sha256":"d3ff50cd88da311e85c91f2a4a483f859778030b11d73c964a26b72cc54cba38"}}