{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PAIJFYRR3P2RW72SJXRKBARXUI","short_pith_number":"pith:PAIJFYRR","canonical_record":{"source":{"id":"1210.5724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-21T13:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"d2e31294ff880323eb0443e94a772ed036d3a9957b48d5b37a73a98831fff65c","abstract_canon_sha256":"bdda4a3e7a1046957d405fe76b79100239d18c7bb4cdb410419b0f91cca07b0f"},"schema_version":"1.0"},"canonical_sha256":"781092e231dbf51b7f524de2a08237a2193eac3edfeb7280af84ba9763c25a1b","source":{"kind":"arxiv","id":"1210.5724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5724","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5724v1","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5724","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"PAIJFYRR3P2R","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PAIJFYRR3P2RW72S","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PAIJFYRR","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PAIJFYRR3P2RW72SJXRKBARXUI","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-21T13:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"d2e31294ff880323eb0443e94a772ed036d3a9957b48d5b37a73a98831fff65c","abstract_canon_sha256":"bdda4a3e7a1046957d405fe76b79100239d18c7bb4cdb410419b0f91cca07b0f"},"schema_version":"1.0"},"canonical_sha256":"781092e231dbf51b7f524de2a08237a2193eac3edfeb7280af84ba9763c25a1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:43.212141Z","signature_b64":"YduEfcmHrSfJza/iYDoWcq+KL5GGXYjn1fpJDTSScO7IoxmhDOdUrdsLXL/A0/wOoH40mMdnkTyIIMSw0ydTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"781092e231dbf51b7f524de2a08237a2193eac3edfeb7280af84ba9763c25a1b","last_reissued_at":"2026-05-18T03:42:43.211536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:43.211536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5724","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":"2026-05-18T03:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TFZozIU/TwjuH2Hj/tslajaiF0I4jvYaS5sTSvT72+2IOv2grZ9sSfW5aEtZ3Dw/+4ho4QpImGD9CIgEA9EJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:38:18.861617Z"},"content_sha256":"f701b72983ec78cc3354228193a5db2c98092ae45b70fe192caf53dfd3e78c4c","schema_version":"1.0","event_id":"sha256:f701b72983ec78cc3354228193a5db2c98092ae45b70fe192caf53dfd3e78c4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PAIJFYRR3P2RW72SJXRKBARXUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphisms of Codes in the Grassmann Scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Vardy, Tuvi Etzion","submitted_at":"2012-10-21T13:05:30Z","abstract_excerpt":"Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on lines in PG($n,p$) or codes in the Grassmannian, to form automorphisms groups in the Grassmanian and in its codes. These automorphisms are examined on two classical coding problems in the Grassmannian. The first is the existence of a parallelism with lines in the related projective geometry and the second is the existence of a Steiner structure. A computer search was applied to find parallelisms and codes. A new parallelism of lines in PG(5,3) was formed. A parallelism with these parameters was n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5724","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":"2026-05-18T03:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nF0ABdO1BPAA2cxH8ESWS33OJ6sCugUtnZXkjdmgoCksANhD5IfptwS7JAjqUClW6/wZbkfm7V5k2xGwA9ElBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:38:18.861983Z"},"content_sha256":"f9e515337e79fe2f59f98207617ba8c7964b50fe7075db64e8bc9594c0fcdb3d","schema_version":"1.0","event_id":"sha256:f9e515337e79fe2f59f98207617ba8c7964b50fe7075db64e8bc9594c0fcdb3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PAIJFYRR3P2RW72SJXRKBARXUI/bundle.json","state_url":"https://pith.science/pith/PAIJFYRR3P2RW72SJXRKBARXUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PAIJFYRR3P2RW72SJXRKBARXUI/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":"2026-05-30T10:38:18Z","links":{"resolver":"https://pith.science/pith/PAIJFYRR3P2RW72SJXRKBARXUI","bundle":"https://pith.science/pith/PAIJFYRR3P2RW72SJXRKBARXUI/bundle.json","state":"https://pith.science/pith/PAIJFYRR3P2RW72SJXRKBARXUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PAIJFYRR3P2RW72SJXRKBARXUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PAIJFYRR3P2RW72SJXRKBARXUI","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":"bdda4a3e7a1046957d405fe76b79100239d18c7bb4cdb410419b0f91cca07b0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-21T13:05:30Z","title_canon_sha256":"d2e31294ff880323eb0443e94a772ed036d3a9957b48d5b37a73a98831fff65c"},"schema_version":"1.0","source":{"id":"1210.5724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5724","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5724v1","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5724","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"PAIJFYRR3P2R","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PAIJFYRR3P2RW72S","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PAIJFYRR","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:f9e515337e79fe2f59f98207617ba8c7964b50fe7075db64e8bc9594c0fcdb3d","target":"graph","created_at":"2026-05-18T03:42:43Z","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":"Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on lines in PG($n,p$) or codes in the Grassmannian, to form automorphisms groups in the Grassmanian and in its codes. These automorphisms are examined on two classical coding problems in the Grassmannian. The first is the existence of a parallelism with lines in the related projective geometry and the second is the existence of a Steiner structure. A computer search was applied to find parallelisms and codes. A new parallelism of lines in PG(5,3) was formed. A parallelism with these parameters was n","authors_text":"Alexander Vardy, Tuvi Etzion","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-21T13:05:30Z","title":"Automorphisms of Codes in the Grassmann Scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5724","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:f701b72983ec78cc3354228193a5db2c98092ae45b70fe192caf53dfd3e78c4c","target":"record","created_at":"2026-05-18T03:42:43Z","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":"bdda4a3e7a1046957d405fe76b79100239d18c7bb4cdb410419b0f91cca07b0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-21T13:05:30Z","title_canon_sha256":"d2e31294ff880323eb0443e94a772ed036d3a9957b48d5b37a73a98831fff65c"},"schema_version":"1.0","source":{"id":"1210.5724","kind":"arxiv","version":1}},"canonical_sha256":"781092e231dbf51b7f524de2a08237a2193eac3edfeb7280af84ba9763c25a1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"781092e231dbf51b7f524de2a08237a2193eac3edfeb7280af84ba9763c25a1b","first_computed_at":"2026-05-18T03:42:43.211536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:43.211536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YduEfcmHrSfJza/iYDoWcq+KL5GGXYjn1fpJDTSScO7IoxmhDOdUrdsLXL/A0/wOoH40mMdnkTyIIMSw0ydTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:43.212141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f701b72983ec78cc3354228193a5db2c98092ae45b70fe192caf53dfd3e78c4c","sha256:f9e515337e79fe2f59f98207617ba8c7964b50fe7075db64e8bc9594c0fcdb3d"],"state_sha256":"644faa78dfcc8a59eec460ac222bddef665944e2e77ae85707c6ec5f8f836e98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VR5CdwRwhbGU9OnVkpONEqVwFAhIe3TNvlyAA172l2YIGTkKERcRo19rCcso/l0M/XHIJ/RXR8ZFr71hWBeJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:38:18.864306Z","bundle_sha256":"82d4054f30559c625a56b96db71637debbf2a11817d95509052fc8a7989b3254"}}