{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:S3EYDRB7PY7TBXX2O4SUOJ44XT","short_pith_number":"pith:S3EYDRB7","canonical_record":{"source":{"id":"2506.03688","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-06-04T08:18:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1f5a44de1972ca089eb3a5bc00957974d8671643d0a5e83c397e046e59002b7e","abstract_canon_sha256":"98ccacf7562058b8ea7cf27022f6928eb8e63c66b63388d5d83702d47f9570d6"},"schema_version":"1.0"},"canonical_sha256":"96c981c43f7e3f30defa772547279cbce8c574ad28c8837744bc29df7c301c9c","source":{"kind":"arxiv","id":"2506.03688","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.03688","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"arxiv_version","alias_value":"2506.03688v1","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03688","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"pith_short_12","alias_value":"S3EYDRB7PY7T","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"pith_short_16","alias_value":"S3EYDRB7PY7TBXX2","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"pith_short_8","alias_value":"S3EYDRB7","created_at":"2026-07-05T11:15:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:S3EYDRB7PY7TBXX2O4SUOJ44XT","target":"record","payload":{"canonical_record":{"source":{"id":"2506.03688","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-06-04T08:18:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1f5a44de1972ca089eb3a5bc00957974d8671643d0a5e83c397e046e59002b7e","abstract_canon_sha256":"98ccacf7562058b8ea7cf27022f6928eb8e63c66b63388d5d83702d47f9570d6"},"schema_version":"1.0"},"canonical_sha256":"96c981c43f7e3f30defa772547279cbce8c574ad28c8837744bc29df7c301c9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:50.036072Z","signature_b64":"5JgGVfDOzBCNzduj+6C4pK96hhIM16xH8lMhY23qLDtl/v+GXDpfDh3dmSKy2gA8j9f4kZlod6NGfjacF5FAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96c981c43f7e3f30defa772547279cbce8c574ad28c8837744bc29df7c301c9c","last_reissued_at":"2026-07-05T11:15:50.035604Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:50.035604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.03688","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":"2026-07-05T11:15:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOd6YIDO8U3tZs6YnDBbPGjmfFHmnc29iZolHo2DLXlP5Ahjki/CgGnDYf866SLkFTHpWWqbdSQ5dJeUVxnxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T08:26:01.601527Z"},"content_sha256":"223a2c75aa501d5c8c6027022a9392213edade3f0f93012870e7df32751079a1","schema_version":"1.0","event_id":"sha256:223a2c75aa501d5c8c6027022a9392213edade3f0f93012870e7df32751079a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:S3EYDRB7PY7TBXX2O4SUOJ44XT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On irredundant orthogonal arrays","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Maryam Bajalan, Peter Boyvalenkov","submitted_at":"2025-06-04T08:18:36Z","abstract_excerpt":"An orthogonal array (OA), denoted by $\\text{OA}(M, n, q, t)$, is an $M \\times n$ matrix over an alphabet of size $q$ such that every selection of $t$ columns contains each possible $t$-tuple exactly $\\lambda=M / q^t$ times. An irredundant orthogonal array (IrOA) is an OA with the additional property that, in any selection of $n - t$ columns, all resulting rows are distinct. IrOAs were first introduced by Goyeneche and \\.{Z}yczkowski in 2014 to construct $t$-uniform quantum states without redundant information. Beyond their quantum applications, we focus on IrOAs as a combinatorial and coding t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03688","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/2506.03688/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":"2026-07-05T11:15:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xzqfWqZhhybKKwPsczjkNqsNk2GwFrVaOnkXy8cu10JhRvIq2GPzKfDFDyrjXesRnKkhH5FxCH1Tjw6GsHWCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T08:26:01.602537Z"},"content_sha256":"888f0bf2f6c572001b78982424b04d31cfb2e03bb475b115c780ee2fdbc966a8","schema_version":"1.0","event_id":"sha256:888f0bf2f6c572001b78982424b04d31cfb2e03bb475b115c780ee2fdbc966a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S3EYDRB7PY7TBXX2O4SUOJ44XT/bundle.json","state_url":"https://pith.science/pith/S3EYDRB7PY7TBXX2O4SUOJ44XT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S3EYDRB7PY7TBXX2O4SUOJ44XT/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":"2026-08-18T08:26:01Z","links":{"resolver":"https://pith.science/pith/S3EYDRB7PY7TBXX2O4SUOJ44XT","bundle":"https://pith.science/pith/S3EYDRB7PY7TBXX2O4SUOJ44XT/bundle.json","state":"https://pith.science/pith/S3EYDRB7PY7TBXX2O4SUOJ44XT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S3EYDRB7PY7TBXX2O4SUOJ44XT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:S3EYDRB7PY7TBXX2O4SUOJ44XT","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":"98ccacf7562058b8ea7cf27022f6928eb8e63c66b63388d5d83702d47f9570d6","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-06-04T08:18:36Z","title_canon_sha256":"1f5a44de1972ca089eb3a5bc00957974d8671643d0a5e83c397e046e59002b7e"},"schema_version":"1.0","source":{"id":"2506.03688","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.03688","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"arxiv_version","alias_value":"2506.03688v1","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03688","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"pith_short_12","alias_value":"S3EYDRB7PY7T","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"pith_short_16","alias_value":"S3EYDRB7PY7TBXX2","created_at":"2026-07-05T11:15:50Z"},{"alias_kind":"pith_short_8","alias_value":"S3EYDRB7","created_at":"2026-07-05T11:15:50Z"}],"graph_snapshots":[{"event_id":"sha256:888f0bf2f6c572001b78982424b04d31cfb2e03bb475b115c780ee2fdbc966a8","target":"graph","created_at":"2026-07-05T11:15:50Z","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/2506.03688/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An orthogonal array (OA), denoted by $\\text{OA}(M, n, q, t)$, is an $M \\times n$ matrix over an alphabet of size $q$ such that every selection of $t$ columns contains each possible $t$-tuple exactly $\\lambda=M / q^t$ times. An irredundant orthogonal array (IrOA) is an OA with the additional property that, in any selection of $n - t$ columns, all resulting rows are distinct. IrOAs were first introduced by Goyeneche and \\.{Z}yczkowski in 2014 to construct $t$-uniform quantum states without redundant information. Beyond their quantum applications, we focus on IrOAs as a combinatorial and coding t","authors_text":"Maryam Bajalan, Peter Boyvalenkov","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-06-04T08:18:36Z","title":"On irredundant orthogonal arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03688","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":"sha256:223a2c75aa501d5c8c6027022a9392213edade3f0f93012870e7df32751079a1","target":"record","created_at":"2026-07-05T11:15:50Z","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":"98ccacf7562058b8ea7cf27022f6928eb8e63c66b63388d5d83702d47f9570d6","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-06-04T08:18:36Z","title_canon_sha256":"1f5a44de1972ca089eb3a5bc00957974d8671643d0a5e83c397e046e59002b7e"},"schema_version":"1.0","source":{"id":"2506.03688","kind":"arxiv","version":1}},"canonical_sha256":"96c981c43f7e3f30defa772547279cbce8c574ad28c8837744bc29df7c301c9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96c981c43f7e3f30defa772547279cbce8c574ad28c8837744bc29df7c301c9c","first_computed_at":"2026-07-05T11:15:50.035604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:50.035604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5JgGVfDOzBCNzduj+6C4pK96hhIM16xH8lMhY23qLDtl/v+GXDpfDh3dmSKy2gA8j9f4kZlod6NGfjacF5FAAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:50.036072Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.03688","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:223a2c75aa501d5c8c6027022a9392213edade3f0f93012870e7df32751079a1","sha256:888f0bf2f6c572001b78982424b04d31cfb2e03bb475b115c780ee2fdbc966a8"],"state_sha256":"4f2b6e2743882db0887936798f9f8047c1ade5dac67171ed07248534a6f6b55b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BqZX4Xwk0ZXQOuM+AtBNqq/OtQDuLV/qTmiki6/+PDwJXsxEOGQVQ6b/oegA2st/cTuwTarkJsAiFcYQ71uLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T08:26:01.609525Z","bundle_sha256":"a02c8bec51a92174dbd990038ef597700d5719ce96e37b9f178540b6a712ff25"}}