{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GWBIJ3GZCEB4TSIB64C7BF5KCX","short_pith_number":"pith:GWBIJ3GZ","canonical_record":{"source":{"id":"1701.02325","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-09T19:13:11Z","cross_cats_sorted":[],"title_canon_sha256":"f1769b48993bd5dca5f41924848c8ddd380fc614b343314419ccd7ce51c8e15b","abstract_canon_sha256":"8d5e58bce110288ae8fb3415da5c9ca94d4f3df060b2fff5c8504a05d939a3b1"},"schema_version":"1.0"},"canonical_sha256":"358284ecd91103c9c901f705f097aa15feea0928bdbebcf1b2fc6ba52bb31daf","source":{"kind":"arxiv","id":"1701.02325","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02325","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02325v1","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02325","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"pith_short_12","alias_value":"GWBIJ3GZCEB4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GWBIJ3GZCEB4TSIB","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GWBIJ3GZ","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GWBIJ3GZCEB4TSIB64C7BF5KCX","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02325","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-09T19:13:11Z","cross_cats_sorted":[],"title_canon_sha256":"f1769b48993bd5dca5f41924848c8ddd380fc614b343314419ccd7ce51c8e15b","abstract_canon_sha256":"8d5e58bce110288ae8fb3415da5c9ca94d4f3df060b2fff5c8504a05d939a3b1"},"schema_version":"1.0"},"canonical_sha256":"358284ecd91103c9c901f705f097aa15feea0928bdbebcf1b2fc6ba52bb31daf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:04.549509Z","signature_b64":"J2PuPMKs18yo8/mewe7Ipakm0dBHSv0MSjGj0eiM3DAaxvVODcxwej7ZDy1C/9ed5y9yDSBq/lNlOfQjhrhiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"358284ecd91103c9c901f705f097aa15feea0928bdbebcf1b2fc6ba52bb31daf","last_reissued_at":"2026-05-18T00:53:04.548917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:04.548917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02325","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":"2026-05-18T00:53:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UyGsKCbLMN4e8VuDrAwETAEDVbLmjPeaxbxd/TNDApe8uf/mR0MKkx8UrlPuDD9EnThDjDj/hOFlYcP8GjU2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:38:38.048609Z"},"content_sha256":"39e0fd4239711876c361279ff5999aeed823cac9de4a77a92df52276225bec17","schema_version":"1.0","event_id":"sha256:39e0fd4239711876c361279ff5999aeed823cac9de4a77a92df52276225bec17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GWBIJ3GZCEB4TSIB64C7BF5KCX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shuffled equi-n-squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"M. Van de Vel (Vrije Universiteit Amsterdam, Universiteit Antwerpen)","submitted_at":"2017-01-09T19:13:11Z","abstract_excerpt":"A formal n-square is the set of positions in an square matrix of size n. A shuffle of a formal n-square consists of independent rotations of each row and of each column. A key result turns out to be valid at least for n <= 34 and n = 37: Each set of n positions can be mapped with one shuffle onto a transversal of the columns. We consider two applications to equi-n-squares (i.e., n-matrices filled with digits 0, .., n - 1 in equal amounts).\n  First, a shuffled equi-n-square can be seen as a torus with n colors and two orthogonal layers of n rings that can be rotated. Unlike Rubik's cube, each p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02325","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":"2026-05-18T00:53:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9x2L/ZA0f7B3nzicu04i3m1qf42y7pp0x63aeG8VG88cOEWGbn6MMOtP19LsPaesGskbX5lvpEgAFKulZqaaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:38:38.049349Z"},"content_sha256":"83a5757319c2eb43804462b294878a220132f62be7868e730aef82fd5f2261e4","schema_version":"1.0","event_id":"sha256:83a5757319c2eb43804462b294878a220132f62be7868e730aef82fd5f2261e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GWBIJ3GZCEB4TSIB64C7BF5KCX/bundle.json","state_url":"https://pith.science/pith/GWBIJ3GZCEB4TSIB64C7BF5KCX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GWBIJ3GZCEB4TSIB64C7BF5KCX/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":"2026-06-09T08:38:38Z","links":{"resolver":"https://pith.science/pith/GWBIJ3GZCEB4TSIB64C7BF5KCX","bundle":"https://pith.science/pith/GWBIJ3GZCEB4TSIB64C7BF5KCX/bundle.json","state":"https://pith.science/pith/GWBIJ3GZCEB4TSIB64C7BF5KCX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GWBIJ3GZCEB4TSIB64C7BF5KCX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GWBIJ3GZCEB4TSIB64C7BF5KCX","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":"8d5e58bce110288ae8fb3415da5c9ca94d4f3df060b2fff5c8504a05d939a3b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-09T19:13:11Z","title_canon_sha256":"f1769b48993bd5dca5f41924848c8ddd380fc614b343314419ccd7ce51c8e15b"},"schema_version":"1.0","source":{"id":"1701.02325","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02325","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02325v1","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02325","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"pith_short_12","alias_value":"GWBIJ3GZCEB4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GWBIJ3GZCEB4TSIB","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GWBIJ3GZ","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:83a5757319c2eb43804462b294878a220132f62be7868e730aef82fd5f2261e4","target":"graph","created_at":"2026-05-18T00:53:04Z","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":"A formal n-square is the set of positions in an square matrix of size n. A shuffle of a formal n-square consists of independent rotations of each row and of each column. A key result turns out to be valid at least for n <= 34 and n = 37: Each set of n positions can be mapped with one shuffle onto a transversal of the columns. We consider two applications to equi-n-squares (i.e., n-matrices filled with digits 0, .., n - 1 in equal amounts).\n  First, a shuffled equi-n-square can be seen as a torus with n colors and two orthogonal layers of n rings that can be rotated. Unlike Rubik's cube, each p","authors_text":"M. Van de Vel (Vrije Universiteit Amsterdam, Universiteit Antwerpen)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-09T19:13:11Z","title":"Shuffled equi-n-squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02325","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":"sha256:39e0fd4239711876c361279ff5999aeed823cac9de4a77a92df52276225bec17","target":"record","created_at":"2026-05-18T00:53:04Z","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":"8d5e58bce110288ae8fb3415da5c9ca94d4f3df060b2fff5c8504a05d939a3b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-09T19:13:11Z","title_canon_sha256":"f1769b48993bd5dca5f41924848c8ddd380fc614b343314419ccd7ce51c8e15b"},"schema_version":"1.0","source":{"id":"1701.02325","kind":"arxiv","version":1}},"canonical_sha256":"358284ecd91103c9c901f705f097aa15feea0928bdbebcf1b2fc6ba52bb31daf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"358284ecd91103c9c901f705f097aa15feea0928bdbebcf1b2fc6ba52bb31daf","first_computed_at":"2026-05-18T00:53:04.548917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:04.548917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J2PuPMKs18yo8/mewe7Ipakm0dBHSv0MSjGj0eiM3DAaxvVODcxwej7ZDy1C/9ed5y9yDSBq/lNlOfQjhrhiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:04.549509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02325","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39e0fd4239711876c361279ff5999aeed823cac9de4a77a92df52276225bec17","sha256:83a5757319c2eb43804462b294878a220132f62be7868e730aef82fd5f2261e4"],"state_sha256":"8a9bad72858e3a91771c00355a3b3ee206cd10fe1d7108a7561c57f722114010"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qKC+Mp/xJFhKNEuF3F1lgE3nv1+FC1o3BhcjswR4BZUeraBXDwqni2JsHcfhbHrKnNbJzpSnq7p5aRXHA8FaAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:38:38.053255Z","bundle_sha256":"38eee65a132f9a08f15f497813263d603f2a9c38cea8c6056d1d3ce8956d6ac7"}}