{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GMEPDE2B6UKAORT357WBFSG5GL","short_pith_number":"pith:GMEPDE2B","canonical_record":{"source":{"id":"1007.5434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-30T12:56:25Z","cross_cats_sorted":[],"title_canon_sha256":"3bc7c65c37df424e513967f9c4cc14d7e2b05c79e4043834b5157a431aa89cea","abstract_canon_sha256":"54ef5f6f5d8eb1e3b262ac0607e096afcf6d75569489f4012322b00b784d42d4"},"schema_version":"1.0"},"canonical_sha256":"3308f19341f51407467befec12c8dd32fa6fdb55aca36494c3da97c08b4dae83","source":{"kind":"arxiv","id":"1007.5434","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5434","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5434v1","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5434","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"GMEPDE2B6UKA","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GMEPDE2B6UKAORT3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GMEPDE2B","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GMEPDE2B6UKAORT357WBFSG5GL","target":"record","payload":{"canonical_record":{"source":{"id":"1007.5434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-30T12:56:25Z","cross_cats_sorted":[],"title_canon_sha256":"3bc7c65c37df424e513967f9c4cc14d7e2b05c79e4043834b5157a431aa89cea","abstract_canon_sha256":"54ef5f6f5d8eb1e3b262ac0607e096afcf6d75569489f4012322b00b784d42d4"},"schema_version":"1.0"},"canonical_sha256":"3308f19341f51407467befec12c8dd32fa6fdb55aca36494c3da97c08b4dae83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:45.221507Z","signature_b64":"aHFRRHyw4Ai66XIBTeEPrMNV3LHWK8ysi4pV5RxQihCwJin0S4mHtQgSceSma+7Pa2X0qh7JSHimcv+dbQVvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3308f19341f51407467befec12c8dd32fa6fdb55aca36494c3da97c08b4dae83","last_reissued_at":"2026-05-18T04:42:45.220953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:45.220953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.5434","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":"2026-05-18T04:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LRTFYfsrqP5IL93f732XxIM3odxGN4EqMhQMCcsKLSuBiNamWy3Bv0kkTBzNOc7+NZN++T1KbxACWIJPU+tFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:32:30.052465Z"},"content_sha256":"4606d145c91fe0553917fabc3f4c7aa797cb28ae2bdeb59a2cd4d39cf92b3f5d","schema_version":"1.0","event_id":"sha256:4606d145c91fe0553917fabc3f4c7aa797cb28ae2bdeb59a2cd4d39cf92b3f5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GMEPDE2B6UKAORT357WBFSG5GL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new Yang number and consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dragomir Z. Djokovic","submitted_at":"2010-07-30T12:56:25Z","abstract_excerpt":"Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, A and B of length m and C and D of length n, the sum of whose non-periodic auto-correlation functions is zero. Base sequences and some special subclasses of BS(n+1,n) known as normal and near-normal sequences, NS(n) and NN(n), as well as T-sequences and orthogonal designs play a prominent role in modern constructions of Hadamard matrices. In our previous papers (see the references) we have classified the near-normal sequences NN(s) for all even integers s <= 32 (they do not exist for odd s>1). We now extend the classificatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5434","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":"2026-05-18T04:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQU9Ly3fsH78k8J6Ls3T+UVG4bCRs6F+ybOA6ZSFIqo55SCoPxlPMtUWx7cUWE7eWUK5jPXPl7/JzZ5iYxGhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:32:30.052795Z"},"content_sha256":"2787ebc3d87a29802d6198e7b2fccafef246fd80bb9718c339d6b8409697a338","schema_version":"1.0","event_id":"sha256:2787ebc3d87a29802d6198e7b2fccafef246fd80bb9718c339d6b8409697a338"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GMEPDE2B6UKAORT357WBFSG5GL/bundle.json","state_url":"https://pith.science/pith/GMEPDE2B6UKAORT357WBFSG5GL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GMEPDE2B6UKAORT357WBFSG5GL/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":"2026-06-08T09:32:30Z","links":{"resolver":"https://pith.science/pith/GMEPDE2B6UKAORT357WBFSG5GL","bundle":"https://pith.science/pith/GMEPDE2B6UKAORT357WBFSG5GL/bundle.json","state":"https://pith.science/pith/GMEPDE2B6UKAORT357WBFSG5GL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GMEPDE2B6UKAORT357WBFSG5GL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GMEPDE2B6UKAORT357WBFSG5GL","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":"54ef5f6f5d8eb1e3b262ac0607e096afcf6d75569489f4012322b00b784d42d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-30T12:56:25Z","title_canon_sha256":"3bc7c65c37df424e513967f9c4cc14d7e2b05c79e4043834b5157a431aa89cea"},"schema_version":"1.0","source":{"id":"1007.5434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5434","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5434v1","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5434","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"GMEPDE2B6UKA","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GMEPDE2B6UKAORT3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GMEPDE2B","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:2787ebc3d87a29802d6198e7b2fccafef246fd80bb9718c339d6b8409697a338","target":"graph","created_at":"2026-05-18T04:42:45Z","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":"Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, A and B of length m and C and D of length n, the sum of whose non-periodic auto-correlation functions is zero. Base sequences and some special subclasses of BS(n+1,n) known as normal and near-normal sequences, NS(n) and NN(n), as well as T-sequences and orthogonal designs play a prominent role in modern constructions of Hadamard matrices. In our previous papers (see the references) we have classified the near-normal sequences NN(s) for all even integers s <= 32 (they do not exist for odd s>1). We now extend the classificatio","authors_text":"Dragomir Z. Djokovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-30T12:56:25Z","title":"A new Yang number and consequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5434","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":"sha256:4606d145c91fe0553917fabc3f4c7aa797cb28ae2bdeb59a2cd4d39cf92b3f5d","target":"record","created_at":"2026-05-18T04:42:45Z","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":"54ef5f6f5d8eb1e3b262ac0607e096afcf6d75569489f4012322b00b784d42d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-30T12:56:25Z","title_canon_sha256":"3bc7c65c37df424e513967f9c4cc14d7e2b05c79e4043834b5157a431aa89cea"},"schema_version":"1.0","source":{"id":"1007.5434","kind":"arxiv","version":1}},"canonical_sha256":"3308f19341f51407467befec12c8dd32fa6fdb55aca36494c3da97c08b4dae83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3308f19341f51407467befec12c8dd32fa6fdb55aca36494c3da97c08b4dae83","first_computed_at":"2026-05-18T04:42:45.220953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:45.220953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aHFRRHyw4Ai66XIBTeEPrMNV3LHWK8ysi4pV5RxQihCwJin0S4mHtQgSceSma+7Pa2X0qh7JSHimcv+dbQVvDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:45.221507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4606d145c91fe0553917fabc3f4c7aa797cb28ae2bdeb59a2cd4d39cf92b3f5d","sha256:2787ebc3d87a29802d6198e7b2fccafef246fd80bb9718c339d6b8409697a338"],"state_sha256":"50ebcddca0ff395cef134766bd85d57e069d08ff2695a0701828f0539435e2d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V84KcEvpPNcw5xz3/VMb0iMg9kqfl/QjaKJlv2bNpNQa6KOTwOWP3HvB0EjLz+ztvDMXQEDtdnrb57J5QAuNBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:32:30.054830Z","bundle_sha256":"db229827df7825105e20c16bca56432e038de877a920dcad559c829a4ffdc7f8"}}