{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BQPKH6QBIV2ZSKSDYLVL6B2EXW","short_pith_number":"pith:BQPKH6QB","canonical_record":{"source":{"id":"1602.07944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-23T12:33:53Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"24feca5bdaad2e0c15c142c8ea8bd8876bc0adbecae2d900e19b6aa6212d6f93","abstract_canon_sha256":"4779795e0ccecf401bd9a28dafba5ad10093bf55a21b30f9618580e5545072a0"},"schema_version":"1.0"},"canonical_sha256":"0c1ea3fa014575992a43c2eabf0744bdbde026c7f374bbc1b44e9ec8a5a8cdda","source":{"kind":"arxiv","id":"1602.07944","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07944","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07944v1","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07944","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"pith_short_12","alias_value":"BQPKH6QBIV2Z","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BQPKH6QBIV2ZSKSD","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BQPKH6QB","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BQPKH6QBIV2ZSKSDYLVL6B2EXW","target":"record","payload":{"canonical_record":{"source":{"id":"1602.07944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-23T12:33:53Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"24feca5bdaad2e0c15c142c8ea8bd8876bc0adbecae2d900e19b6aa6212d6f93","abstract_canon_sha256":"4779795e0ccecf401bd9a28dafba5ad10093bf55a21b30f9618580e5545072a0"},"schema_version":"1.0"},"canonical_sha256":"0c1ea3fa014575992a43c2eabf0744bdbde026c7f374bbc1b44e9ec8a5a8cdda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:58.219848Z","signature_b64":"W+BxQ6u5wm5IPjihrsaVb01B4b5UPNKgWnKng6pam1GcMB3E+rUBqROZ9Gtq23TT+LxSMEQqN1X3aIk4MSBbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c1ea3fa014575992a43c2eabf0744bdbde026c7f374bbc1b44e9ec8a5a8cdda","last_reissued_at":"2026-05-18T01:19:58.219144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:58.219144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.07944","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":"2026-05-18T01:19:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SWg/utiZqb3sLbTJQlljfVkSOqXBKxHW+UG+/fMQ/S1VsbiJEKxWvvqZgFEkSH4b184CPe2od4kIUzRMEI89Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:01:58.313966Z"},"content_sha256":"ee5495d4538144be74e3f37e6e934e55d1a44073342f6d5465de43221a47a1ed","schema_version":"1.0","event_id":"sha256:ee5495d4538144be74e3f37e6e934e55d1a44073342f6d5465de43221a47a1ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BQPKH6QBIV2ZSKSDYLVL6B2EXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Determination of sizes of optimal three-dimensional optical orthogonal codes of weight three with the AM-OPP restriction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Lidong Wang, Yanxun Chang","submitted_at":"2016-01-23T12:33:53Z","abstract_excerpt":"In this paper, we further investigate the constructions on three-dimensional $(u\\times v\\times w,k,1)$ optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM-OPP $3$-D $(u\\times v\\times w,k,1)$-OOCs) by way of the corresponding designs. Several new auxiliary designs such as incomplete holey group divisible designs and incomplete group divisible packings are introduced and therefore new constructions are presented. As a consequence, the exact number of codewords of an optimal AM-OPP $3$-D $(u\\times v\\times w,3,1)$-OOC is finally determined "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07944","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":"2026-05-18T01:19:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eONsf3dueHLLCnoPYRnfvUHdQIEoDHuzfW+s5m6StuumYAAPU4I58ntBZaJWnc/gDGfXZdOC/si2mRsyLxs4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:01:58.314310Z"},"content_sha256":"25165f7ae06920b8e52499b9c42b12dc62c95a14ea5c489dc837bfb734472d09","schema_version":"1.0","event_id":"sha256:25165f7ae06920b8e52499b9c42b12dc62c95a14ea5c489dc837bfb734472d09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQPKH6QBIV2ZSKSDYLVL6B2EXW/bundle.json","state_url":"https://pith.science/pith/BQPKH6QBIV2ZSKSDYLVL6B2EXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQPKH6QBIV2ZSKSDYLVL6B2EXW/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":"2026-06-09T18:01:58Z","links":{"resolver":"https://pith.science/pith/BQPKH6QBIV2ZSKSDYLVL6B2EXW","bundle":"https://pith.science/pith/BQPKH6QBIV2ZSKSDYLVL6B2EXW/bundle.json","state":"https://pith.science/pith/BQPKH6QBIV2ZSKSDYLVL6B2EXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQPKH6QBIV2ZSKSDYLVL6B2EXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BQPKH6QBIV2ZSKSDYLVL6B2EXW","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":"4779795e0ccecf401bd9a28dafba5ad10093bf55a21b30f9618580e5545072a0","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-23T12:33:53Z","title_canon_sha256":"24feca5bdaad2e0c15c142c8ea8bd8876bc0adbecae2d900e19b6aa6212d6f93"},"schema_version":"1.0","source":{"id":"1602.07944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07944","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07944v1","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07944","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"pith_short_12","alias_value":"BQPKH6QBIV2Z","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BQPKH6QBIV2ZSKSD","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BQPKH6QB","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:25165f7ae06920b8e52499b9c42b12dc62c95a14ea5c489dc837bfb734472d09","target":"graph","created_at":"2026-05-18T01:19:58Z","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":"In this paper, we further investigate the constructions on three-dimensional $(u\\times v\\times w,k,1)$ optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM-OPP $3$-D $(u\\times v\\times w,k,1)$-OOCs) by way of the corresponding designs. Several new auxiliary designs such as incomplete holey group divisible designs and incomplete group divisible packings are introduced and therefore new constructions are presented. As a consequence, the exact number of codewords of an optimal AM-OPP $3$-D $(u\\times v\\times w,3,1)$-OOC is finally determined ","authors_text":"Lidong Wang, Yanxun Chang","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-23T12:33:53Z","title":"Determination of sizes of optimal three-dimensional optical orthogonal codes of weight three with the AM-OPP restriction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07944","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:ee5495d4538144be74e3f37e6e934e55d1a44073342f6d5465de43221a47a1ed","target":"record","created_at":"2026-05-18T01:19:58Z","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":"4779795e0ccecf401bd9a28dafba5ad10093bf55a21b30f9618580e5545072a0","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-23T12:33:53Z","title_canon_sha256":"24feca5bdaad2e0c15c142c8ea8bd8876bc0adbecae2d900e19b6aa6212d6f93"},"schema_version":"1.0","source":{"id":"1602.07944","kind":"arxiv","version":1}},"canonical_sha256":"0c1ea3fa014575992a43c2eabf0744bdbde026c7f374bbc1b44e9ec8a5a8cdda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c1ea3fa014575992a43c2eabf0744bdbde026c7f374bbc1b44e9ec8a5a8cdda","first_computed_at":"2026-05-18T01:19:58.219144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:58.219144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W+BxQ6u5wm5IPjihrsaVb01B4b5UPNKgWnKng6pam1GcMB3E+rUBqROZ9Gtq23TT+LxSMEQqN1X3aIk4MSBbCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:58.219848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee5495d4538144be74e3f37e6e934e55d1a44073342f6d5465de43221a47a1ed","sha256:25165f7ae06920b8e52499b9c42b12dc62c95a14ea5c489dc837bfb734472d09"],"state_sha256":"57528305db840448aa07f8d64c21993b52389ba418b6f1939c63a0cb53b3f921"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xT/OYkw0BthDOWUWvb3jBbVm1a9J1aKs3RyJblIOjGv9fCFVOmzdwDDyFi+cakohsgM2KgiwtIerifNuq9rRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T18:01:58.316242Z","bundle_sha256":"0c9e5fc403f9528c230bc0574ecf2686d024fbafe8cc8957a63689b577b30582"}}