{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3AY2EXMLYQ3U3O76LZ7O7X5XTU","short_pith_number":"pith:3AY2EXML","canonical_record":{"source":{"id":"2506.00945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-06-01T10:29:47Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9f1ce08a14335607c2f1d09ebd17e4e4967e1111613a0078f72b98aeb3c7e1d6","abstract_canon_sha256":"2e398370133b5de6c556122f151d3ff535c43fab24d7d493f3fa593e7e87cdb0"},"schema_version":"1.0"},"canonical_sha256":"d831a25d8bc4374dbbfe5e7eefdfb79d219ce1bceb9d7e0a3f61a8bf2d887be6","source":{"kind":"arxiv","id":"2506.00945","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00945","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00945v1","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00945","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"3AY2EXMLYQ3U","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"pith_short_16","alias_value":"3AY2EXMLYQ3U3O76","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"pith_short_8","alias_value":"3AY2EXML","created_at":"2026-07-05T11:13:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3AY2EXMLYQ3U3O76LZ7O7X5XTU","target":"record","payload":{"canonical_record":{"source":{"id":"2506.00945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-06-01T10:29:47Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9f1ce08a14335607c2f1d09ebd17e4e4967e1111613a0078f72b98aeb3c7e1d6","abstract_canon_sha256":"2e398370133b5de6c556122f151d3ff535c43fab24d7d493f3fa593e7e87cdb0"},"schema_version":"1.0"},"canonical_sha256":"d831a25d8bc4374dbbfe5e7eefdfb79d219ce1bceb9d7e0a3f61a8bf2d887be6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:13:43.263822Z","signature_b64":"D7KYYWl0919CSwNkGrexg6CVni3dc4gfFI+OXa876yd33ih3R5qLLfCwB3YMCUCLUblQLFqsKrmJCLUtIGyeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d831a25d8bc4374dbbfe5e7eefdfb79d219ce1bceb9d7e0a3f61a8bf2d887be6","last_reissued_at":"2026-07-05T11:13:43.263346Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:13:43.263346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.00945","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":"2026-07-05T11:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jc9g6jtwo7ogTZ+L/k96G+VByxpOufUVYn60UhaU309IdEQ5tDJXLIv2yTc12q6TdPzxsueGphcxZOQ7bOrRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:26:11.586580Z"},"content_sha256":"268b16f2ee034a1515048b08c13005785728843820a750af4c1221aad95b52c1","schema_version":"1.0","event_id":"sha256:268b16f2ee034a1515048b08c13005785728843820a750af4c1221aad95b52c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3AY2EXMLYQ3U3O76LZ7O7X5XTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructions of Optimal Frequency-Hopping Sequences with Controlled Minimum Gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chen Li, Chunlei Li, Dian Li, Xiangyong Zeng","submitted_at":"2025-06-01T10:29:47Z","abstract_excerpt":"Frequency-hopping sequences (FHSs) with low Hamming correlation and wide gaps significantly contribute to the anti-interference performance in FH communication systems. This paper investigates FHSs with optimal Hamming correlation and controlled minimum gaps. We start with the discussion of the upper bounds on the minimum gaps of uniform FHSs and then propose a general construction of optimal uniform wide-gap FHSs with length 2l and 3l, which includes the work by Li et al. in IEEE Trans. Inf. Theory, vol. 68, no. 1, 2022 as a special case. Furthermore, we present a recursive construction of FH"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00945","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/2506.00945/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":"2026-07-05T11:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvWBTK/+vLOfzlNqvhg5VMZWK6G9PnBdK+kCP44sgAQlZQ1g6cWIPgFr+OWhcOLlqe7sUyu/G/gN06ieiLLpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:26:11.587642Z"},"content_sha256":"c6c6b91e4053827b9d6f1df59830910045ff4d474931d92da563b66391abfc74","schema_version":"1.0","event_id":"sha256:c6c6b91e4053827b9d6f1df59830910045ff4d474931d92da563b66391abfc74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3AY2EXMLYQ3U3O76LZ7O7X5XTU/bundle.json","state_url":"https://pith.science/pith/3AY2EXMLYQ3U3O76LZ7O7X5XTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3AY2EXMLYQ3U3O76LZ7O7X5XTU/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":"2026-08-08T11:26:11Z","links":{"resolver":"https://pith.science/pith/3AY2EXMLYQ3U3O76LZ7O7X5XTU","bundle":"https://pith.science/pith/3AY2EXMLYQ3U3O76LZ7O7X5XTU/bundle.json","state":"https://pith.science/pith/3AY2EXMLYQ3U3O76LZ7O7X5XTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3AY2EXMLYQ3U3O76LZ7O7X5XTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3AY2EXMLYQ3U3O76LZ7O7X5XTU","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":"2e398370133b5de6c556122f151d3ff535c43fab24d7d493f3fa593e7e87cdb0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-06-01T10:29:47Z","title_canon_sha256":"9f1ce08a14335607c2f1d09ebd17e4e4967e1111613a0078f72b98aeb3c7e1d6"},"schema_version":"1.0","source":{"id":"2506.00945","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00945","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00945v1","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00945","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"3AY2EXMLYQ3U","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"pith_short_16","alias_value":"3AY2EXMLYQ3U3O76","created_at":"2026-07-05T11:13:43Z"},{"alias_kind":"pith_short_8","alias_value":"3AY2EXML","created_at":"2026-07-05T11:13:43Z"}],"graph_snapshots":[{"event_id":"sha256:c6c6b91e4053827b9d6f1df59830910045ff4d474931d92da563b66391abfc74","target":"graph","created_at":"2026-07-05T11:13:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.00945/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Frequency-hopping sequences (FHSs) with low Hamming correlation and wide gaps significantly contribute to the anti-interference performance in FH communication systems. This paper investigates FHSs with optimal Hamming correlation and controlled minimum gaps. We start with the discussion of the upper bounds on the minimum gaps of uniform FHSs and then propose a general construction of optimal uniform wide-gap FHSs with length 2l and 3l, which includes the work by Li et al. in IEEE Trans. Inf. Theory, vol. 68, no. 1, 2022 as a special case. Furthermore, we present a recursive construction of FH","authors_text":"Chen Li, Chunlei Li, Dian Li, Xiangyong Zeng","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-06-01T10:29:47Z","title":"Constructions of Optimal Frequency-Hopping Sequences with Controlled Minimum Gaps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00945","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":"sha256:268b16f2ee034a1515048b08c13005785728843820a750af4c1221aad95b52c1","target":"record","created_at":"2026-07-05T11:13:43Z","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":"2e398370133b5de6c556122f151d3ff535c43fab24d7d493f3fa593e7e87cdb0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-06-01T10:29:47Z","title_canon_sha256":"9f1ce08a14335607c2f1d09ebd17e4e4967e1111613a0078f72b98aeb3c7e1d6"},"schema_version":"1.0","source":{"id":"2506.00945","kind":"arxiv","version":1}},"canonical_sha256":"d831a25d8bc4374dbbfe5e7eefdfb79d219ce1bceb9d7e0a3f61a8bf2d887be6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d831a25d8bc4374dbbfe5e7eefdfb79d219ce1bceb9d7e0a3f61a8bf2d887be6","first_computed_at":"2026-07-05T11:13:43.263346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:43.263346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D7KYYWl0919CSwNkGrexg6CVni3dc4gfFI+OXa876yd33ih3R5qLLfCwB3YMCUCLUblQLFqsKrmJCLUtIGyeBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:43.263822Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.00945","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:268b16f2ee034a1515048b08c13005785728843820a750af4c1221aad95b52c1","sha256:c6c6b91e4053827b9d6f1df59830910045ff4d474931d92da563b66391abfc74"],"state_sha256":"922d6b1196d4b71a851fd827f5096e290a03be549d240f801b526a04395c44a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJEBVQDo5BruZS/wPZv7ScJ95+5JKtQYN70ttvtyBasEPb5CGO4c9B4a5GnYqBCt3dbrM2EaRTOuknC5x6UzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:26:11.594851Z","bundle_sha256":"3671cdd13fd0b7220a131d476629920c0d41860ddac52df08551b10a24db9408"}}