{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KYUSM3LLDYT74A7VMLL6NFOTAX","short_pith_number":"pith:KYUSM3LL","canonical_record":{"source":{"id":"1312.4521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-24T05:36:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"63f470fe87b28d8b9e17c970f4179b91bb5ebc719c463f7e4022d79e8473e806","abstract_canon_sha256":"f8391ef3e264fa9ec5816ba64d7c3c47a3492196a2f8a9419ba31116b9078c87"},"schema_version":"1.0"},"canonical_sha256":"5629266d6b1e27fe03f562d7e695d305c3c63d94e7343ad60332e68841076dab","source":{"kind":"arxiv","id":"1312.4521","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4521","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4521v1","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4521","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"KYUSM3LLDYT7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KYUSM3LLDYT74A7V","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KYUSM3LL","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KYUSM3LLDYT74A7VMLL6NFOTAX","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-24T05:36:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"63f470fe87b28d8b9e17c970f4179b91bb5ebc719c463f7e4022d79e8473e806","abstract_canon_sha256":"f8391ef3e264fa9ec5816ba64d7c3c47a3492196a2f8a9419ba31116b9078c87"},"schema_version":"1.0"},"canonical_sha256":"5629266d6b1e27fe03f562d7e695d305c3c63d94e7343ad60332e68841076dab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:24.516398Z","signature_b64":"iz/30aEQGtnD4WdtEs6Rwy0p0hOiyD4/YIw3OazWkvJmj5eGUe9/F/tqWVbOnwl1XXrIUF7OZ9FZ6HMi0+DoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5629266d6b1e27fe03f562d7e695d305c3c63d94e7343ad60332e68841076dab","last_reissued_at":"2026-05-18T03:04:24.515878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:24.515878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4521","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":"2026-05-18T03:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZBXwdp7ptLnYqpbiPBzeIqmRQrHMT6NRvQsogJ8DbYhcDlzGh3dt8aFFu/AjBnZx2v6tMiTFQJMj6ShPE91VBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:55:49.627824Z"},"content_sha256":"c6fcf5a37db7568d5ba9f0c61c15858b4e7c1992e800b355798a0e87cc6ca8f7","schema_version":"1.0","event_id":"sha256:c6fcf5a37db7568d5ba9f0c61c15858b4e7c1992e800b355798a0e87cc6ca8f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KYUSM3LLDYT74A7VMLL6NFOTAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weyl-Heisenberg Spaces for Robust Orthogonal Frequency Division Multiplexing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Vincent Sinn, Zoran Cvetkovic","submitted_at":"2013-11-24T05:36:53Z","abstract_excerpt":"Design of Weyl-Heisenberg sets of waveforms for robust orthogonal frequency division multiplex- ing (OFDM) has been the subject of a considerable volume of work. In this paper, a complete parameterization of orthogonal Weyl-Heisenberg sets and their corresponding biorthogonal sets is given. Several examples of Weyl-Heisenberg sets designed using this parameterization are pre- sented, which in simulations show a high potential for enabling OFDM robust to frequency offset, timing mismatch, and narrow-band interference."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4521","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":"2026-05-18T03:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xkrzej7Ee+2Z8lozIOUya8RIY7RXr+3/vex+6S8gra/VPfbC0ie2kiMWRv72kYMFDErAVhsQT28d1C3KlJ/3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:55:49.628167Z"},"content_sha256":"c8c28e3ad8240a0ee4e303fd0aa2bc67e55d51e334e11475da22b7c9e6f7d6e1","schema_version":"1.0","event_id":"sha256:c8c28e3ad8240a0ee4e303fd0aa2bc67e55d51e334e11475da22b7c9e6f7d6e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KYUSM3LLDYT74A7VMLL6NFOTAX/bundle.json","state_url":"https://pith.science/pith/KYUSM3LLDYT74A7VMLL6NFOTAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KYUSM3LLDYT74A7VMLL6NFOTAX/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":"2026-06-03T18:55:49Z","links":{"resolver":"https://pith.science/pith/KYUSM3LLDYT74A7VMLL6NFOTAX","bundle":"https://pith.science/pith/KYUSM3LLDYT74A7VMLL6NFOTAX/bundle.json","state":"https://pith.science/pith/KYUSM3LLDYT74A7VMLL6NFOTAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KYUSM3LLDYT74A7VMLL6NFOTAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KYUSM3LLDYT74A7VMLL6NFOTAX","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":"f8391ef3e264fa9ec5816ba64d7c3c47a3492196a2f8a9419ba31116b9078c87","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-24T05:36:53Z","title_canon_sha256":"63f470fe87b28d8b9e17c970f4179b91bb5ebc719c463f7e4022d79e8473e806"},"schema_version":"1.0","source":{"id":"1312.4521","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4521","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4521v1","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4521","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"KYUSM3LLDYT7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KYUSM3LLDYT74A7V","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KYUSM3LL","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:c8c28e3ad8240a0ee4e303fd0aa2bc67e55d51e334e11475da22b7c9e6f7d6e1","target":"graph","created_at":"2026-05-18T03:04:24Z","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":"Design of Weyl-Heisenberg sets of waveforms for robust orthogonal frequency division multiplex- ing (OFDM) has been the subject of a considerable volume of work. In this paper, a complete parameterization of orthogonal Weyl-Heisenberg sets and their corresponding biorthogonal sets is given. Several examples of Weyl-Heisenberg sets designed using this parameterization are pre- sented, which in simulations show a high potential for enabling OFDM robust to frequency offset, timing mismatch, and narrow-band interference.","authors_text":"Vincent Sinn, Zoran Cvetkovic","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-24T05:36:53Z","title":"Weyl-Heisenberg Spaces for Robust Orthogonal Frequency Division Multiplexing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4521","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:c6fcf5a37db7568d5ba9f0c61c15858b4e7c1992e800b355798a0e87cc6ca8f7","target":"record","created_at":"2026-05-18T03:04:24Z","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":"f8391ef3e264fa9ec5816ba64d7c3c47a3492196a2f8a9419ba31116b9078c87","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-24T05:36:53Z","title_canon_sha256":"63f470fe87b28d8b9e17c970f4179b91bb5ebc719c463f7e4022d79e8473e806"},"schema_version":"1.0","source":{"id":"1312.4521","kind":"arxiv","version":1}},"canonical_sha256":"5629266d6b1e27fe03f562d7e695d305c3c63d94e7343ad60332e68841076dab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5629266d6b1e27fe03f562d7e695d305c3c63d94e7343ad60332e68841076dab","first_computed_at":"2026-05-18T03:04:24.515878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:24.515878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iz/30aEQGtnD4WdtEs6Rwy0p0hOiyD4/YIw3OazWkvJmj5eGUe9/F/tqWVbOnwl1XXrIUF7OZ9FZ6HMi0+DoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:24.516398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4521","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6fcf5a37db7568d5ba9f0c61c15858b4e7c1992e800b355798a0e87cc6ca8f7","sha256:c8c28e3ad8240a0ee4e303fd0aa2bc67e55d51e334e11475da22b7c9e6f7d6e1"],"state_sha256":"c4b6d16008b7a22433a52848672e519b010440dba15e9d6f670faec202dc3ef9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhAU/EvDTtFXT+iD2fSf3v/zsG6m5wKvH8lfeXNsB19NExnrNCsYKbclj0x8B1l6iIW1ZNS1wPQsQeDcxstjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:55:49.630164Z","bundle_sha256":"cccdb5bae98486f8345a6197df2b980c6b48f93317ec94a5fb00abd493792ea1"}}