{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KPEXF4B26FXUG4MOR7YFD4ZZOJ","short_pith_number":"pith:KPEXF4B2","canonical_record":{"source":{"id":"1506.06114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-19T19:14:55Z","cross_cats_sorted":["cs.CR","math.IT"],"title_canon_sha256":"f6e8e0160046f70807857d8061495d4bdf369060332e24eebc7cccc570c3ad96","abstract_canon_sha256":"37f9f40a14b204d377b5de4299adc2f93b1f510429de49f5a318f087fe466035"},"schema_version":"1.0"},"canonical_sha256":"53c972f03af16f43718e8ff051f3397258cbe749df97df2d5029d7352c7f5ae4","source":{"kind":"arxiv","id":"1506.06114","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06114","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06114v1","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06114","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"pith_short_12","alias_value":"KPEXF4B26FXU","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KPEXF4B26FXUG4MO","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KPEXF4B2","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KPEXF4B26FXUG4MOR7YFD4ZZOJ","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-19T19:14:55Z","cross_cats_sorted":["cs.CR","math.IT"],"title_canon_sha256":"f6e8e0160046f70807857d8061495d4bdf369060332e24eebc7cccc570c3ad96","abstract_canon_sha256":"37f9f40a14b204d377b5de4299adc2f93b1f510429de49f5a318f087fe466035"},"schema_version":"1.0"},"canonical_sha256":"53c972f03af16f43718e8ff051f3397258cbe749df97df2d5029d7352c7f5ae4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:35.457426Z","signature_b64":"F3dzmTV5BK2ga7/6obx70xydETmOBK7lBJN7mDf/3/6vVUU5143Iw/Wlp3ELVlztQP4HjzmYwxxgYPd++GoODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53c972f03af16f43718e8ff051f3397258cbe749df97df2d5029d7352c7f5ae4","last_reissued_at":"2026-05-18T00:58:35.456940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:35.456940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06114","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":"2026-05-18T00:58:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b0QmGxLVmlqFPaqpjANjR6epwFdc+yDG+B/IACIX+8ShYXoDjc3J81+W1Q2aj5nZQJtk6jPjiIv6Bk4tmX+RAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:49:43.285753Z"},"content_sha256":"25dd46b5dd7e5194d6daa5b1233ede4673feb9936959d49ad1e68546e52edef6","schema_version":"1.0","event_id":"sha256:25dd46b5dd7e5194d6daa5b1233ede4673feb9936959d49ad1e68546e52edef6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KPEXF4B26FXUG4MOR7YFD4ZZOJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secure Degrees of Freedom of One-hop Wireless Networks with No Eavesdropper CSIT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.IT"],"primary_cat":"cs.IT","authors_text":"Jianwei Xie, Pritam Mukherjee, Sennur Ulukus","submitted_at":"2015-06-19T19:14:55Z","abstract_excerpt":"We consider three channel models: the wiretap channel with $M$ helpers, the $K$-user multiple access wiretap channel, and the $K$-user interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSIT does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06114","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":"2026-05-18T00:58:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"46VH4dBfw3/Ret+WAckFe9IgpJcYpzoM8bpnoXyFLqP0YgcJb3Ni8vp5bm46fm5fA+jUMTiCZctYVbKP5XuyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:49:43.286083Z"},"content_sha256":"7db6cf670b313f519afe8d900e36294456f2b302643b148ed2ee852f3f33c641","schema_version":"1.0","event_id":"sha256:7db6cf670b313f519afe8d900e36294456f2b302643b148ed2ee852f3f33c641"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KPEXF4B26FXUG4MOR7YFD4ZZOJ/bundle.json","state_url":"https://pith.science/pith/KPEXF4B26FXUG4MOR7YFD4ZZOJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KPEXF4B26FXUG4MOR7YFD4ZZOJ/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":"2026-06-29T19:49:43Z","links":{"resolver":"https://pith.science/pith/KPEXF4B26FXUG4MOR7YFD4ZZOJ","bundle":"https://pith.science/pith/KPEXF4B26FXUG4MOR7YFD4ZZOJ/bundle.json","state":"https://pith.science/pith/KPEXF4B26FXUG4MOR7YFD4ZZOJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KPEXF4B26FXUG4MOR7YFD4ZZOJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KPEXF4B26FXUG4MOR7YFD4ZZOJ","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":"37f9f40a14b204d377b5de4299adc2f93b1f510429de49f5a318f087fe466035","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-19T19:14:55Z","title_canon_sha256":"f6e8e0160046f70807857d8061495d4bdf369060332e24eebc7cccc570c3ad96"},"schema_version":"1.0","source":{"id":"1506.06114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06114","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06114v1","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06114","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"pith_short_12","alias_value":"KPEXF4B26FXU","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KPEXF4B26FXUG4MO","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KPEXF4B2","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:7db6cf670b313f519afe8d900e36294456f2b302643b148ed2ee852f3f33c641","target":"graph","created_at":"2026-05-18T00:58:35Z","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":"We consider three channel models: the wiretap channel with $M$ helpers, the $K$-user multiple access wiretap channel, and the $K$-user interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSIT does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access","authors_text":"Jianwei Xie, Pritam Mukherjee, Sennur Ulukus","cross_cats":["cs.CR","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-19T19:14:55Z","title":"Secure Degrees of Freedom of One-hop Wireless Networks with No Eavesdropper CSIT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06114","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":"sha256:25dd46b5dd7e5194d6daa5b1233ede4673feb9936959d49ad1e68546e52edef6","target":"record","created_at":"2026-05-18T00:58:35Z","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":"37f9f40a14b204d377b5de4299adc2f93b1f510429de49f5a318f087fe466035","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-19T19:14:55Z","title_canon_sha256":"f6e8e0160046f70807857d8061495d4bdf369060332e24eebc7cccc570c3ad96"},"schema_version":"1.0","source":{"id":"1506.06114","kind":"arxiv","version":1}},"canonical_sha256":"53c972f03af16f43718e8ff051f3397258cbe749df97df2d5029d7352c7f5ae4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53c972f03af16f43718e8ff051f3397258cbe749df97df2d5029d7352c7f5ae4","first_computed_at":"2026-05-18T00:58:35.456940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:35.456940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F3dzmTV5BK2ga7/6obx70xydETmOBK7lBJN7mDf/3/6vVUU5143Iw/Wlp3ELVlztQP4HjzmYwxxgYPd++GoODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:35.457426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25dd46b5dd7e5194d6daa5b1233ede4673feb9936959d49ad1e68546e52edef6","sha256:7db6cf670b313f519afe8d900e36294456f2b302643b148ed2ee852f3f33c641"],"state_sha256":"02fef588f8a42d1c3ada4853315acebbba76f9a15ad9c776d7fc61d15c140b8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e7+2NWpHfRp3+OESAWDKofGflRI43SNttCnPvl8R1ooyPEcboPxDtxQYZsBs7C8f2d6TtTbCy2OKelstK6SqBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:49:43.287909Z","bundle_sha256":"649bf45597066c73e6e8d029629e7f25fd1f004f63cdd5e32ab41b43b82a8682"}}