{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OMJVPBD77WX6X727TPGWDUA4UP","short_pith_number":"pith:OMJVPBD7","canonical_record":{"source":{"id":"1703.07973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-23T09:13:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"03e860a794c1fe14549ea42f79b58f498ec9db42570149d144f0be0f4f8f3015","abstract_canon_sha256":"ac474016c901e3760e33fbf8dadd976f22098f29b09faac639b9489d437028ab"},"schema_version":"1.0"},"canonical_sha256":"731357847ffdafebff5f9bcd61d01ca3c5a8c71ca26d7edba4d30f41adf0db0a","source":{"kind":"arxiv","id":"1703.07973","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07973","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07973v2","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07973","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"OMJVPBD77WX6","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OMJVPBD77WX6X727","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OMJVPBD7","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OMJVPBD77WX6X727TPGWDUA4UP","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-23T09:13:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"03e860a794c1fe14549ea42f79b58f498ec9db42570149d144f0be0f4f8f3015","abstract_canon_sha256":"ac474016c901e3760e33fbf8dadd976f22098f29b09faac639b9489d437028ab"},"schema_version":"1.0"},"canonical_sha256":"731357847ffdafebff5f9bcd61d01ca3c5a8c71ca26d7edba4d30f41adf0db0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:16.239792Z","signature_b64":"CsMNgAJyz4pg/3RcC0FL6B5JdWDZb8MD5O1tlnjgl/X74iGhbDBkx/eTigy5SZwfQdTK+xJZ1+4xtiFNE0uFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"731357847ffdafebff5f9bcd61d01ca3c5a8c71ca26d7edba4d30f41adf0db0a","last_reissued_at":"2026-05-18T00:08:16.239371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:16.239371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07973","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zd78yPlA9K1zy6zf9aeqTIrVPA/XIFEJFkc2k6EwLklZom5cXDPuiDtw2iQh8RXJqns6Hi3Vw/can4Ytt/aHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:34:03.588233Z"},"content_sha256":"a01537c80aa9dd100bd3eefa22365607c54a000427ec743c3746df77e2495f0f","schema_version":"1.0","event_id":"sha256:a01537c80aa9dd100bd3eefa22365607c54a000427ec743c3746df77e2495f0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OMJVPBD77WX6X727TPGWDUA4UP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructing an LDPC Code Containing a Given Vector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Martin Bossert, Sven M\\\"uelich, Sven Puchinger","submitted_at":"2017-03-23T09:13:26Z","abstract_excerpt":"The coding problem considered in this work is to construct a linear code $\\mathcal{C}$ of given length $n$ and dimension $k<n$ such that a given binary vector $\\mathbf{r} \\in \\mathbb{F}^{n}$ is contained in the code. We study a recent solution of this problem by M\\\"uelich and Bossert, which is based on LDPC codes. We address two open questions of this construction. First, we show that under certain assumptions, this code construction is possible with high probability if $\\mathbf{r}$ is chosen uniformly at random. Second, we calculate the uncertainty of $\\mathbf{r}$ given the constructed code $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07973","kind":"arxiv","version":2},"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":"2026-05-18T00:08:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kEQUWec6eOG4svfcQddwMD21K2c6Nh3IDdCKLTohxwYmHZqqlHN03bQ3KIK62NqZmgKKhY4qaHxr8c1C7GjyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:34:03.588868Z"},"content_sha256":"948247e39d52f746c896df651558d81ebb88e1ab2f3a56129bdf444ce0df649e","schema_version":"1.0","event_id":"sha256:948247e39d52f746c896df651558d81ebb88e1ab2f3a56129bdf444ce0df649e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMJVPBD77WX6X727TPGWDUA4UP/bundle.json","state_url":"https://pith.science/pith/OMJVPBD77WX6X727TPGWDUA4UP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMJVPBD77WX6X727TPGWDUA4UP/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":"2026-05-31T21:34:03Z","links":{"resolver":"https://pith.science/pith/OMJVPBD77WX6X727TPGWDUA4UP","bundle":"https://pith.science/pith/OMJVPBD77WX6X727TPGWDUA4UP/bundle.json","state":"https://pith.science/pith/OMJVPBD77WX6X727TPGWDUA4UP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMJVPBD77WX6X727TPGWDUA4UP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OMJVPBD77WX6X727TPGWDUA4UP","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":"ac474016c901e3760e33fbf8dadd976f22098f29b09faac639b9489d437028ab","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-23T09:13:26Z","title_canon_sha256":"03e860a794c1fe14549ea42f79b58f498ec9db42570149d144f0be0f4f8f3015"},"schema_version":"1.0","source":{"id":"1703.07973","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07973","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07973v2","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07973","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"OMJVPBD77WX6","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OMJVPBD77WX6X727","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OMJVPBD7","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:948247e39d52f746c896df651558d81ebb88e1ab2f3a56129bdf444ce0df649e","target":"graph","created_at":"2026-05-18T00:08:16Z","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":"The coding problem considered in this work is to construct a linear code $\\mathcal{C}$ of given length $n$ and dimension $k<n$ such that a given binary vector $\\mathbf{r} \\in \\mathbb{F}^{n}$ is contained in the code. We study a recent solution of this problem by M\\\"uelich and Bossert, which is based on LDPC codes. We address two open questions of this construction. First, we show that under certain assumptions, this code construction is possible with high probability if $\\mathbf{r}$ is chosen uniformly at random. Second, we calculate the uncertainty of $\\mathbf{r}$ given the constructed code $","authors_text":"Martin Bossert, Sven M\\\"uelich, Sven Puchinger","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-23T09:13:26Z","title":"Constructing an LDPC Code Containing a Given Vector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07973","kind":"arxiv","version":2},"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:a01537c80aa9dd100bd3eefa22365607c54a000427ec743c3746df77e2495f0f","target":"record","created_at":"2026-05-18T00:08:16Z","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":"ac474016c901e3760e33fbf8dadd976f22098f29b09faac639b9489d437028ab","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-23T09:13:26Z","title_canon_sha256":"03e860a794c1fe14549ea42f79b58f498ec9db42570149d144f0be0f4f8f3015"},"schema_version":"1.0","source":{"id":"1703.07973","kind":"arxiv","version":2}},"canonical_sha256":"731357847ffdafebff5f9bcd61d01ca3c5a8c71ca26d7edba4d30f41adf0db0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"731357847ffdafebff5f9bcd61d01ca3c5a8c71ca26d7edba4d30f41adf0db0a","first_computed_at":"2026-05-18T00:08:16.239371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:16.239371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CsMNgAJyz4pg/3RcC0FL6B5JdWDZb8MD5O1tlnjgl/X74iGhbDBkx/eTigy5SZwfQdTK+xJZ1+4xtiFNE0uFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:16.239792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07973","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a01537c80aa9dd100bd3eefa22365607c54a000427ec743c3746df77e2495f0f","sha256:948247e39d52f746c896df651558d81ebb88e1ab2f3a56129bdf444ce0df649e"],"state_sha256":"f3761399a516cdb3330568b6b558a74763c9528662cc996b1285c403a8f9c4a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IL3YcaDuC7HTLNh4g8CuCUXhYtKQemEfgxoDPMSFAo0QUzBHrBEAA8UrY3pHXMCz6jatbmqzYAAiqL11D3XDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:34:03.591612Z","bundle_sha256":"dc6428004547a440428a0a71cfbb49306036df9b4fa3c77ed3d41dc264186fc5"}}