{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O7FUED4LDAFSDK5G7EHQU7WCDC","short_pith_number":"pith:O7FUED4L","canonical_record":{"source":{"id":"1311.7113","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T20:28:20Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0a146f02d132d353022bbac662d776228ac381824de115ec734e026c7f29ce3d","abstract_canon_sha256":"b86a9d4b658dd2916b9c9eea5ee0223173243d7c6e2233c0037d5be531867818"},"schema_version":"1.0"},"canonical_sha256":"77cb420f8b180b21aba6f90f0a7ec218bd28d4998ea0ad1ea1a668b26f6ad2d6","source":{"kind":"arxiv","id":"1311.7113","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7113","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7113v3","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7113","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"pith_short_12","alias_value":"O7FUED4LDAFS","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O7FUED4LDAFSDK5G","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O7FUED4L","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O7FUED4LDAFSDK5G7EHQU7WCDC","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7113","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T20:28:20Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0a146f02d132d353022bbac662d776228ac381824de115ec734e026c7f29ce3d","abstract_canon_sha256":"b86a9d4b658dd2916b9c9eea5ee0223173243d7c6e2233c0037d5be531867818"},"schema_version":"1.0"},"canonical_sha256":"77cb420f8b180b21aba6f90f0a7ec218bd28d4998ea0ad1ea1a668b26f6ad2d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:53.427909Z","signature_b64":"3tJfO64vneWW8CB9/9Hk4hT2+CRVc/UsWPJ8qa8dcD94R/chR1n8h4O0vjjBra243pufBODRQk3+YMJZMIHuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77cb420f8b180b21aba6f90f0a7ec218bd28d4998ea0ad1ea1a668b26f6ad2d6","last_reissued_at":"2026-05-18T02:53:53.427085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:53.427085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7113","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:53:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rt4wD41YuJFA+l0qSInuunjJjbN+s/lNmu2iZQfHK/bjyaSXsKY8rQ874H9qLZUgolZn8TfcFQ6+Rx1MxrlJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:03:14.139530Z"},"content_sha256":"ac79908f9da41897b61bbf1f88bbdabf43e76d2c94e853a5614ef27f624a432e","schema_version":"1.0","event_id":"sha256:ac79908f9da41897b61bbf1f88bbdabf43e76d2c94e853a5614ef27f624a432e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O7FUED4LDAFSDK5G7EHQU7WCDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Systematic Codes for Rank Modulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Eitan Yaakobi, Jehoshua Bruck, Sarit Buzaglo, Tuvi Etzion","submitted_at":"2013-11-27T20:28:20Z","abstract_excerpt":"The goal of this paper is to construct systematic error-correcting codes for permutations and multi-permutations in the Kendall's $\\tau$-metric. These codes are important in new applications such as rank modulation for flash memories. The construction is based on error-correcting codes for multi-permutations and a partition of the set of permutations into error-correcting codes. For a given large enough number of information symbols $k$, and for any integer $t$, we present a construction for ${(k+r,k)}$ systematic $t$-error-correcting codes, for permutations from $S_{k+r}$, with less redundanc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7113","kind":"arxiv","version":3},"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":"2026-05-18T02:53:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KPW3QsxtZWCi39PtasIFEv4BXoHzQ80COZIusVmGIquhBZK+LnZbqayM2ecX0HuA6dTgdRS68Cy1aM1jPBiqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:03:14.139884Z"},"content_sha256":"ed348ac6b0c05d0b0a18241ba5d81a579024a8ef6c7df1d709934100ebf39520","schema_version":"1.0","event_id":"sha256:ed348ac6b0c05d0b0a18241ba5d81a579024a8ef6c7df1d709934100ebf39520"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7FUED4LDAFSDK5G7EHQU7WCDC/bundle.json","state_url":"https://pith.science/pith/O7FUED4LDAFSDK5G7EHQU7WCDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7FUED4LDAFSDK5G7EHQU7WCDC/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":"2026-05-30T20:03:14Z","links":{"resolver":"https://pith.science/pith/O7FUED4LDAFSDK5G7EHQU7WCDC","bundle":"https://pith.science/pith/O7FUED4LDAFSDK5G7EHQU7WCDC/bundle.json","state":"https://pith.science/pith/O7FUED4LDAFSDK5G7EHQU7WCDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7FUED4LDAFSDK5G7EHQU7WCDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O7FUED4LDAFSDK5G7EHQU7WCDC","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":"b86a9d4b658dd2916b9c9eea5ee0223173243d7c6e2233c0037d5be531867818","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T20:28:20Z","title_canon_sha256":"0a146f02d132d353022bbac662d776228ac381824de115ec734e026c7f29ce3d"},"schema_version":"1.0","source":{"id":"1311.7113","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7113","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7113v3","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7113","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"pith_short_12","alias_value":"O7FUED4LDAFS","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O7FUED4LDAFSDK5G","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O7FUED4L","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:ed348ac6b0c05d0b0a18241ba5d81a579024a8ef6c7df1d709934100ebf39520","target":"graph","created_at":"2026-05-18T02:53:53Z","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 goal of this paper is to construct systematic error-correcting codes for permutations and multi-permutations in the Kendall's $\\tau$-metric. These codes are important in new applications such as rank modulation for flash memories. The construction is based on error-correcting codes for multi-permutations and a partition of the set of permutations into error-correcting codes. For a given large enough number of information symbols $k$, and for any integer $t$, we present a construction for ${(k+r,k)}$ systematic $t$-error-correcting codes, for permutations from $S_{k+r}$, with less redundanc","authors_text":"Eitan Yaakobi, Jehoshua Bruck, Sarit Buzaglo, Tuvi Etzion","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T20:28:20Z","title":"Systematic Codes for Rank Modulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7113","kind":"arxiv","version":3},"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:ac79908f9da41897b61bbf1f88bbdabf43e76d2c94e853a5614ef27f624a432e","target":"record","created_at":"2026-05-18T02:53:53Z","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":"b86a9d4b658dd2916b9c9eea5ee0223173243d7c6e2233c0037d5be531867818","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T20:28:20Z","title_canon_sha256":"0a146f02d132d353022bbac662d776228ac381824de115ec734e026c7f29ce3d"},"schema_version":"1.0","source":{"id":"1311.7113","kind":"arxiv","version":3}},"canonical_sha256":"77cb420f8b180b21aba6f90f0a7ec218bd28d4998ea0ad1ea1a668b26f6ad2d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77cb420f8b180b21aba6f90f0a7ec218bd28d4998ea0ad1ea1a668b26f6ad2d6","first_computed_at":"2026-05-18T02:53:53.427085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:53.427085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3tJfO64vneWW8CB9/9Hk4hT2+CRVc/UsWPJ8qa8dcD94R/chR1n8h4O0vjjBra243pufBODRQk3+YMJZMIHuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:53.427909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7113","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac79908f9da41897b61bbf1f88bbdabf43e76d2c94e853a5614ef27f624a432e","sha256:ed348ac6b0c05d0b0a18241ba5d81a579024a8ef6c7df1d709934100ebf39520"],"state_sha256":"fe5a90c1652d5377b8ce2bdd038d4abb5b65a88bfc99ff006d50708e8cdc458f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P87cyFgrVL6O+GAUKoSSnj8HMLPGpfgWCTUhYlV07dSP/fWt0JUPxNNG4eCFzSq3yXgV11VBAP2/b5H74A5cCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:03:14.142052Z","bundle_sha256":"78091c7ab6524affd49ddba7959ac1196e51a2fe877986ba09e420016bdd6e7c"}}