{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VQGMY7WAHEOQBGLZL6OWIFZPX7","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":"89bb280a1742e6a145fd219a99c879d5a54ba5d9c977e202be43baf81d66ac23","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2022-05-09T10:04:17Z","title_canon_sha256":"4326f8a882a3c7020226ca6c9b24b9029e71095199474da3c0c66639b41d5317"},"schema_version":"1.0","source":{"id":"2205.04153","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.04153","created_at":"2026-07-05T04:45:59Z"},{"alias_kind":"arxiv_version","alias_value":"2205.04153v2","created_at":"2026-07-05T04:45:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.04153","created_at":"2026-07-05T04:45:59Z"},{"alias_kind":"pith_short_12","alias_value":"VQGMY7WAHEOQ","created_at":"2026-07-05T04:45:59Z"},{"alias_kind":"pith_short_16","alias_value":"VQGMY7WAHEOQBGLZ","created_at":"2026-07-05T04:45:59Z"},{"alias_kind":"pith_short_8","alias_value":"VQGMY7WA","created_at":"2026-07-05T04:45:59Z"}],"graph_snapshots":[{"event_id":"sha256:cdb3ee4831b1b4778af064a60cc40d4e966703854b1698d718604710c9fb0c42","target":"graph","created_at":"2026-07-05T04:45:59Z","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/2205.04153/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we address the question of the largest rate of linear subcodes of Reed-Muller (RM) codes, all of whose codewords respect a runlength-limited (RLL) constraint. Our interest is in the $(d,\\infty)$-RLL constraint, which mandates that every pair of successive $1$s be separated by at least $d$ $0$s. Consider any sequence $\\{{\\mathcal{C}_m}\\}_{m\\geq 1}$ of RM codes with increasing blocklength, whose rates approach $R$, in the limit as the blocklength goes to infinity. We show that for any linear $(d,\\infty)$-RLL subcode, $\\hat{\\mathcal{C}}_m$, of the code $\\mathcal{C}_m$, it holds that","authors_text":"Navin Kashyap, V. Arvind Rameshwar","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2022-05-09T10:04:17Z","title":"Linear Runlength-Limited Subcodes of Reed-Muller Codes and Coding Schemes for Input-Constrained BMS Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.04153","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":"sha256:39fc5b869105bf0f88709938a510dd58c7547230a886981b567aee3e7e31550f","target":"record","created_at":"2026-07-05T04:45:59Z","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":"89bb280a1742e6a145fd219a99c879d5a54ba5d9c977e202be43baf81d66ac23","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2022-05-09T10:04:17Z","title_canon_sha256":"4326f8a882a3c7020226ca6c9b24b9029e71095199474da3c0c66639b41d5317"},"schema_version":"1.0","source":{"id":"2205.04153","kind":"arxiv","version":2}},"canonical_sha256":"ac0ccc7ec0391d0099795f9d64172fbff48a0f5a1383f43aec8c703bae65e3a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac0ccc7ec0391d0099795f9d64172fbff48a0f5a1383f43aec8c703bae65e3a5","first_computed_at":"2026-07-05T04:45:59.525816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:45:59.525816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gBdQuvGyn73hFHzUcH8/k1TCWoegAOfUnMJsI4eKylGbHU+ItMnbivqgdhTM4BcueIA+tUiQ9atzzPtIT/sFAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:45:59.526337Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.04153","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39fc5b869105bf0f88709938a510dd58c7547230a886981b567aee3e7e31550f","sha256:cdb3ee4831b1b4778af064a60cc40d4e966703854b1698d718604710c9fb0c42"],"state_sha256":"50d26338996b23d1b1648295d62c3fbd76c5915ee328627ef0a7c3c55e6390e5"}