Pith Number

pith:VZIOS55I

pith:2026:VZIOS55IPHLUWWNURZJVQ7LKS3

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Error-Correcting Weakly Constrained Codes: Constructions and Achievable Rates

Michael Langberg, Navin Kashyap, Prachi Mishra, Sidharth Jaggi

Weakly constrained codes achieve capacity using Eulerian cycle constructions on graphs and yield positive-rate error-correcting versions after expurgation.

arxiv:2605.09113 v2 · 2026-05-09 · cs.IT · math.IT

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\pithnumber{VZIOS55IPHLUWWNURZJVQ7LKS3}

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding.

C2weakest assumption

That the Eulerian cycle construction exactly meets the frequency prescriptions at capacity and that expurgation can be performed without violating the weak constraints or dropping the rate below positive while achieving linear distance.

C3one line summary

Weakly constrained codes achieve capacity via Eulerian cycle constructions and support error correction with linear distance and positive rate through expurgation and concatenation.

Receipt and verification

First computed	2026-05-22T01:04:05.753785Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae50e977a879d74b59b48e53587d6a96d8e9b8822dbf4c0992111037952d9cdf

Aliases

arxiv: 2605.09113 · arxiv_version: 2605.09113v2 · doi: 10.48550/arxiv.2605.09113 · pith_short_12: VZIOS55IPHLU · pith_short_16: VZIOS55IPHLUWWNU · pith_short_8: VZIOS55I

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VZIOS55IPHLUWWNURZJVQ7LKS3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ae50e977a879d74b59b48e53587d6a96d8e9b8822dbf4c0992111037952d9cdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2028f0bad261d67f57cc9e5d092714ca846457914b2d92716cc1c8c4ad3a622d",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-09T18:53:56Z",
    "title_canon_sha256": "4aead488153e26944c2d0ad1b7f928065f07840139569a0915583c5e55206ca4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09113",
    "kind": "arxiv",
    "version": 2
  }
}