Pith Number

pith:JMFSU3WM

pith:2026:JMFSU3WM2GYZHQWLWYZRUX4RCK

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Covert Multi-bit LLM Watermarking: An Information Theory and Coding Approach

Matthieu R. Bloch, Sidong Guo, Teodora Baluta, Tyler Kann

Multi-bit covert watermarking for LLMs has an exactly characterized capacity that supports practical embedding at 0.375 bits per token.

arxiv:2605.16709 v1 · 2026-05-15 · cs.IT · math.IT

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Claims

C1strongest claim

We study the information-theoretic limits of the model by combining Gelfand-Pinsker and channel synthesis coding techniques and obtain an exact characterization of the capacity. Our algorithm achieves a bit-error rate below 10 percent with a rate of 0.375 bits/token over short token lengths with negligible perplexity and distortion degradation.

C2weakest assumption

The formulation assumes the encoder has limited non-causal access to token distributions within each block and that LLM cover statistics are known and can be leveraged for covert embedding; if this access or knowledge is unavailable in fully causal real-world sampling, the capacity characterization and performance claims would not apply.

C3one line summary

Characterizes the exact capacity of multi-bit covert LLM watermarking via Gelfand-Pinsker and channel synthesis, then gives a polar-code algorithm achieving 0.375 bits/token at under 10% BER with negligible perplexity impact.

References

46 extracted · 46 resolved · 3 Pith anchors

[1] A watermark for large language models, 2023

[2] Undetectable watermarks for language models, 2024

[3] Heavywater and simplexwater: Distortion- free llm watermarks for low-entropy distributions, 2025

[4] Provable robust watermarking for AI-generated text 2023

[5] Robust content-dependent high- fidelity watermark for tracking in digital cinema, 2003

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:37.673341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b0b2a6eccd1b193c2cbb6331a5f91129660c483a188377524ed8b7201fd24fc

Aliases

arxiv: 2605.16709 · arxiv_version: 2605.16709v1 · doi: 10.48550/arxiv.2605.16709 · pith_short_12: JMFSU3WM2GYZ · pith_short_16: JMFSU3WM2GYZHQWL · pith_short_8: JMFSU3WM

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JMFSU3WM2GYZHQWLWYZRUX4RCK \
  | 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: 4b0b2a6eccd1b193c2cbb6331a5f91129660c483a188377524ed8b7201fd24fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4b4745ff40a3882c510ccaa98166f9ae2db476d60f30047983682b4370c73a7",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-15T23:46:22Z",
    "title_canon_sha256": "9fa072348073860d6117401e6c15035fb9087e3f17baeb48fbdf6f68db980f80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16709",
    "kind": "arxiv",
    "version": 1
  }
}