{
  "abstract": "We study deterministic causal quantization with pathwise error at most $\\varepsilon$, using $ω$ shared representatives updated from transmitted addresses alone. For a midpoint realization with first-in, first-out replacement, we compare address entropy rates with process $\\varepsilon$-entropy, the least entropy rate of any block quantizer meeting the same constraint. From $\\varepsilon$-separated initialization, the gap is at most two bits per sample for every stationary source with finite scalar $\\varepsilon$-entropy, without density, independence or mixing assumptions. A causal address-tree argument extends this comparison to any synchronized quantizer with cell overlap $m$, giving $\\log_2 m$ bits. Lattice initialization with consistent boundary ownership realizes uniform grids with sharp one-bit scalar and process comparisons. Under an entropy condition and finite Fisher information rate $J$, the gap is at most $2J\\varepsilon^2/(π^2\\ln 2)$; general initializations add a term of order $ω\\varepsilon\\sqrt{J}$. The scalar grid estimate gives a nonasymptotic form of Rényi's theorem. Since a grid is causal, the price of causality is at most $\\min\\{1,2J\\varepsilon^2/(π^2\\ln 2)\\}$ bits per sample, versus the high-resolution squared-error loss $\\tfrac12\\log_2(πe/6)$. These bounds certify $\\varepsilon$-entropy brackets for autoregressive Laplace and Gaussian sources. For memoryless sources, the optimal causal rate equals the scalar $\\varepsilon$-entropy. For a stationary process on finitely many $2\\varepsilon$-separated centers, adding independent uniform noise of width $2\\varepsilon$ gives exact Shannon lower-bound equality at every block length, attained by storing those centers. This includes histograms with finitely many bins. Storing two non-lattice centers beats every uniform grid of the same cell width by half a bit per sample.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35933",
  "author_total": 2,
  "authors": [
    {
      "name": "Rama Cont"
    },
    {
      "name": "Massoud Heidari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d5gsxgzpf2thn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35933",
  "fulltext_url": null,
  "id": "d5gsxgzpf2thn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35933",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1707|Advanced Data Compression Techniques"
    ]
  ],
  "openalex": "W7224100313",
  "pdf_url": "https://arxiv.org/pdf/2610.35933",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d5gsxgzpf2thn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.35933",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35933"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Deterministic Causal Quantization with Representative States and Bounded Error",
  "title_text": "Deterministic Causal Quantization with Representative States and Bounded Error",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/d5gsxgzpf2thn",
  "venue": "arXiv",
  "versions": []
}