{
  "id": "oai:papers.qnfo.org:prime-valuation-qec-implications",
  "slug": "prime-valuation-qec-implications",
  "title": "Implications for Computing and Quantum Error Correction",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The anchor paper introduced the branch-depth reading: the p-adic valuation v_p(n) is a measure of depth along a prime branch of the integer factorization tree (not a measure of size), and because the tensor product multiplies Hilbert-space dimensions, v₂(dim H) = n counts tensor-branch depth for n qubits. This follow-on subjects that reading to its own stated falsifiability condition in the two domains the anchor flagged but did not pursue — computing and quantum error correction. The central finding is a correction, not a confirmation: the naive mapping of a [[n,k,d]] stabilizer code to branch depths, n = v₂(dim H) and k = v₂(dim H_L), is trivially true by definition (a code is defined on n qubits encoding 2^k logical states) and therefore carries no new content; and the code distance d — a minimum operator weight, not a depth — does not admit a valuation reading at all. [...]",
  "abstract_markdown": "The anchor paper introduced the *branch-depth reading*: the p-adic valuation $v_p(n)$ is a measure of depth along a prime branch of the integer factorization tree (not a measure of size), and because the tensor product multiplies Hilbert-space dimensions, $v_2(\\dim H) = n$ counts tensor-branch depth for n qubits. This follow-on subjects that reading to its own stated falsifiability condition in the two domains the anchor flagged but did not pursue — computing and quantum error correction. The central finding is a *correction, not a confirmation*: the naive mapping of a $[[n,k,d]]$ stabilizer code to branch depths, $n = v_2(\\dim H)$ and $k = v_2(\\dim H_L)$, is **trivially true by definition** (a code is defined on n qubits encoding $2^k$ logical states) and therefore carries no new content; and the code distance d — a minimum operator *weight*, not a *depth* — does not admit a valuation reading at all. [...]",
  "date": "2026-08-13",
  "first_published": "2026-08-13",
  "last_revised": "2026-10-29T07:11:11Z",
  "modified": "2026-10-29T07:11:11Z",
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  "url": "https://papers.qnfo.org/papers/prime-valuation-qec-implications",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Implications for Computing and Quantum Error Correction"
      }
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    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-08-13",
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        "description": "The anchor paper introduced the branch-depth reading: the p-adic valuation v_p(n) is a measure of depth along a prime branch of the integer factorization tree (not a measure of size), and because the tensor product multiplies Hilbert-space dimensions, v₂(dim H) = n counts tensor-branch depth for n qubits. This follow-on subjects that reading to its own stated falsifiability condition in the two domains the anchor flagged but did not pursue — computing and quantum error correction. The central finding is a correction, not a confirmation: the naive mapping of a [[n,k,d]] stabilizer code to branch depths, n = v₂(dim H) and k = v₂(dim H_L), is trivially true by definition (a code is defined on n qubits encoding 2^k logical states) and therefore carries no new content; and the code distance d — a minimum operator weight, not a depth — does not admit a valuation reading at all. [...]",
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