{
  "id": "oai:papers.qnfo.org:prime-indexed-addressing-collision-free-computational-units-from-the-prime-seque",
  "slug": "prime-indexed-addressing-collision-free-computational-units-from-the-prime-seque",
  "title": "Prime-Indexed Addressing: Collision-Free Computational Units from the Prime Sequence, with Entropy and Physicality Bounds",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Large-scale computing systems spend substantial resources resolving address collisions: hash tables rehash, distributed key-value stores reconcile conflicting writes, and language models dedicate parameters to disambiguating positional encodings. A concrete gap is the absence of a deterministic, unbounded, collision-free addressing primitive whose resource cost can be bounded analytically before any hardware is built. This paper formalizes a candidate in which the address space itself is the sequence of prime numbers: each stored value is assigned a unique prime index N, so that the map from values to addresses is injective by construction and the address density follows the prime number theorem, π(x) ∼ x/ln x. We prove collision-freedom, derive the address-length overhead log₂ ln N bits over a dense integer encoding, and quantify a hierarchical variant built from prime-indexed primes, whose counting function scales as x/(ln x)². We compute the Landauer cost of address erasure, k_B T ln 2 ≈ 2.87 × 10^-21 J per bit at $T = 300$ K, giving 6.89 × 10^-14 J to erase a full N = 10⁶ address table and 1.00 × 10^-10 J at N = 10⁹; a bounded-physicality check passes with margins of order 10⁶6 in atoms. Via the Chinese Remainder Theorem, the first eight primes address 9,699,690 values in $27$ bits against $24$ dense bits. The principal result is that prime-indexed addressing is provably collision-free with a logarithmic address overhead, but its viability as a storage or token-embedding mechanism rests on unproven assumptions about retrieval hardware; we state these assumptions explicitly and propose the smallest experiment that would test them.",
  "abstract_markdown": "Large-scale computing systems spend substantial resources resolving address collisions: hash tables rehash, distributed key-value stores reconcile conflicting writes, and language models dedicate parameters to disambiguating positional encodings. A concrete gap is the absence of a deterministic, unbounded, collision-free addressing primitive whose resource cost can be bounded analytically before any hardware is built. This paper formalizes a candidate in which the address space itself is the sequence of prime numbers: each stored value is assigned a unique prime index $N$, so that the map from values to addresses is injective by construction and the address density follows the prime number theorem, $\\pi(x) \\sim x/\\ln x$. We prove collision-freedom, derive the address-length overhead $\\log_2 \\ln N$ bits over a dense integer encoding, and quantify a hierarchical variant built from prime-indexed primes, whose counting function scales as $x/(\\ln x)^2$. We compute the Landauer cost of address erasure, $k_B T \\ln 2 \\approx 2.87 \\times 10^{-21}$ J per bit at $T = 300$ K, giving $6.89 \\times 10^{-14}$ J to erase a full $N = 10^6$ address table and $1.00 \\times 10^{-10}$ J at $N = 10^9$; a bounded-physicality check passes with margins of order $10^{66}$ in atoms. Via the Chinese Remainder Theorem, the first eight primes address $9{,}699{,}690$ values in $27$ bits against $24$ dense bits. The principal result is that prime-indexed addressing is provably collision-free with a logarithmic address overhead, but its viability as a storage or token-embedding mechanism rests on unproven assumptions about retrieval hardware; we state these assumptions explicitly and propose the smallest experiment that would test them.",
  "date": "2026-11-12",
  "first_published": "2026-11-12",
  "last_revised": "2026-11-12T00:00:00Z",
  "modified": "2026-11-12T00:00:00Z",
  "version": "1.0.0",
  "version_count": 1,
  "language": "en",
  "keywords": [],
  "quality_tags": [
    "High-quality scholarly research",
    "open-access scholarly work",
    "versioned research publication"
  ],
  "quality_label": "High-quality scholarly research",
  "quality_basis": "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
  "quality_evidence_url": "https://qnfo.org/about",
  "peer_review_status": "Not independently peer-reviewed",
  "resource_type": "ScholarlyArticle",
  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/prime-indexed-addressing-collision-free-computational-units-from-the-prime-seque",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "6aac1c9dbbf9c773cd844eb2f8335fa7873a8788686b6c15dd108b5fc4d334a4",
  "version_url": "https://papers.qnfo.org/papers/prime-indexed-addressing-collision-free-computational-units-from-the-prime-seque/v/1.0.0",
  "datacite": {
    "schemaVersion": "http://datacite.org/schema/kernel-4",
    "identifiers": [
      {
        "identifier": "https://papers.qnfo.org/papers/prime-indexed-addressing-collision-free-computational-units-from-the-prime-seque",
        "identifierType": "URL"
      }
    ],
    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
        "nameType": "Personal",
        "nameIdentifiers": [
          {
            "nameIdentifier": "https://orcid.org/0009-0002-4317-5604",
            "nameIdentifierScheme": "ORCID",
            "schemeUri": "https://orcid.org"
          }
        ]
      }
    ],
    "titles": [
      {
        "title": "Prime-Indexed Addressing: Collision-Free Computational Units from the Prime Sequence, with Entropy and Physicality Bounds"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
    "resourceType": {
      "resourceTypeGeneral": "Text",
      "resourceType": "ScholarlyArticle"
    },
    "subjects": [
      {
        "subject": "High-quality scholarly research",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "open-access scholarly work",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "versioned research publication",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      }
    ],
    "dates": [
      {
        "date": "2026-11-12",
        "dateType": "Issued"
      },
      {
        "date": "2026-11-12",
        "dateType": "Updated"
      }
    ],
    "language": "en",
    "version": "1.0.0",
    "rightsList": [
      {
        "rightsUri": "https://legal.qnfo.org/"
      }
    ],
    "descriptions": [
      {
        "description": "Large-scale computing systems spend substantial resources resolving address collisions: hash tables rehash, distributed key-value stores reconcile conflicting writes, and language models dedicate parameters to disambiguating positional encodings. A concrete gap is the absence of a deterministic, unbounded, collision-free addressing primitive whose resource cost can be bounded analytically before any hardware is built. This paper formalizes a candidate in which the address space itself is the sequence of prime numbers: each stored value is assigned a unique prime index N, so that the map from values to addresses is injective by construction and the address density follows the prime number theorem, π(x) ∼ x/ln x. We prove collision-freedom, derive the address-length overhead log₂ ln N bits over a dense integer encoding, and quantify a hierarchical variant built from prime-indexed primes, whose counting function scales as x/(ln x)². We compute the Landauer cost of address erasure, k_B T ln 2 ≈ 2.87 × 10^-21 J per bit at $T = 300$ K, giving 6.89 × 10^-14 J to erase a full N = 10⁶ address table and 1.00 × 10^-10 J at N = 10⁹; a bounded-physicality check passes with margins of order 10⁶6 in atoms. Via the Chinese Remainder Theorem, the first eight primes address 9,699,690 values in $27$ bits against $24$ dense bits. The principal result is that prime-indexed addressing is provably collision-free with a logarithmic address overhead, but its viability as a storage or token-embedding mechanism rests on unproven assumptions about retrieval hardware; we state these assumptions explicitly and propose the smallest experiment that would test them.",
        "descriptionType": "Abstract"
      },
      {
        "description": "Publisher quality classification: High-quality scholarly research. QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
        "descriptionType": "Other"
      },
      {
        "description": "Peer review status: Not independently peer-reviewed",
        "descriptionType": "Other"
      }
    ],
    "formats": [
      "text/html"
    ]
  }
}