Framework

The Quantized Dimensional Ledger Framework

The Quantized Dimensional Ledger (QDL) framework treats dimensional analysis as a prediction-filter architecture, not just a consistency check. Every physical quantity is represented by a five-component integer ledger vector in a 3L + 2F length–frequency basis, and all admissible interactions must close onto a conserved Quantized Dimensional Cell (QDC). This framework links the Standard Model, gravitation, metrology, and precision experiments through a common dimensional-closure structure.

This page summarizes the core elements of the QDL framework and points to primary references for deeper technical detail.

1. Core dimensional structure

QDL begins with a length–frequency dimensional basis and a conserved Quantized Dimensional Cell. From these ingredients, a ledger representation for physical quantities is defined and used as the backbone for closure rules.

  • 3L + 2F length–frequency basis.
    The framework uses a three-length, two-frequency exponent space instead of the conventional M–L–T system. Physical quantities are expanded in this basis with integer exponents.
    Details: metrology and QMU ledger paper (17619526).
  • Quantized Dimensional Cell (QDC).
    The QDC is a conserved dimensional “cell”: AQDC ∼ L3F2

    The QDC acts as the conserved dimensional “cell” of the ledger. Every admissible action or interaction is required to close onto an integer multiple of this cell.

    Details: SO(3,2) QDC structure (17683786).
  • Ledger vector for a physical quantity.
    X → [L1, L2, L3, F1, F2]

    Each physical quantity is mapped to a five-component integer vector in the 3L + 2F basis. These ledger vectors are then combined according to simple integer rules when constructing actions, Lagrangians, or measurement chains.

    Details: unified framework and QMU papers (17704896, 17619526).

2. Ledger closure & field content

With a ledger representation in place, QDL introduces a strict closure condition: admissible actions, interactions, and measurement relations must close onto integer multiples of the QDC. This turns dimensional analysis into a structural filter on field content and constants.

  • Ledger-closure principle. Instead of “dimensional consistency” as a loose check, QDL imposes an exact ledger-closure condition: sums of field and coupling exponents must map onto integer multiples of the QDC. This provides a structural filter on admissible Lagrangian terms and interaction vertices.
    Details: unified framework and metrology/constant papers (17742903, 17619526, 17663436).
  • Ledger representation of Standard Model fields. Gauge fields, matter fields, and couplings are each assigned a 5-component ledger vector. Gauge invariance, anomaly cancellation, and interaction structure are rephrased as integer relations between these vectors under the closure principle.
    Details: unified Standard Model + gravity framework (17742903).
  • Prediction-filter role. Because only certain combinations of fields, couplings, and constants are compatible with QDL closure, the framework acts as a prediction filter on EFT and SMEFT operator content, as well as on which constant combinations may appear in measurable relations.
    Details: prediction-filter capstone (17848782).

3. Gravity, scalar–tensor structure, and quantum coherence

QDL extends the ledger framework to gravitation by imposing dimensional coherence at the level of the action and by linking gravitational terms to the same QDC that constrains Standard Model fields and constants.

  • Scalar–tensor gravitation in a QDL basis. The gravitational sector is reformulated with scalar–tensor terms whose dimensional content is tied to the QDC. This leads to constraints on allowable couplings and on how gravitational and electromagnetic sectors can be unified.
    Details: scalar–tensor framework and unified SM + gravity (17704896, 17742903).
  • Quantum gravity from dimensional coherence. A dedicated quantum-gravity construction uses QDL closure as a guiding principle for minimum-length geometry and coherence structure, again tied back to the same dimensional cell that governs EFT and constants.
    Details: quantum-gravity from dimensional coherence (17848573).
  • Coherent ledger fields. The Coherent Ledger Fields (CLF) formulation connects SO(3,2)-like QDC geometry to scalar–tensor–electromagnetic phenomenology, suggesting signatures in torsion balances, NV centers, cavity scaling, and metamaterials.
    Details: CLF paper (17803804).

4. EFT / SMEFT and lattice structure

When EFT or SMEFT operators are expressed in ledger form, their dimensional content lies on an integer lattice. QDL uses this to derive constraints on admissible operators and on possible relations between Wilson coefficients.

  • Ledger lattice for operators. Each operator in an EFT or SMEFT basis is associated with a ledger vector determined by the exponents of the fields and couplings it contains. These vectors populate a discrete lattice within the 3L + 2F space.
    Details: ledger-lattice EFT work (17773324).
  • Operator exclusions and relations. Ledger-closure rules can exclude operators whose ledger vectors are incompatible with the QDC structure, and they can impose integer relations among Wilson coefficients when multiple operators share related ledger patterns.
    Details: SMEFT ledger-closure paper (17780443).
  • Connection to precision measurements. Because QDL ties operator content to dimensional closure with constants and metrology, precision experiments can be used to test which ledger-compatible operator sets are realized in nature.
    Details: prediction-filter capstone and metrology paper (17848782, 17619526).

5. Metrology, constants, and experimental roadmap

QDL is built to be testable. The metrology and constants work provides ledger descriptions of measurement chains and constant combinations, while the experimental roadmap outlines specific torsion, NV-center, cavity, and metamaterial tests.

  • QMU ledgers and dimensional audits. The Quantized Measurement Unit (QMU) ledger provides a structured dimensional audit for mechanical, electromagnetic, gravitational, and thermodynamic quantities, with a tabulated 100-entry ledger covering standard units and constants.
    Details: QMU and metrology paper (17619526).
  • Ontology of physical constants. Constants are classified according to their ledger roles and whether they represent ratios, conversion factors, or deeper structural parameters, all referenced back to the QDC.
    Details: ontology of constants and dimensional-closure framework (17663436, 17663501).
  • Experimental validation roadmap. A structured roadmap lays out how torsion balances, NV centers, cavity experiments, and metamaterials can be used to test QDL’s ledger predictions and to search for coherence signatures.
    Details: experimental validation protocol and CLF paper (17654442, 17803804).

6. How to read the QDL program

For readers encountering QDL for the first time, the recommended entry points are the capstone prediction-filter paper, the quantum-gravity coherence paper, the unified SM + gravity framework, and the Coherent Ledger Fields (CLF) paper.