Framework

Quantized Dimensional Ledger (QDL): Dimensional Closure as an Admissibility Framework

QDL treats dimensional analysis as a model-admissibility and validation layer: not merely “units consistent,” but “structurally allowed.” Physical quantities are represented as integer ledger vectors in a 3L + 2F length–frequency basis, and admissible constructions are required to close onto a conserved Quantized Dimensional Cell (QDC).

This page summarizes the core ideas, makes the core assumptions explicit, states falsification boundaries, and preserves a framework-first reading order for the QDL program.

Scope & Status (read this first)
Core formalism: defined here Applications: hypothesis stage
QDL is presented as a pre-dynamical admissibility layer. This page distinguishes: (i) what is defined as the QDL formalism, (ii) what is asserted as a postulate, and (iii) what is explored as an application.
Defined on this page

Ledger representation in a 3L + 2F basis; a closure-style admissibility predicate; declared transform/equivalence intent; reading order.

Postulates

Existence of a conserved QDC target (L³F²) and the claim that closure adds constraint beyond dimensional homogeneity.

Applications

Gravity/coherence, EFT/SMEFT, constants/metrology, and experiments are presented as downstream uses of the admissibility layer, not as established results.

Not claimed here

QDL does not replace dynamics or fit data by itself; it classifies constructions as admissible/inadmissible under declared rules and transforms.

If you are looking for a framework-independent operational layer, see the national standards paper on dimensional admissibility (linked on the Home page).
Canonical Definition & Recommended Reading Order (Framework-first)
#1 Canonical framework #2 Reconstruction #3 Prediction filter #4 Renormalization #5 Auditing / application

If you want the cleanest entry path (and the one reflected across the site), start here:

Top 5 on Publications Read canonical paper

Domain applications (unified SM+gravity, minimum-length geometry, coherent ledger fields, SMEFT, metrology, experiments, cosmology) are best read after this core path.

One-picture mental model
QDL is a pre-dynamical admissibility layer: represent quantities as integer ledger vectors in a 3L + 2F basis, apply a closure check onto the QDC, and propagate the allowed/disallowed classification into operators, constants, and validation workflows.
Ledger representation Map quantities to integer vectors X → [L1, L2, L3, F1, F2] QDC ~ L³F² Closure / admissibility Pre-dynamical filter Does construction close onto QDC? Allowed Excluded Downstream What the filter controls Operators / EFT bases Constants / relations Benchmarks / null tests
Practical reading strategy: use the Top 5 above for framework-first onboarding, then branch into applications once the closure rule is internalized.

Definitions (v1.0)

Takeaway: QDL is a defined representation + an explicit admissibility predicate; everything downstream inherits its meaning from these definitions.

The items below state the minimal objects used throughout this page. They are phrased as definitions of use, not as claims of physical necessity.

  1. Ledger basis. A 5-component exponent basis ⟨L1,L2,L3,F1,F2⟩ used to encode dimensional exponents as integers. (This page does not require the basis to be physically privileged; applications that argue privilege are treated separately.)
  2. Ledger map. A map from a quantity X to an integer vector v(X) = [L1,L2,L3,F1,F2] ∈ ℤ⁵, combined by integer addition under multiplication of quantities.
  3. QDC target. A designated conserved target monomial A_QDC ~ L³F² used as the closure reference in the admissibility predicate below.
  4. Closure predicate (admissibility test). A construction is “admissible” if the declared ledger sum for the construction satisfies a closure rule of the form Σ v(terms) = n · v(QDC) for some integer n, under a declared equivalence/transform set (next item).
  5. Declared equivalence / transforms. A declared set of representation changes (basis reparameterizations, unit changes, and other allowed rewrites) under which admissibility claims are asserted to be invariant. (If a transform is not declared, invariance is not claimed.)
  6. Output type. The framework-level output is a classification: admissible / excluded under the declared rules. It is not a dynamical fit, and it does not substitute for empirical validation.
Canonical definition and worked examples are developed in the validation-layer paper (17979789).

Assumptions & commitments

Takeaway: These are the explicit commitments required for QDL claims to be meaningful; unstated commitments are not implied.

The list below is intentionally direct: it states what must be accepted for the framework, as presented here, to be used as an admissibility filter.

  • Integer exponent encoding. The target class of models admits an integer-lattice representation of dimensional exponents (ledger vectors in ℤ⁵).
  • QDC postulate. A conserved QDC target L³F² is adopted as the closure reference.
  • Closure adds constraint. The closure predicate is asserted to be strictly stronger than dimensional homogeneity for at least some model classes.
  • Declared transforms only. Any invariance claim is scoped to a declared set of transforms/equivalences; undisclosed invariances are not claimed.
  • Interpretation discipline. “Excluded” means excluded by the admissibility predicate; it is not, by itself, an empirical refutation of a physical model unless tied to a falsification protocol (see below).
Where a physically privileged reading of the basis or group structure is argued, those arguments belong in the technical papers; this page keeps the framework definition operational.

1. Core dimensional structure

Takeaway: Represent quantities as integer vectors in a 3L + 2F basis, and treat QDC closure as the target that structures admissibility.

QDL begins with a length–frequency dimensional basis and a conserved Quantized Dimensional Cell. These define the ledger representation and the closure target used by the admissibility rule.

  • 3L + 2F length–frequency basis.
    The framework uses a three-length, two-frequency exponent space rather than M–L–T. Physical quantities are expanded in this basis with integer exponents.
    Accessible entry: structural reconstruction paper (17882709). Technical support: metrology/QMU ledger (17619526).
  • Quantized Dimensional Cell (QDC).
    The QDC is a conserved dimensional “cell”: AQDC ∼ L3F2

    QDL treats closure onto integer multiples of this cell as the admissibility target for actions, interactions, and (in metrology) measurement-chain relations.

    Geometry support: SO(3,2) QDC structure (17683786).
  • Ledger vector representation.
    X → [L1, L2, L3, F1, F2]

    Each physical quantity maps to a five-component integer vector in the 3L + 2F basis. Ledger vectors combine by integer addition when constructing admissible terms or tracing measurement chains.

    Method-first reference: prediction filter paper (17848782).

2. Ledger closure as an admissibility rule

Takeaway: Closure is a strict pre-fit constraint that can filter admissible constructions before phenomenological tuning.

QDL replaces “dimensional consistency” as a loose check with a strict closure constraint: admissible constructions must close onto integer multiples of the QDC, under declared transforms.

  • Ledger-closure principle.
    Instead of simply matching units, QDL imposes a closure predicate: declared sums of field and coupling exponents must map onto integer multiples of the QDC.
    Canonical definition: validation-layer paper (17979789).
  • What QDL claims beyond dimensional homogeneity.
    Dimensional homogeneity constrains functional form; QDL claims an additional constraint: closure onto integer multiples of a conserved target under declared equivalences. This page states the claim and points to technical development; it does not assert independent external validation by itself.
    Core method and worked constructions: prediction filter paper (17848782).
  • Technical anchor: renormalization and operator pruning.
    The closure rule can be applied as a pruning constraint, sharpening the admissibility framework into an operator rule set (technical treatment).
    Technical anchor: renormalization paper (18025072).
Baseline comparison: SMEFT

SMEFT claims are intended to be checked against canonical operator enumerations and redundancy handling. Where QDL yields “exclusions,” they should be reported as either (i) re-derivations of known redundancies or (ii) genuinely additional constraints, with explicit reconciliation.

Baseline comparison: SI & metrology

SI 2019 fixes numerical values of certain constants by definition. QDL “constants ontology” is treated as a structural taxonomy unless a separate metrological constraint is explicitly derived and operationalized.

Structural positioning (historical analogies)

Takeaway: This is a conceptual placement tool: it clarifies QDL’s functional role as a constraint/admissibility layer, not a claim of historical equivalence.

The following comparisons are structural analogies, not claims of historical equivalence or scope. They indicate the role QDL plays relative to well-established frameworks, viewed post-verification as an admissibility and constraint layer.

Historical precedent Structural role QDL analog (post-verification)
Maxwell Field unification → emergent phenomena L–F ledger constraints → emergent coupled field sectors
Einstein Geometric constraint replaces force law Closure filters admissible operators and constants
Dirac Formal necessity → unexpected spectrum QDC structure constrains mass hierarchies and nuclear systematics
Standard Model Symmetry restricts interactions SO(3,2) ledger lattice restricts representable models

These analogies clarify conceptual function only. Differences in maturity, empirical scope, and historical impact are not implied.

Falsification (framework-level)

Takeaway: QDL is rejectable only if the closure claim is tied to declared transforms, declared model families, and pre-stated failure conditions.

This section states the framework-level failure modes in plain terms. Detailed protocols and benchmarks live on the Experiments page and in the associated Zenodo records.

Declared transforms required Declared model family required No post-hoc reinterpretation
  • Closure falsification (invariance failure). If a declared class of empirically adequate models (under a declared transform/equivalence set) repeatedly violates closure in a way that cannot be removed by the declared equivalences, then the closure claim fails for that model class.
  • Operator-constraint falsification (baseline conflict). If QDL-derived operator constraints, when mapped into standard EFT/SMEFT baselines, reduce entirely to known redundancy elimination, then QDL has not added new exclusion content for that case. If QDL claims additional exclusions, those exclusions must survive a baseline reconciliation; if they do not, the claim must be withdrawn or re-scoped.
  • Experimental falsification (scaling test). If a proposed QDL-distinct scaling signature is not observed within stated sensitivity under a pre-registered analysis plan, the specific experimental claim fails.
Validation roadmap: QDL Experimental Validation Protocol (17654442). Benchmarks and replication materials: see Experiments.

3. Gravity, coherence, and phenomenology (applications)

Takeaway: With closure fixed, QDL can be explored as a constraint on gravity/coherence constructions and then assessed via concrete phenomenology and scaling signatures.

Once the framework core is in place, QDL can be explored as a constraint layer in gravity and quantum-coherence constructions, then evaluated via concrete phenomenology (CLF) and scaling tests.

  • Quantum gravity from dimensional coherence.
    Explores whether closure and coherence constraints can motivate minimum-length geometry and related structure tied back to the QDC.
    Reference: 17848573.
  • Unified SM + gravity (field content under closure).
    Applies the closure rule to Standard Model and scalar–tensor gravity sectors under a shared ledger, with downstream claims intended for baseline and phenomenology checks.
    Reference: 17742903.
  • Coherent ledger fields (CLF).
    Connects QDC geometry to scalar–tensor–electromagnetic phenomenology, proposing signatures in torsion balances, NV centers, cavity scaling, and metamaterials.
    Reference: 17803804.

4. EFT / SMEFT as ledger lattices (applications)

Takeaway: Ledger form turns operator content into an integer lattice where closure is proposed as an additional admissibility constraint beyond standard organization.

Expressing EFT and SMEFT operator bases in ledger form yields an integer lattice. QDL proposes closure as a constraint that may exclude operators and impose structured coefficient relations, subject to explicit reconciliation with standard EFT/SMEFT baselines.

  • Ledger lattice for EFT operators.
    Operator content becomes a discrete lattice in 3L + 2F space, enabling structural organization and candidate exclusions.
    Reference: 17773324.
  • SMEFT exclusions and relations.
    Closure-derived constraints are presented as potentially excluding incompatible operators and yielding structured relations among Wilson coefficients; these claims are intended to be checked against canonical operator bases and redundancy handling.
    Reference: 17780443.
If you are evaluating SMEFT claims: treat “exclusion” as a technical statement only after mapping to a standard basis and reporting what is novel vs redundant.

5. Metrology, constants, and experimental validation (applications)

Takeaway: QDL is designed to be testable: measurement-chain ledgers and benchmark protocols connect closure claims to public data and tabletop tests.

QDL is built to be testable. Metrology and constants work provides ledger descriptions of measurement chains, while the validation protocol specifies falsifiable tabletop experiments and benchmark-style null tests.

  • QMU ledgers and dimensional audits.
    Structured dimensional audits for units and constants; supports measurement-chain reasoning under closure.
    Reference: 17619526.
  • Ontology of constants.
    Classifies constants by ledger role and structural meaning under closure; treated as taxonomy unless a separate operational constraint is explicitly derived.
    References: 17663436, 17663501.
  • Experimental validation roadmap.
    Torsion balances, NV centers, cavity experiments, and metamaterials as falsifiable probes of ledger-driven scaling laws.
    Reference: 17654442.
  • Engineering and pipeline auditing (practical layer).
    Demonstrates closure-style tests as a pre-verification method for real modeling and measurement pipelines.
    Reference: 18025343.

6. Quick-start summary

Takeaway: If you’re new: follow the Top 5 framework-first path, then branch into applications; if you’re validation-first: start from Experiments and loop back here to interpret results.

If you only take one thing from this page: QDL is a closure-based admissibility framework that turns dimensional analysis into a structural filter. For first-time readers, follow the framework-first Top 5 and then branch into applications.