FQFT Paper I — Scale-First Spectral Field Formalism ​

This page is the public technical entry route for FQFT Paper I: A Scale-First Spectral Field Formalism for Hierarchical Matter Structure.

It summarizes the Paper I kernel for review and navigation. It does not claim peer-review acceptance, external validation, experimental confirmation, or accepted physics (within negated context) status.

Public Record ​

  • Title: FQFT Paper I: A Scale-First Spectral Field Formalism for Hierarchical Matter Structure
  • Zenodo record: https://Zenodo.org/records/20489060
  • Status: public provenance record
  • DOI: pending manual verification unless visible on Zenodo

Abstract Route ​

Paper I presents Fractal Quantum Field Theory as a scale-first formalism in which Planck-scale geometry is modeled through a q-regular Ramanujan graph, with the low-energy field theory routed through a Hausdorff-dimensional measure-space limit.

The paper's public review route centers on:

  • the graph substrate assumption,
  • the Hausdorff-dimensional field action,
  • the dimensional beta-function,
  • the fixed-point value,
  • the standard QFT recovery claim,
  • the spectral mass formula,
  • the three-generation spectral-band claim,
  • falsifiable prediction routes.

Kernel Map ​

1. Kernel Definitions

Ramanujan graph substrate

Paper I models Planck-scale geometry as a q-regular Ramanujan graph, with q = 5 used as the principal kernel case.

Review Need: Review mathematical assumptions behind using a finite/spectral graph substrate as a Planck-scale geometry model.

Hausdorff measure space

The low-energy field-theoretic construction is routed through a Hausdorff-dimensional measure space built from the graph substrate.

Review Need: Clarify construction, limit behavior, and relationship to standard field-theoretic measure assumptions.

Dimensional fixed point

The Hausdorff dimension is treated as a running quantity with a proposed fixed point D*H = 27.6 ± 0.3 in the v2.0 FQFT series.

Review Need: Audit derivation, inputs, uncertainty handling, and sensitivity of predictions to this value.

Spectral mass formula

Paper I routes mass hierarchy through spectral eigenvalues and a dimension-dependent power law.

Review Need: Formalize eigenvalue-to-particle assignment and test sensitivity to assignment rules.

Three-generation spectral-band claim

Paper I states that q = 5 produces three natural spectral bands associated with three fermion generations.

Review Need: Separate the mathematical band claim from the physical generation-assignment claim.

2. Equation Spine

1Kesten–McKay spectral density
ρ_KM(λ; q) = q√(4(q−1)−(λ−q)^2) / (2π(q^2−(λ−q)^2))

Spectral density used to describe the q-regular Ramanujan graph spectrum.

Review Need: Verify normalization, support, and downstream use in band assignment.
2FQFT action on Hausdorff measure space
S[Φ; D_H] = ∫ d^{D_H}x μ^{4−D_H} [1/2 g^{μν}_{D_H}∂_μΦ∂_νΦ − V(Φ) − ξR_{D_H}Φ²]

Kernel action stated by Paper I for scalar-field construction over the Hausdorff-dimensional measure space.

Review Need: Audit measure, dimensional analysis, curvature term, and QFT-limit assumptions.
3Dimensional beta-function
β_D(D_H) = μ∂D_H/∂μ

Running-dimension formalism used to define the fixed-point route.

Review Need: Formalize assumptions required to treat D_H as a running coupling.
4Dimensional fixed point
β_D(D*H) = 0

Fixed-point condition around which the v2.0 FQFT prediction spine is organized.

Review Need: Check whether the fixed point follows from stated assumptions and how it is constrained.
5Spectral mass formula
m_k² = m_0² + Λ_σ² λ_k^{D*H/2}

Mass formula connecting spectral eigenvalues to sector-dependent mass scales.

Review Need: Audit assignment rules, scale choices, dimensional consistency, and empirical comparison.
6Generation assignment rule
generation k ↔ λ_k, k = 1,2,3

Paper I route from spectral bands to three fermion generations.

Review Need: Formalize and test uniqueness/non-arbitrariness of the assignment.

3. Theorem & Formalization Targets

Standard QFT Recovery Target

Paper I states that the FQFT action recovers standard QFT in the D_H → 4 limit.

Formalization Need: State topology/limit assumptions and prove or refute the claimed recovery conditions.
formalization-targetGo to Route →

Three-Generation Spectral Band Target

Paper I states that q = 5 yields three spectral bands used to route the three-generation claim.

Formalization Need: Separate graph-spectrum band structure from physical generation assignment and formalize both levels.
formalization-targetGo to Route →

Dimensional Fixed-Point Target

Paper I uses D*H = 27.6 ± 0.3 as the fixed-point value throughout the v2.0 FQFT series.

Formalization Need: Audit all five stated inputs, uncertainty combination, and prediction sensitivity.
requires-independent-reviewGo to Route →

Prediction Spine Target

Paper I and the prediction ledger route specific numerical predictions into near- and medium-term tests.

Formalization Need: Connect each prediction to exact formulas, inputs, computation outputs, and falsification conditions.
requires-independent-reviewGo to Route →

4. Review Boundary

This kernel map summarizes Paper I for public review. It does not convert paper-internal claims into accepted physics or formal proof.

Paper I should be read together with the public FQFT falsifiability route.

Paper I should also be read with the computational companion and artifact map.

Review Boundary ​

This page presents an authorial theoretical kernel and public research record. It does not claim peer-review acceptance, external validation, certification, or accepted physics (within negated context) status.

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