Maldonado ε‑Lattice Theory‑of‑Everything Program (NEXTLEVEL v5)

Short version:

This record presents the Maldonado ε‑lattice Theory‑of‑Everything program at NEXTLEVEL v5. The central hypothesis is that many of the small dimensionless constants of the Standard Model and cosmology are not independent, but can be written as

q_i ≈ C_i ε^{n_i}

where ε ≡ sqrt(m_mu/m_tau) ≈ 0.244, n_i are integers, and C_i are order‑one coefficients.

Using 24 observables (lepton and quark mass ratios, CKM mixing, neutrino hierarchy proxies, α_em, A_s, η_b, a hidden‑sector ΔN_eff, and the electron gravitational coupling α_G(m_e)), I show that all of them lie on an ε‑lattice with 0.5 ≲ |C_i| ≲ 2 and RMS scatter σ(log10|C_i|) ≈ 0.16.

A key new result is that the tiny gravitational coupling of the electron can be expressed as α_G(m_e) ≈ 0.96 ε^{73}, bringing gravity onto the same ε‑lattice as particle and cosmological hierarchies. I also define a ToE distance D_ToE that combines cosmological, gravitational‑wave, and lattice‑tightness information into a single quality score.

This record should be viewed as a structured, falsifiable hypothesis program, not as a completed Theory of Everything. The accompanying JSON file provides the full ε‑lattice data and statistics for further analysis.

Plain‑Language Summary

This work explores a simple but powerful idea:

    Many of the “mystery numbers” of physics
    might not be independent at all.
    They might all be different powers of one single small number.

In everyday language, physicists describe our universe using many
tiny, unexplained numbers:

  • the ratios of particle masses, like electron vs muon vs tau,
  • the angles that describe how quarks and neutrinos mix,
  • the strength of gravity for an electron,
  • and small cosmological numbers, like the size of the early‑universe
    density ripples and the tiny excess of matter over antimatter.

Right now, in standard physics, these are treated as separate “input
parameters”. The theory does not say why they have these values. We
simply measure them and plug them in.

In this Theory‑of‑Everything (ToE) program, I test the hypothesis
that many of these numbers are built from a single small
parameter ε (epsilon). That is,

    Every weird small number in nature is roughly
    ε to some integer power, times a simple factor of order one.

Concretely, I take

    ε ≡ sqrt(m_mu / m_tau) ≈ 0.243851...

where m_mu and m_tau are the muon and tau masses. This ε is not
invented; it is measured from the lepton sector.

Then I take a list of 24 important dimensionless quantities:

  • lepton mass ratios,
  • quark mass ratios,
  • quark mixing (“Cabibbo”) angle,
  • neutrino mass and mixing proxies,
  • the fine‑structure constant α_em,
  • cosmological amplitudes (A_s, η_b, a small extra ΔN_eff),
  • and, in this v5 update, the dimensionless gravitational
    coupling of the electron, α_G(m_e).

For each quantity q_i I fit a relation of the form

    q_i  ≈  C_i · ε^{n_i}

where n_i is an integer and C_i is a “coefficient of order one”.

The main empirical findings are:

  1. All 24 quantities can be fitted with integer exponents
     n_i and coefficients C_i that are modest, between about
     0.5 and 2.0.

  2. The scatter of log10|C_i| around zero is only about 0.16.
     In other words, once you factor out ε^{n_i}, the remaining
     pieces are all close to 1, within a factor of ≈2 either way.

  3. The same fourth power ε^4 that controls how light the
     electron is compared to the muon and tau also controls the
     natural scale of a small extra radiation component in the
     early universe (ΔN_eff ≈ 10^{-3}).

  4. The new “v5 with gravity” result: the tiny gravitational
     coupling of the electron is also on the same ladder,

         α_G(m_e) ≈ 0.96 · ε^{73}.

     That is, the famous 10^{-45} weakness of gravity (compared
     to electromagnetism) appears as the 73rd rung on the same
     ε ladder.

These patterns are strong enough to deserve serious attention, but
I do NOT claim that this is a finished Theory of Everything. What I
propose here is a structured program — a set of hypotheses and
targets that a deeper theory must hit if the ε‑lattice picture is
on the right track.

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1. Definition of ε and the ε‑lattice
------------------------------------------------------------

The basic construction is:

  • Choose a single small parameter ε from the lepton masses.

    ε ≡ sqrt(m_mu / m_tau)
      ≈ 0.2438514583.

  • For each dimensionless observable q_i, try to write

      q_i ≈ C_i · ε^{n_i},

    where:

      – n_i is an integer (positive, negative, or zero),
      – C_i is “order one”, i.e. |C_i| is between about 0.5 and 2,
      – we keep track of log10|C_i| as a measure of how natural
        the fit is.

This construction defines the “ε‑lattice”: each integer n
labels a rung, and each observable chooses a rung and an order‑one
coefficient.

The current v5 lattice includes 24 observables:

  • ε itself,
  • ten core observables (lepton ratios, α_em, Cabibbo angle,
    a simple sinθ_13, neutrino mass ratio, A_s, η_b,
    a small hidden ΔN_eff),
  • thirteen additional observables in the quark and CKM sector,
  • plus the new gravity rung α_G(m_e).

The companion JSON file
  “Maldonado_ToE_epsilon_lattice_NEXTLEVEL_v5_with_gravity.json”
contains the exact list of quantities, their raw values, best_n,
best_c, and log10_abs_c for each fit, along with summary statistics
and an example “ToE distance” calculation.

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2. Examples of ε‑lattice fits
------------------------------------------------------------

Some representative examples (numbers rounded for clarity):

  • Lepton hierarchies

      m_mu / m_tau  ≈ 1.00 · ε^2,
      m_e  / m_mu   ≈ 1.37 · ε^4.

  • Fine‑structure constant

      α_em ≈ 0.50 · ε^3.

  • Quark mixing (Cabibbo angle)

      sin θ_12 ≈ 0.92 · ε.

  • Neutrino mass‑squared ratio

      Δm^2_21 / Δm^2_31 ≈ 0.50 · ε^2.

  • Cosmological amplitudes

      A_s   ≈ 0.80 · ε^14,
      η_b   ≈ 0.95 · ε^15.

  • Hidden‑sector energy fraction at ΔN_eff = 10^{-3}

      ε_energy(ΔN_eff = 10^{-3}) ≈ 0.94 · ε^4.

  • New in v5: electron gravitational coupling

      α_G(m_e) ≡ G m_e^2 / (ħ c)
               ≈ 1.75 × 10^{-45}
               ≈ 0.96 · ε^{73}.

------------------------------------------------------------
3. Statistical structure
------------------------------------------------------------

In the v5 lattice with gravity:

  • For the 24 quantities considered, the coefficients C_i satisfy

      0.5 ≲ |C_i| ≲ 2.0.

  • The RMS scatter σ(log10|C_i|) is about 0.16.

This means that, once you factor out ε^{n_i}, the remaining pieces
are all modest deformations around unity, not large or random
numbers.

------------------------------------------------------------
4. ToE distance D_ToE
------------------------------------------------------------

To keep track of how “healthy” a theory point is, I define a
dimensionless ToE distance D_ToE that combines four ingredients:

  1. Cosmological energy budget (ΔN_eff / ΔN_eff^max),
  2. PTA gravitational‑wave coherence (1 − PCI),
  3. Ringdown tests of GR (ε_ring / σ_ε),
  4. Tightness of the ε‑lattice (σ_log10|C_i|).

The definition is

  D_ToE^2 =
      (ΔN_eff / ΔN_eff^max)^2
    + (1 − PCI)^2
    + (ε_ring / σ_ε)^2
    + σ_log10|C_i|^2.

A point with D_ToE ≲ 1 is considered “allowed”. In the current v5
example point (ΔN_eff = 10^{-3}, ΔN_eff^max = 0.3, PCI ≈ 0.95,
GR‑consistent ringdowns, σ_log10|C_i| ≈ 0.16), we find D_ToE ≪ 1,
meaning this configuration is comfortably inside the allowed ball.

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5. Hypotheses and outlook
------------------------------------------------------------

The Maldonado ε‑lattice ToE program at NEXTLEVEL v5 can be
summarised in four hypotheses:

  H1: (ε‑lattice universality)
      Important dimensionless constants of nature lie on
      q_i ≈ C_i · ε^{n_i} with integer exponents and modest C_i.

  H2: (micro–macro bridges)
      The same ε‑powers that control microscopic hierarchies
      also control cosmological amplitudes and hidden‑sector
      contributions to ΔN_eff.

  H3: (gravity rung)
      The weakness of gravity for the electron is encoded as a
      high‑rung ε^{73} factor with an order‑one coefficient.

  H4: (rung‑compatibility test)
      Any new dimensionless constant q_new should either land on
      some ε^{n_new} with order‑one C_new, or else force a revision
      or rejection of the ε‑lattice picture.

This is not yet a complete Theory of Everything. It is a structured,
falsifiable pattern that a deeper theory could explain or contradict.
A future UV‑complete theory (string/M‑theory, quantum gravity, etc.)
would need to:

  • derive ε and the integer exponent spectrum {n_i} from first
    principles, and
  • reproduce the observed constants as q_i ≈ C_i ε^{n_i} with
    C_i ≈ 1.

If that ever happens, the ε‑lattice would move from “interesting
pattern” to “deep organizing principle” for the constants of nature.

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Companion data file for this record
------------------------------------------------------------

This text is meant to be archived together with the machine‑readable
file

  Maldonado_ToE_epsilon_lattice_NEXTLEVEL_v5_with_gravity.json

which contains:

  • epsilon_l: the numerical value of ε,
  • a list of quantities with fields:
      quantity, raw_value, best_n, best_c, log10_abs_c,
  • summary statistics of the coefficient distribution,
  • an example ToE‑distance calculation.

Together, these files define the Maldonado ε‑lattice Theory‑of‑Everything
Program at NEXTLEVEL v5, including the new gravity rung.