Particle masses / The derivation

Deriving every particle mass.

We are deriving the masses of the elementary particles from the recognition ledger, with no measured input and no fitted number. This page lists the fourteen numbers we have to reach, the structure underneath them, and where each one stands today.

The destination

Fourteen numbers from one ledger

The masses of the electron, muon and tau, the six quarks, the W, Z and Higgs bosons, the neutrino splitting ratio and the proton-to-electron ratio. A particle's mass is the energy of its pattern at rest on the recognition ledger, and that energy is the recognition cost of holding the pattern. Nothing is fitted.

Numbers derived

0 of 14

Derived, given named premises

1

Still open

13

Independent verifications passed

43 since 2 Nov

Updated 2 Nov 2026, 6:44 pm CT. 43 of 45 steps on the structure below are independently verified.

What moved

  1. 28 Oct

    The neutrino splitting ratio assembled at 17 − 12√2 = 0.029437 with no measured input. It sits inside the measured 0.02948 ± 0.00090 and holds given premises that are named and still being derived. The golden-ratio alternative was ruled out by theorem, not by the data.

  2. 2 Nov

    Program restarted at 8:58 am CT with nine derivation teams, a question-and-answer loop, and an independent verification that rebuilds every result before it counts.

  3. 2 Nov

    The native recognition cost, written in the right field coordinate, is exactly the Standard Model Higgs potential, and the kinetic term comes from the same native step: at the vacuum the two share one curvature.

  4. 2 Nov

    The heavier neutrino needs its own internal clock: a single continuous spin path has only one lift. A separate internal clock path was then constructed and independently verified; its physical enactment is the open step.

  5. 2 Nov

    Forty-three independent verifications passed and none failed. Most results are exact obstructions that close a route and name the premise the answer needs. The lepton work now has a verified rest law for prepared charged patterns, given the preparation of each generation.

  6. 2 Nov

    Native colour hopping generates the proton's three-quark transfer exactly, and the Higgs transfer has a controlled Gaussian limit. Both are independently verified.

  7. 2 Nov

    The native Higgs transfer has a verified first excitation with a gap that persists in the exact finite transfer: the quantity a rest energy is read from. A new team now computes mass ratios directly as spectral gaps of the native transfer, sector by sector.

  8. 2 Nov

    The proton's binding is now bounded natively: the full colour contact compression holds and gives binding coercivity for every nonzero baryon index (verified).

  9. 2 Nov

    First forward spectral result: on the existing native transfer with the source off, two sector gaps stand in the ratio 3 exactly, and the carrier turns out to hold no net-charge sector. Mass ratios need the physical charged carrier; that is now the target.

Every result is checked by an independent verification that rebuilds its proof from the sources before it counts here. Since the restart on 2 Nov 2026, 8:58 am CT, 43 have passed and 0 have failed; a failed claim is withdrawn and the work continues.

The fourteen numbers

  1. Electron0.51099895069 MeVOpen
  2. Muon105.6583755 MeV (206.768 electron masses)Open
  3. Tau1776.93 ± 0.09 MeVOpen
  4. Up1.90 to 2.65 MeV (at 2 GeV)Open
  5. Down4.53 to 5.18 MeV (at 2 GeV)Open
  6. Strange92.7 to 94.3 MeV (at 2 GeV)Open
  7. Charm1268.4 to 1277.6 MeVOpen
  8. Bottom4176 to 4190 MeVOpen
  9. Top172,280 to 172,860 MeVOpen
  10. W boson80,369.2 ± 13.3 MeVOpen
  11. Z boson91,187.6 ± 2.1 MeVOpen
  12. Higgs boson125,200 ± 110 MeVOpen
  13. Neutrino splitting ratio0.02948 ± 0.00090Derived, given named premises
  14. Proton-to-electron ratio1836.152673426Open

What it takes to reach a number

Thirteen of the fourteen numbers are pure ratios: eleven masses relative to the electron, the neutrino splitting ratio and the proton-to-electron ratio. The electron's mass in MeV needs one more thing, the absolute unit. In SI units every mass is a ratio to the cesium clock frequency that defines the second, so the electron row is met when the chain reaches that clock. Its ratio to the Planck mass, the hierarchy number, is what the unit work derives.

3 numbers

Charged leptons

The electron, muon and tau: three generations of one charged pattern on the ledger, each a step up the golden ladder, with a native correction that turns the bare step into the physical mass.

0 of 3 derived

  1. Open

    Electron

    Measured 0.51099895069 MeV

    The reference for every ratio. Its value in MeV needs the absolute unit, the electron's mass relative to the Planck mass.

    Next Construct the native posting operation that fixes a unit, and the clock reading that reaches the SI second.

  2. Open

    Muon

    Measured 105.6583755 MeV (206.768 electron masses)

    Its generation step and its dressing both need derivation. Earlier dressing forms were chosen with the data in view and do not count.

    Next Instantiate the proved preparation-to-rest law for the muon's generation branch.

  3. Open

    Tau

    Measured 1776.93 ± 0.09 MeV

    Same derivation as the muon: the third generation's step and the same dressing law.

    Next Follows the muon once the generation branches are selected.

6 numbers

Quarks

Six quark masses, each carried in three colours. Quark masses are quoted at a running scale, so the derivation also needs the native running scheme.

0 of 6 derived

  1. Open

    Up

    Measured 1.90 to 2.65 MeV (at 2 GeV)

    Together with the down quark, the first target: a same-scale ratio needs no scheme bridge.

    Next The native quark dressing on the colour carrier, then u/d.

  2. Open

    Down

    Measured 4.53 to 5.18 MeV (at 2 GeV)

    Same-scale partner of the up quark.

    Next u/d and s/d first.

  3. Open

    Strange

    Measured 92.7 to 94.3 MeV (at 2 GeV)

    Same-scale ratio s/d is the second target.

    Next s/d from the native dressing.

  4. Open

    Charm

    Measured 1268.4 to 1277.6 MeV

    Needs the native running scheme to compare with its own-scale mass.

    Next Derive the scale a posted rest eigenvalue refers to.

  5. Open

    Bottom

    Measured 4176 to 4190 MeV

    Needs the running scheme and the corrected down ladder.

    Next After the rung table and the running scheme.

  6. Open

    Top

    Measured 172,280 to 172,860 MeV

    The library's earlier up-type ladder is ruled out at every scale; the trailing step needs a derivation.

    Next Derive the up-type rung table from native dynamics.

3 numbers

Electroweak bosons

The W, Z and Higgs as rest energies of gauge and scalar excitations on the same ledger. Three ratios carry all of their information: W/Z, Z/e and H/Z.

0 of 3 derived

  1. Open

    W boson

    Measured 80,369.2 ± 13.3 MeV

    The tree factor between W and Z comes from doublet joins; the native correction is open. An earlier reading used the measured Z and does not count.

    Next The native gauge-response curvature on the cube's faces.

  2. Open

    Z boson

    Measured 91,187.6 ± 2.1 MeV

    Its ratio to the electron sets the electroweak sector against the lepton ladder.

    Next After the gauge curvature and the unit.

  3. Open

    Higgs boson

    Measured 125,200 ± 110 MeV

    The native cost is exactly the Standard Model Higgs potential in the right coordinate, and the kinetic term follows from the same step. The mass itself needs the rest normalization, without the measured vacuum value.

    Next Normalize the verified first-excitation gap of the native Higgs transfer into a rest energy, without the measured vacuum value.

1 number

Neutrinos

Massive neutral patterns that hold their clock phase at rest. The splitting ratio Δm²₂₁/Δm²₃₁ needs no absolute unit.

0 of 1 derived

  1. Derived, given named premises

    Neutrino splitting ratio

    Measured 0.02948 ± 0.00090

    Our value 17 − 12√2 = 0.029437

    Reached with no measured input, given premises still being derived: the rest cost of a held clock phase obeys the composition law on the eight clock phases; the two massive neutrinos are spin-½ patterns on two distinct clock lifts; a neutral pattern that holds no clock phase has no rest energy; the held ratio's own rest term vanishes for neutral patterns; and the masses are distinct and normally ordered.

    Next The physical enactment of the separate internal clock path, then the rest-energy accounting.

1 number

The proton

Almost all of the proton's mass is binding: three colour charges held in a colour-neutral pattern. Its ratio to the electron needs no absolute unit.

0 of 1 derived

  1. Open

    Proton-to-electron ratio

    Measured 1836.152673426

    Needs the native confinement cost of a three-colour singlet and its normalization against the electron's rest energy. Earlier closure chains were circular and are withdrawn.

    Next Turn the verified binding coercivity into the proton's rest energy relative to the electron's.

Underneath every row

The structure the numbers need

Each number rests on the same layers: which patterns exist, their generation steps, each sector’s reference energy, the native corrections, and the absolute unit. Most results so far are exact obstructions: each closes a route and names the premise the answer needs.

  1. Open

    The native transfer spectrum

    The forward route: a mass ratio is a ratio of spectral gaps of the ledger's native transfer, sector by sector. No mass formula goes in; the gaps come out.

    Progress

    1. 2 Nov On the existing native transfer with the source off, the neutral and dipole sector gaps are 3c₁ and c₁ with c₁ = −log(I₁(β)/I₀(β)): their ratio is exactly 3. With the source on, the gaps exist with explicit error bounds. That carrier has no net-charge sector, so the physical charged carrier is the next step. Awaiting verification

  2. Open

    Charges and colour

    Which charged patterns exist, with charges −1, +2/3 and −1/3 and three colours, from the ledger's own dynamics.

    Progress

    1. 2 Nov A parity readout conserved under every transfer is constant on the whole even carrier, and the posting cost is the same for every transfer, so neither selects the charges. Verified
    2. 2 Nov Native current transport, five invariant source sectors and an exact finite-time current law. Verified
    3. 2 Nov Global charge descent holds exactly in the even case; the full face-group twist needs its double cover. Verified
    4. 2 Nov The exact five-sector source algebra, coherent current limits, retained-history second moments, and matter-field compensation. Verified

  3. Open

    Generations and rungs

    Why there are three generations, and the integer steps of each sector's ladder.

    Progress

    1. 2 Nov Stable patterns are not fixed by their support alone: the missing laws are selection, retention and rung pricing. Verified
    2. 2 Nov Native retention, constrained selection and attained registration minima constructed. Verified
    3. 2 Nov Native selector and retained-payload constructions. Verified
    4. 2 Nov The finite account-ledger loading minimum and all its minimizers, with exact exchange and tie boundaries for every three-load assignment. Verified
    5. 2 Nov Native conserved reference sectors, constructive winding control and coherent positive-post operators. Awaiting verification

  4. Open

    Sector yardsticks

    The powers of two and offsets that set each sector's reference energy.

    Progress

    1. 2 Nov The posting laws admit every positive base and every sector origin, so they cannot select the factor of two alone. Verified
    2. 2 Nov Adding one fixed quantum per posting cannot double the energy step after step against a fixed reference. Verified
    3. 2 Nov Reference energies from the native source response, and a composite operation that doubles energy, constructed. Verified
    4. 2 Nov Intrinsic minima and neutral source operations with their spectral references. Verified

  5. Open

    The absolute unit

    The electron's mass relative to the Planck mass, and the chain to the cesium clock that defines the SI second.

    Progress

    1. 2 Nov A native activity readout with exact posting costs, and the SI anchor stated exactly. Verified
    2. 2 Nov The native fixed-quantum readout and its phase transport, with the hierarchy consequence proved for any prepared pair. Verified
    3. 2 Nov Native source phase and action, and literal current-history bridges, constructed; the physical electron and vacuum selection still has to fix the unit. Verified
    4. 2 Nov Native current acquisition and its action; the physical gain, the source and vacuum selection and the clock anchoring still have to fix the unit. Verified

  6. Open

    Lepton dressing

    The native correction that turns a bare ladder step into a charged lepton's physical rest energy.

    Progress

    1. 2 Nov An added constant cost rescales the native transfer exactly by e−b; stationary calorimetry proved. Verified
    2. 2 Nov The rest law of a prepared charged branch, for every preparation that reads the native rest generator. Verified
    3. 2 Nov The preparation-to-rest law for enacted transfer histories. Verified
    4. 2 Nov The native mixed return is not central: it acts differently on internal states, first at source-word length 3, so the internal states can be told apart natively. Verified
    5. 2 Nov Native record and control operations, a charged-support source lift and relative transfer gaps. Verified

  7. Open

    Quark dressing and running

    The native colour dressing and the scale a quark's rest energy refers to.

    Progress

    1. 2 Nov A fixed endpoint cost cannot supply the gap's constant displacement; a shared running law transports same-scale ratios. Verified
    2. 2 Nov The native colour contact and return, a local interacting inverse and reference-normalized spectral bridges. Verified
    3. 2 Nov Under arbitrary flavour mixing, only the trivial mass-only combination is invariant. Verified
    4. 2 Nov Native contact modes and the effective return; the full logarithmic generator is unique in its class. Verified

  8. Open

    Electroweak bosons

    Gauge and scalar rest energies from the ledger's face comparisons.

    Progress

    1. 2 Nov In the coordinate q(t) = 2 arsinh(t/2 + t²/4) the native cost is exactly t²/2 + t³/2 + t⁴/8, the Standard Model Higgs potential. Verified
    2. 2 Nov The kinetic term comes from the native transfer step itself; at the vacuum it shares the potential's curvature. Verified
    3. 2 Nov Exact internal-reference dynamics and a gauge-invariant relative comparison. Verified
    4. 2 Nov The native weighted face comparison gives the doublet's gauge curvature: its complete normal form, kernel and spectrum, with every normalization explicit. Verified
    5. 2 Nov The finite cosh transfer has a controlled Gaussian limit, in operator norm, with unitary normalization. Verified
    6. 2 Nov The constructed Gaussian mode is the first excitation on the full space, with a simple top eigenvalue and exact two-step ordering. Verified
    7. 2 Nov Native doublet mixers, finite gauge orbits and a gauge-invariant two-path kinetic comparison. Verified
    8. 2 Nov The first-excitation gap persists in the exact finite transfer, for every size and all small enough amplitudes. Verified
    9. 2 Nov The original reference integral gives a positive finite-temperature correction, with its curvature and controlled limit. Verified

  9. Open

    Hadron binding

    The confinement cost of a colour-neutral three-quark pattern.

    Progress

    1. 2 Nov Native singlet transfer bounds, and countermodels showing which separations do not fix the ratio. Verified
    2. 2 Nov The full cubic SU(3) Haar hop equals the signed three-quark transfer exactly, with every spin and flavour term: native colour hopping generates the baryon transfer. Verified
    3. 2 Nov A native colour-singlet source, Haar operator identities and conditional coercivity. Verified
    4. 2 Nov The full Haar contact compression holds, and native binding coercivity follows for every nonzero baryon index. Verified

  10. Derived, given named premises

    The neutrino premises

    The premises under the neutrino splitting ratio.

    Progress

    1. 2 Nov The clock cost law follows from a native energy measurement at the scope of that measurement; local curvature alone does not force it. Verified
    2. 2 Nov A single continuous spin path has a unique lift, so the heavier neutrino needs a separate internal clock. Verified
    3. 2 Nov Native comparison ports and separate spatial and internal clock paths constructed. Verified
    4. 2 Nov Finite clock storage and its correspondence with the native update. Verified
    5. 2 Nov The full native comparator, its retained-port eigenmodes, and positive orientation and response candidates. Verified

  11. Open

    The rest of the same excitation

    That a pattern's rest energy and its inertia are the same quantity, from one native generator. This is the mass formation program's subject; every row above uses it.

How we count

A number counts as derived only when it follows from the recognition ledger with no measured input and no fitted integer, the proof is complete, and an independent verification has rebuilt it from its sources. Earlier forms that were chosen with the data in view do not count, however close they come.

Derived · independently verified
The value follows from the ledger alone, and an independent verification rebuilt the proof.
Derived, given named premises
The value follows with no measured input, given premises that are named and still being derived.
Open
Still to derive. These are what the work is on now.

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