# n90 — what the gravity-EM link teaches: charge, mass, proton, neutron
# (2026-07-10)

## The structural identity
In this framework one object carries both couplings: a particle IS a
consumption pattern c_i >= 0 on the substrate, and
   MASS   ∝ its SMOOTH component   (Σ c_i        — gravity's charge)
   CHARGE =  its STAGGERED component (Σ (-1)^i c_i — EM's charge)
Gravity and electromagnetism are two orthogonal Fourier projections
of the same coupling. Everything below follows from that plus one
inequality.

## The charge-mass inequality [structural, from c >= 0]
Consumption is non-negative (a drain cannot be a source), so by the
triangle inequality
   |Q_staggered| <= M_smooth        — CHARGE <= MASS, always,
with equality iff the dressing lives on a single parity class: the
EXTREMAL (elementary) dressing. Consequences, checked against nature:
- NO MASSLESS CHARGED PARTICLE CAN EXIST — structural, not accidental.
  (Nature: every charged particle is massive; the photon, gluon, and
  all massless states are neutral. Holds for all known particles.)
- The lightest unit-charge particle saturates the bound: THE ELECTRON
  IS THE FRAMEWORK'S EXTREMAL DRESSING — single-parity, maximally
  charged for its consumption. Its m/q sets the conversion unit.
- FALSIFIER (live, against millicharged-particle searches): a particle
  of charge eps*e must weigh at least eps*m_e (eps = 1e-3 -> 511 eV
  minimum). Any confirmed light millicharged particle below the line
  kills the parity reading of charge outright.

## What it says about the proton and the neutron
- PROTON: charge e, mass 1836 m_e -> its staggered fraction is 5.4e-4:
  99.95% of the proton's consumption is CHARGE-NEUTRAL. The framework
  thus requires that almost all nucleon mass be neutral-sector
  consumption — and QCD independently says exactly that (quark masses
  ~1% of m_p; binding/gluon energy ~99%). A shape-level consistency
  the framework did not tune for.
- NEUTRON: zero net staggered charge, full smooth consumption —
  gravitates identically (m_n ≈ m_p to 0.14%), couples to EM only
  through the measured neutral residual (r^-3.5, parity-oscillating —
  the framework's vdW analog) and through internal structure. That a
  neutral composite still has EM interactions of shorter range is not
  an addition; it was measured (n69-E5) before this reading existed.
- THE n-p MASS SPLIT (m_n - m_p = +1.29 MeV): the framework's charged
  dressing pays an EXTRA staggered-field cost — charge ADDS mass, so
  from the EM channel alone the PROTON should be heavier. Nature says
  the neutron is heavier: the matter sector must overcompensate
  (nature's version: m_d > m_u beats the EM self-energy). The
  framework reproduces the standard tension and its resolution
  requirement — a consistency, not a prediction, flagged as such.
- CHARGE QUANTIZATION IS NOT DELIVERED: staggered charge is continuous
  in c; why charge comes in units of e needs the matter sector
  (headstone-27 territory). Named, not hidden.

## The one-line teaching
Mass is the total bill; charge is the bill's parity imbalance; no
imbalance can exceed its total — so charge is bounded by mass, the
electron sits exactly on the line, the proton is 99.95% neutral
bookkeeping, and any light millicharged particle would tear the whole
reading down. The gravity-EM link does not compute m_p or e — it
explains their ORDERING, and stakes a falsifiable line under every
charged particle nature will ever show us.