# E8 projected-chain quasiparticle

**Status:** finite projected-chain carrier identified; thermodynamic and rigorous dressing bounds open  
**Machine authority:** [quasiparticle evidence](../../../evidence/data/translation-free-e8-projected-chain-quasiparticle-v1.json)

The width-six plateau is carried by a dressed, mobile defect rather than an unexplained collective eigenvalue. In the local eigenbasis, the periodic ground state acquires a small extensive virtual-excitation background. Subtracting that background from the first inversion-odd, reflection-even state leaves 0.995748, 0.995754, 0.995755 and 0.995755 excess local excitation units at widths three through six. The last increment is only $3.7\times10^{-9}$. The carrier is therefore almost exactly one added local quantum above the same dressed vacuum.

Projecting onto all seven one-local-excitation flavours gives a Bloch Hamiltonian whose sampled continuum minimum is at $k=0$, with energy 0.1816600162 above the product vacuum. The exact projected many-body width-six gap is 0.1826155983, a 0.523% difference. Restricting further to the lowest local flavour changes the band estimate by only $7.2\times10^{-5}$. The raw one-excitation-sector weight declines from 98.48% to 96.58% with width because vacuum dressing grows with volume; the background-subtracted excitation count is the size-stable diagnostic.

The simplest drive already addresses this state almost perfectly. Let $O=\sum_n(|1\rangle\langle0|+|0\rangle\langle1|)_n$, the uniform transition between the local ground state and lowest odd state. The normalized fraction of $O|\Omega\rangle$ carried by the first pole is 99.9316%, 99.9320%, 99.9320% and 99.9320% at widths three through six. At width six only 0.06797% leaks into higher odd states, while both the pole weight and oscillator strength per site have converged to a few parts in $10^9$.

The nonzero-momentum sidebands test motion rather than merely state preparation. At widths three through six, the first $k=\pm2\pi/L$ doublet lies at 0.187076, 0.185647, 0.184736 and 0.184161. The one-particle Bloch model predicts 0.185903, 0.184535, 0.183666 and 0.183121: absolute agreement better than 0.63% throughout. Dividing the exact sideband lift by $1-\cos k$ gives a dressed cosine scale that moves monotonically from 0.002973 to 0.003092. Thus the carrier has a resolved phase-frequency dispersion, not just a repeated gap.

## What this changes

The flat finite-size gap now has a concrete effective-theory interpretation: an odd one-quantum quasiparticle with a $k=0$ band minimum and a small multi-particle dressing cloud. The bare uniform odd drive is already an accurate quasi-local creator and an apparatus-facing detector channel. Its small residual spectral leakage supplies the remainder that a controlled Schrieffer-Wolff, Feshbach or finite-size lower-bound argument must bound.

## Claim boundary

The one-particle calculation is variational relative to the product vacuum, while the many-body gap is measured above the dressed vacuum. Their agreement identifies the carrier but is not a variational lower bound on the gap. No thermodynamic gap, full-charge-chain result or rigorous dressing remainder is claimed.