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Verifying the instrument

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FALSIFIED
Wavefunction
physics
coupling
0.040
potential
1.00
packet
2.0
note
0.60
smooth
8
harmony
0.00
dimerize
0 (uniform)
GAPLESS · DIRACbands touch — winding undefined
winding—
Zak φ—
gap Δ0.0000
edges0
edge localization
Q = C = 1 · per cycle (Thouless pump)Zak φ · 0 (δ>0) → π (δ<0) · Q = |w(δ<0)−w(δ>0)|Berry → Thouless · Zak 1989 / Thouless 1983 / Rice–Mele 1982 · enclosing ⇒ ℤ
amp
0 (off)
drive
6.00 Hz
stateOFF
spacing—
bands—
amp 0 — byte-identical, no Floquet term
f = ω_drive/2 = 0.5 · period 2T (time crystal)Rigid · pinned at 1/2 vs pulse error ε · 60.0 Hz @ 120 Hz refFloquet time crystal · Bauer–Nayak 2016 / Khemani 2016 / Yao 2017 · rigid ⇔ disordered+interacting
ψ → modulation source
smooth
80 ms
output
stateOFF
centroid—
cv—
off — instrument emits nothing (pure sink)
r
0 (off)
axis
0°
pump
0.50 Hz
stateOFF
depth—
axis—
off — byte-identical, evolveScalarStep1D untouched
t_rev = 2π√n̄/g = 25.13 · collapse-revival (Jaynes–Cummings)Vac Rabi · Ω₀ = 2g = 2.00 · t_c = √2/g = 1.41 · n̄ = 16 refJaynes–Cummings · Eberly et al. 1980 / Shore–Knight 1993 / Walls–Milburn §10 · silence ≪ revival
csRatio = 1 + 1/(2 sinh²r) = 2.234 · Cauchy–Schwarz violation > 1TMSV · n̄ = sinh²r = 0.405 · S = 0.844 · g²_aa(0) = 2 thermal · r = 0.6 refTwo-mode squeezing · Walls–Milburn §5 / Loudon §6 · twin beams Var(n_a−n_b) ≡ 0 · antibunching ref Kimble–Dagenais–Mandel 1977
eraserContrast = V_+ − V_marked = 1.00 · Scully–Drühl fringe recoveryErased · V_unmarked = 1.00 · V_marked = 0.00 · V_+ = 1.00 · V² + D² = 1.00 · P_± = 0.50Quantum eraser · Scully–Drühl 1982 / Englert 1996 / Bohr 1928 · information not disturbance · Pillar 4 Part B
log n_defect ÷ log τ_Q = -0.50 · universal Kibble–Zurek exponentScaling · n_def(τ_Q=256) = 0.0141 · α = 1.00 · cited 1/(α·π·√(2·τ_Q))Kibble–Zurek · Kibble 1976 / Zurek 1985 / Damski 2005 / Dziarmaga 2010 · universality is the slope · Pillar 4
ω_Z = 2·mc²/ℏ = 2.00 · Dirac-cone gap frequencyTremble · E_±(0) = ±1.00 · gap = 2.00 · P_+ ψ has no tremblingZitterbewegung · Schrödinger 1930 / Thaller §1.4 / Dirac 1928 · the gap IS the trembling · Pillar 4
⟨D⟩(U/J=4) = 0.1464 · Mott crossover (Coleman §3.4)Doublon · E_− = -0.828 · 4J²/U = 1.00 · ⟨D⟩(0) = ½, ⟨D⟩(∞) → 0Hubbard dimer · Hubbard 1963 / Anderson 1959 / Coleman §3.4 · the Mott crossover IS the cited ⟨D⟩(U/J) · Pillar 4
α₁ = 1.85576 · Olver/Airy turning-point (DLMF 10.21.40)Whispering gallery · (j_{m=1000} − m)/m^(1/3) = 1.8661 · next-order 0.0103 · |a_1| = 2.3381Heller scar · Heller 1984 / Olver §11.10 / Stöckmann §3.1 · boundary tube depth ~ R · m^(−2/3) · Pillar 4
⟨r̃⟩_Poisson = 0.3863 · cited Atas 2013 (deep MBL)MBL vs ETH · ⟨r̃⟩_GOE = 0.5359 · gap = 0.1496 · C(8,4) = 70MBL vs ETH · Atas 2013 / Pal-Huse 2010 / Oganesyan-Huse 2007 · 2·ln 2 − 1 vs 4 − 2·√3 universality · Pillar 4
F_14 = 377 · cited PXP dim at N=12 OBC (Fibonacci)PXP SCARS · T_rev = 4.788 · F ≥ 0.50 · floor ≤ 0.10PXP scars · Turner-Papić 2018 / Bernien 2017 / Sun 1989 · Z₂ revival vs generic floor · Pillar 4
R ≤ 0.50 · cited Turner-Papić 2018 factor-2 OTOC suppressionOTOC · PXP · T_rev = 4.788 · r = 6 · C ≤ 4OTOC · Roberts-Stanford 2015 / Larkin-Ovchinnikov 1969 / Turner-Papić 2018 · scrambling suppression · Pillar 4
R_S ≤ 0.50 · cited Turner-Papić 2018 sub-thermal entanglement revivalS(T) « S_PAGE · T_rev = 4.788 · N/2 = 6 · D_A = 21 · S ≤ ln D_AENTANGLEMENT · Bengtsson-Życzkowski 2017 / Page 1993 / Turner-Papić 2018 · sub-thermal revival · Pillar 4
R_LS ≤ 0.85 · cited Turner-Papić 2018 atypical-band scar-tower signature⟨r̃⟩_SCAR « ⟨r̃⟩_BULK · ⟨r̃⟩_P = 0.386 · ⟨r̃⟩_GOE = 0.536 · N+1 = 13 · bulk = 364 · sharp ≥ 10×LEVEL STATISTICS · Atas 2013 / Turner-Papić 2018 / Choi 2019 · atypical Poisson-side band · Pillar 4
R_I ≤ 0.50 · cited Calabrese-Cardy / Vidmar-Rigol / Turner-Papić 2018 sub-thermal mutual infoI(A:B) « 2·S_Page · I = S(A)+S(B)−S(AB) · S(B) ≡ S(AC) · D_A = 8 · D_BC = 55 · Araki-Lieb I ≤ 2·min(S_A,S_B)MUTUAL INFORMATION · Cover-Thomas 2006 / Araki-Lieb 1970 / Calabrese-Cardy 2004 / Vidmar-Rigol 2017 / Turner-Papić 2018 · sub-thermal tripartite revival · Pillar 4
F(T_rev, N=8) = 0.7596 ≥ 0.50 · cited Turner-Papić 2018 realtime scar revival (Wave C #10 L-scoped)F ≥ F_threshold · Δ = 0 ULP vs offline pxpRevivalFidelity · T_rev = 4.788 · N = 8 · D = 55 · scar tower = 9REALTIME SCARRING · Turner-Papić 2018 / Sun 1989 / Bernien 2017 · O(D) eigenbasis-amplitude · sector OFF ⇒ RMS-0 · Pillar 4 L-scoped
R_g (N=8) = 5.844 ≥ 0.50 · cited Anantharaman-Monk 2024/2025 finite-dim spectral-gap (Wave D.1)Δ₀₁ ≫ ⟨s⟩ · BULK · Δ₀₁ = 1.107 · ⟨s⟩ = 0.189 · N = 8 · D = 55 · mult = 1 · headroom = 5.34SPECTRAL GAP · Anantharaman-Monk 2024/2025 / BGS 1984 / Wigner 1955 · Perron-Frobenius · Pillar 4 Wave D.1 Class 0
R_K (N=8) = 1.349 ≥ 0.50 · cited Cotler 2017 SFF slope-dip-ramp-plateau (Wave D.2)SLOPE→DIP→RAMP→PLATEAU · K(0) = 1.00 · K_dip = 2.46e-9 · ⟨K⟩_late·D = 1.349 · t_H = 33.8 · N = 8 · D = 55 · headroom = 0.85SPECTRAL FORM FACTOR · Cotler 2017 / Mehta 2004 / BGS 1984 · Berry 1985 · Pillar 4 Wave D.2 Class 0
class (N=8) = GOE ≡ GOE · cited Dyson 1962 β=1 threefold way (Wave D.3)GOE β=1 · GUE β=2 · GSE β=4 · ⟨r̃⟩ = 0.468 · d_GOE = 0.068 · d_GUE = 0.131 · d_GSE = 0.206 · margin = +0.064 · N = 8 · D = 55DYSON THREEFOLD WAY · Dyson 1962 / Atas 2013 / BGS 1984 · Wigner 1955 · Pillar 4 Wave D.3 Class 0
bulk ⟨r̃⟩ (N=8) = 0.424 ∈ (0.386, 0.536) · cited Anantharaman-Monk Möbius filter analog β=1 basin (Wave D.4)Poisson β=0 · GOE β=1 · GUE β=2 · ⟨r̃⟩_full = 0.468 · ⟨r̃⟩_scar = 0.109 · basinMargin = +0.038 · filterShift = 0.044 · N = 8 · D = 55 · GUE = 0.5996MÖBIUS FILTER · Anantharaman-Monk 2024/2025 · Atas 2013 · Turner-Papić 2018 · Pillar 4 Wave D.4 Class 0
ξ₁_scar (N=8) = 0.6931 < ξ₁_bulk = 1.0668 · cited Li-Haldane 2008 entanglement-spectrum scar/thermal contrast (Wave D.5)ξ_α = −log(s²_α) · Li-Haldane 2008 · xiContrast = +0.374 · s²_max_scar = 0.500 · s²_max_bulk = 0.344 · N = 8 · D = 55 · D_A = 8ENTANGLEMENT SPECTRUM · Li-Haldane 2008 · Turner-Papić 2018 · Bengtsson-Życzkowski 2017 · Pillar 4 Wave D.5 Class 0
gapMin (α=1/3, N=60) = 1.2679 > 0.00 · cited Hofstadter 1976 rational-flux gap-opening (Wave D.6)gapMin ≡ 3−√3 · Hofstadter 1976 · bandsCount = 3 · gapMax = √6 = 2.449 · span = 1+√3+√6 = 5.182 · σ = [+1, −1] · α = 0.3333 · N = 60HOFSTADTER SPECTROGRAM · Hofstadter 1976 · Wannier 1978 · Streda 1982 · TKNN 1982 · Pillar 4 Wave D.6 Class 0
crossPin (N=8, OBC) = 4.9e-15 ≤ 1e-12 · inversion-sector projection UNITARY substrate ULP (Wave D.7)L104 physics-limited · γ-probed N ∈ {6,8,10,12,14} · D = 55 · D₊ = 30 · D₋ = 25 · |r₊ − r₋| = 0.0265 · scar overlap (+) = 0.951 · 5 recipes min |·− rGOE| = 0.04PXP SYMMETRY SECTOR · Turner-Papić 2018 · Lin-Motrunich 2019 · Atas 2013 · Anantharaman-Monk 2024 · Pillar 4 Wave D.7 Class 0
chaosBoundMargin (N=8, β=1, J=1, seed=0xc0ffee) = 4.7277 ≥ 0.00 · cited Maldacena 2016 chaos bound λ_L ≤ 2π/β (Wave E.1)λ_L ≈ 1.5555 ≤ 2π · Maldacena-Shenker-Stanford 2016 · D = 16 · σ_J = √3/16 · bandwidth = 3.008 · R² = 0.9975 · 10 probes all margin > 0 (worst 1.22 at β=5)SYK LYAPUNOV · Maldacena-Shenker-Stanford 2016 · Kitaev 2015 · Roberts-Stanford 2015 · Pillar 4 Wave E.1 Class 2
gapAtZero (N=64, L=64, m=g=n=ℏ=1) = 0.00 ≡ cited 0.00 EXACT · cited Goldstone 1961 universality (Wave E.2)spectrumCrossPin = 5.55e-16 ≤ 1e-12 · Path A ≡ Path B BdG eigendecomp · c = √(gn/m) = 1.00 · ξ = 1/√2 = 0.7071 · k_h = √2 = 1.4142 · Δk = π/32 = 0.0982BOGOLIUBOV SPECTRUM · Bogoliubov 1947 · Pitaevskii-Stringari §4.2 · Goldstone 1961 · Pillar 3 Wave E.2 Class 1
state
n1
δ(W) = 0.21401 · closed form 0.21306∫ W d²β = 1.0000 ≈ 1 · tol 0.001Kenfack-Życzkowski 2004 · δ ≡ 2/√e − 1 = 0.21306WIGNER NEGATIVITY · Wigner 1932 · Hudson 1974 · Kenfack-Życzkowski 2004 · Cahill-Glauber 1969 · Pillar 4 Wave E.3 Class 1 (N_grid=64, H=4)
σ_xy = +1 · e²/h · TKNN 1982 quantized HallC_A (unrounded) = 1.000000 · Riemann sumC_B (unrounded) = 1.000000 · FHS link variables|C_A − C_B| = 0 EXACT · Chern-Gauss-Bonnet cross-pinmax|F_A| = 0.5000 · curvature concentration
TOPOLOGICAL PLATEAU · |C| ≡ 1 EXACT · OFF · closed-form · m = 1.00 · t = 1.00 · N_k = 32CHERN INSULATOR · Qi-Wu-Zhang 2006 · TKNN 1982 · Fukui-Hatsugai-Suzuki 2005 · Bernevig-Hughes 2013 §8.5 · Chern 1946 · Klitzing 1980 · Haldane 1988 · Pillar 1 Wave F.1 Class 2
σ_xy = +1 · e²/h · TKNN 1982 quantized HallC_A (unrounded) = 1.000000 · Riemann sum (rhombic BZ)C_B (unrounded) = 1.000000 · FHS link variables|C_A − C_B| = 0 EXACT · Chern-Gauss-Bonnet cross-pinmax|F_A| = 3.4641 · K / K' valley concentration
M/t₂φTOPOLOGICAL PLATEAU · |C| ≡ 1 EXACT · OFF · closed-form · M = 0.00 · t₁ = 1.00 · t₂ = 0.50 · φ = 1.571 · N_k = 32HALDANE INSULATOR · Haldane 1988 · TKNN 1982 · Fukui-Hatsugai-Suzuki 2005 · Bernevig-Hughes 2013 §8.5 · Chern 1946 · Klitzing 1980 · Qi-Wu-Zhang 2006 · Chang 2013 · Jotzu 2014 · Pillar 1 Wave K.1 Class 2
N
N=8
Ω
1.00
observable
initial |ψ(0)⟩
stateOFF
|⟨Z₂|ψ(t)⟩|²—
scar t · Ω—
dim D = F_{N+2}55
off — sector inert, seam #1 returns false, RMS-0 byte-identical
m
1.00
t
1.00
N_k (BZ grid)
stateOFF
signed C—
|ΔC_A − C_B|—
phase (closed form)topological · C=+1
off — sector inert, seam #1 returns false, RMS-0 byte-identical
M
0.00
t₁
1.00
t₂
0.500
φ
0.50π
N_k (BZ grid)
|M|/t₂0.00
|M_crit|/t₂5.20
M/t₂φ
stateOFF
signed C—
|ΔC_A − C_B|—
phase (closed form)topological · C=+1
off — sector inert, seam #1 returns false, RMS-0 byte-identical
γ
0 (off)
phaseOFF
γ_c = |J|0.0400
spectrum λ—
norm—
γ 0 — byte-identical, evolveScalarStep1D untouched
K
0 (off)
kick Hz
0 (off)
K_c (chaos)0.9716
classicalOFF
quantum—
D(K) = K²/2—
period T—
K 0 — byte-identical, evolveScalarStep1D untouched
walk Hz
0 (off)
σ²/t² (H)0.29289
front ±t/√20.7071·t
regime—
step T—
vs classical—
coin off — byte-identical, evolveScalarStep1D untouched
⟨n̂⟩ ≈—
support—
N±—
packet — the shipped default ψ, byte-identical (opt-in presets above)
anchor↔
bpm
120
cycles
0.500
evol
1.00
blend
0.00
root
m60
fBase
110Hz
octaves
2.0
strength
0.70
Φ⁺ same
CHSH S = 2.828 > 2 ceilingBell violation · rings at 2√2 = 2.828 · crosses 2 @ 0°
group
IDLE
coupling
wells 0.60
smoothing
50ms
gain
×1.00
→ JVOCODER OFF · hop ×1 (E = −2J cos q)
→ J
off
→ J gain
×1.00
⟨e^(−βW)⟩ = e^(−βΔF) = 0.681 · speed-independent (Jarzynski)DQPT · t* = (½)π/ε* = 1.43 · ε* = 1.10 · ΔF = 0.426Quench suite · Jarzynski 1997 / Crooks 1999 / Heyl 2013 · ref crossing quench
bias
0.00
cyc/beat
1.00
tilt 0 · no Bloch oscillation (T_B → ∞)
g
linear
rate
0.00
kT
1.00
accent
0.00
0.0s · 0 marks
click to scrub · shift+drag to set loop · audio keeps marching forward
lattice 2D
stable
2
16.0
4.0
0.00
0.00
0v
damping
0.00
entropy
0.00
env→J
0.00
env→V
0.00
rate
0.00
depth
0
rate
0
zeno
0.00
x · observation: 0.00 Hzy · packet width: 32.0
oct +0
beats
0.500
output
master0.18
observe
16-step
bpm96.00
strength0.18
swing0.00
hintHover any control for a plain-English hint. Toggle the ? to dim everything else.