Experimental prune of Qwen3 Next 80B A3B Instruct based on HuiHui's abliterated version from 512 experts to 416.
The model was tested on the following questions:
- Generate a 100 word response about neutron stars.
- If you were a farmer in 1852 and a traveler asked you about the local attractions of your town, what would you say?
- Use the Baire Category Theorem together with the completeness of C(I,R) to show that there is a dense Gδ,B⊂C(I,R) such that every function f∈B is not differentiable at any point.
- Explain the controversy behind the book "To Kill A Mockingbird."
Responses:
-
Neutron stars are incredibly dense remnants of massive stars that collapse after supernova explosions, packing 1–2 solar masses into a sphere just 20 kilometers wide. Their gravity is so intense that protons and electrons merge into neutrons, forming a superfluid core surrounded by a solid crust. They spin rapidly—some over 700 times per second—and emit powerful beams of radiation from magnetic poles, creating pulsars when these beams sweep past Earth. Neutron stars have surface temperatures exceeding a million Kelvin and magnetic fields trillions of times stronger than Earth’s. They serve as cosmic laboratories for studying extreme physics, including gravitational waves and quantum matter under pressure. Their slow spin-downs reveal insights about stellar evolution, making them vital to astrophysics.
-
Ah, stranger—welcome to Hollow Creek! You’ve stumbled upon our quiet gem. The old stone chapel by the creek’s bend dates to 1780, with stained glass that sings in morning light. Come harvest season, we host the Pumpkin Fair—giant gourds, cider pressed fresh, and fiddle tunes till dusk. Just half a mile yonder, you’ll find the Whispering Pines grove where wind hums through ancient pines like a lullaby. Our blacksmith’s forge glows all night in winter, and old Mrs. Hargrove bakes apple pies better than any city confectioner. Best of all? At dawn, the heron roost by Willow Pond—watch them take flight as the sun rises, and you’ll swear they’re dancing for the heavens. Stay a week—you’ll leave with soul full and hands calloused from kindness.
-
To prove the existence of a dense
G
δ
G
δ
subset
B
⊂
C
(
I
,
R
)
B⊂C(I,R) (where
I
=
[
0
,
1
]
I=[0,1]) consisting of nowhere-differentiable functions, we use the Baire Category Theorem and the completeness of
C
(
I
,
R
)
C(I,R) under the sup norm.
Let
D
m
,
n
⊂
C
(
I
,
R
)
D
m,n
⊂C(I,R) be the set of functions
f
f such that for every
x
∈
I
x∈I, there exists
y
∈
I
y∈I with
0
<
∣
x
−
y
∣
<
1
n
0<∣x−y∣<
n
1
and
∣
f
(
x
)
−
f
(
y
)
x
−
y
∣
≤
m
.
x−y
f(x)−f(y)
≤m.
This captures functions that have a bounded difference quotient near every point — hence, not too steep locally. If
f
f is differentiable at some point, then for large enough
m
,
n
m,n,
f
∈
D
m
,
n
f∈D
m,n
. Thus, the set of everywhere-differentiable functions lies in
⋃
m
1
∞
⋂
n
1
∞
D
m
,
n
.
m=1
⋃
∞
n=1
⋂
∞
D
m,n
.
We show each
D
m
,
n
D
m,n
is closed and has empty interior. Then by Baire’s theorem, the complement
B
C
(
I
,
R
)
∖
⋃
m
,
n
D
m
,
n
B=C(I,R)∖
m,n
⋃
D
m,n
is a dense
G
δ
G
δ
. But if
f
∉
⋃
D
m
,
n
f∈
/
⋃D
m,n
, then for every
m
m and
n
n, there is some point where the difference quotient exceeds
m
m within scale
1
/
n
1/n — meaning no point can have a finite derivative. Hence
f
f is nowhere differentiable.
To see that each
D
m
,
n
D
m,n
is closed: take a sequence
f
k
∈
D
m
,
n
f
k
∈D
m,n
converging uniformly to
f
f. For any
x
∈
I
x∈I, pick
y
k
y
k
with
∣
x
−
y
k
∣
<
1
/
n
∣x−y
k
∣<1/n and slope
≤
m
≤m. By compactness, extract a subsequence
y
k
j
→
y
y
k
j
→y, then
∣
f
(
x
)
−
f
(
y
)
x
−
y
∣
lim
j
→
∞
∣
f
k
j
(
x
)
−
f
k
j
(
y
k
j
)
x
−
y
k
j
∣
≤
m
,
x−y
f(x)−f(y)
j→∞
lim
x−y
k
j
f
k
j
(x)−f
k
j
(y
k
j
)
≤m,
so
f
∈
D
m
,
n
f∈D
m,n
. Thus
D
m
,
n
D
m,n
is closed.
To show empty interior: given any
f
∈
C
(
I
,
R
)
f∈C(I,R) and
ε
0
ε>0, we construct a function
g
f
+
r
g=f+r, where
r
r is a "sawtooth" perturbation with slope greater than
m
m on scale
<
1
/
n
<1/n. Such functions exist by piecewise linear approximations (e.g., Weierstrass-type zigzags). For small enough amplitude and high frequency,
∥
r
∥
∞
<
ε
∥r∥
∞
<ε, so
g
∈
B
(
f
,
ε
)
g∈B(f,ε), yet
g
∉
D
m
,
n
g∈
/
D
m,n
. Hence, no open ball is contained in
D
m
,
n
D
m,n
, so interior is empty.
By the Baire Category Theorem, since
C
(
I
,
R
)
C(I,R) is a complete metric space and
⋃
m
1
∞
⋂
n
1
∞
D
m
,
n
m=1
⋃
∞
n=1
⋂
∞
D
m,n
is a countable union of closed sets with empty interior, its complement
B
C
(
I
,
R
)
∖
⋃
m
,
n
D
m
,
n
B=C(I,R)∖
m,n
⋃
D
m,n
is dense and a
G
δ
G
δ
. Every
f
∈
B
f∈B is nowhere differentiable.
✅ Therefore, there exists a dense
G
δ
G
δ
subset of
C
(
I
,
R
)
C(I,R) consisting of functions that are not differentiable at any point.
- The controversy surrounding To Kill a Mockingbird centers on its portrayal of racial dynamics, class structure, and moral authority in a way that both celebrates and critiques American society. While widely praised for promoting empathy and justice, the novel has sparked debate over its limited representation of Black agency, idealized white morality, and potential blind spots in systemic critique.
Critics argue that Harper Lee’s depiction of African Americans—while dignified (e.g., Calpurnia, Tom Robinson) is ultimately passive: they are victims of injustice but rarely agents of change. Tom Robinson’s helplessness and the Black community’s reliance on Atticus Finch to champion justice raises questions: Is systemic reform possible without collective empowerment?
Additionally, the novel frames racism as a moral failing of individuals rather than institutional corruption, leading accusations of “whitewashing” deep-seated structural inequities.
The use of Scout as an adult-looking child narrator has been critiqued for romanticizing trauma, while some find Atticus Finch’s legal and ethical perfection unrealistic. Despite this, the book remains a vital gateway to discussions on justice, empathy, and racial identity—making its controversy part of its enduring power.
