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perl -e '$|=1; sub c{my$h=shift;[map{hex substr($h,$_*2,2)}0..2]} ($W,$H)=(112,64);$PI=3.14159265; $wh=c("ffffff");$gy=c("9aa0ad");$dk=c("2b2f38");$og=c("e8a33d");$o2=c("c9821f"); $rd=c("d0323f");$sv=c("c8ccd4");$lg=c("d79a4e");$cr=c("f2d98a");$ty=c("23262d"); $pc=c("e3b168");$sa=c("ecd9a3");$s2=c("dcc489");$su=c("ffe24d");$gl=c("fff3a8"); $sh=c("dfe3ec");$k1=c("2f7fd0");$k2=c("bfe2f7");$e1=c("0d5a9e");$e2=c("2f92cf"); sub P{my($x,$y,$c)=@_;return if$x<0||$y<0||$x>=$W||$y>=$H;$Z[int$y][int$x]=$c} sub E{my($X,$Y,$A,$B,$T,$C)=@_;my$s=sin$T;my$k=cos$T;my$m=$A+$B; for my$y(int($Y-$m)..int($Y+$m)){for my$x(int($X-$m)..int($X+$m)){ my$p=$x-$X;my$q=$y-$Y;my$u=($p*$k+$q*$s)/$A;my$v=(-$p*$s+$q*$k)/$B; P($x,$y,$C)if$u*$u+$v*$v<=1}}} sub D{E($_[0],$_[1],$_[2],$_[2],0,$_[3])} sub L{my($a,$b,$f,$g,$r,$C)=@_;my$n=int(sqrt(($f-$a)**2+($g-$b)**2))*2+1; D($a+($f-$a)*$_/$n,$b+($g-$b)*$_/$n,$r,$C)for 0..$n} sub R{my($X,$Y,$r,$w,$C)=@_;for my$y(int($Y-$r-1)..int($Y+$r+1)){ for my$x(int($X-$r-1)..int($X+$r+1)){my$d=sqrt(($x-$X)**

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work through the paper breaking down exactly how the blow-up is obtained, noting what is novel, building an accessible intuition to a layperson (with strong mathematical foundations). conclude by noting the exact preconditions for the blow-up and how it fails if any of them are relaxed. finally discuss abstractly the metamathematical question of why the calculus (PDE system) is able to exhibit singular behaviour in a physical (proxy) quantity despite the game of keeping the boundary conditions smooth and other physical quantities finite. this is a nuanced discussion and probably redudces to the fact that the (physically counterfactual) infinities are lurking everywhere once you use continua but we want to refine that intuition to be as sharp as possible so we can find out what, if anything, has actually been learned.

29 minutes ago

The central result

The paper constructs, for every fixed viscosity $\nu>0$, a forced, three-dimensional incompressible Navier–Stokes flow that starts from rest, remains

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[00:00.000 --> 00:05.440]  And if you beat up somebody enough, it does stop up his or her love springs.
[00:05.440 --> 00:08.240]  They become a being who is incapable of love.
[00:08.240 --> 00:14.000]  I wrote a sonnet once,
[00:14.000 --> 00:32.200]  The man, when all is said, what fallen man calls sin is but another name for love locked in.
[00:34.960 --> 00:41.480]  Here speaks the nature of the damage done that man knew not how it and he are one.
[00:41.480 --> 00:51.080]  Thus outlawed from the secret of the earth, entrusted in his being at his birth,
[00:51.080 --> 01:01.880]  His sin a code, its key a turn of fate, man struck, struck man, ere woman let him mate.
[01:01.880 --> 01:11.460]  But codes made up by man, by man are broken, and names will man to man deny the call.
[01:11.460 --> 01:14.640]  And something, something lost it there.
[01:16.520 --> 01:17.500]  Something token.

Epivalent

#!/usr/bin/env python3
from __future__ import annotations

import argparse
import json
from functools import lru_cache
from typing import Dict, List, Tuple

import mpmath as mp
import sympy as sp

Epivalent

#!/usr/bin/env python3
"""TopCVP_beta CLI

This script packages the current working construction (paper-faithful):

Primitives (all are *string* lambda terms built via plc_suite.terms):
- fetch_{i,n} (paper), with NOT-substitution implemented by swapping CSTT/CSTF
  *only* at the (t==n+1 and j==i) app-slot inside the fetch constructor.
- and'_n (paper)
- OR derived purely by De Morgan using NOT-substitution + and'

Epivalent

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# THRML unified sampler (clean rewrite)
# - Perfect matching on planar cubic bridgeless graphs via 2-face-coloring + NAE vertex constraints.
# - Face K-coloring (default K=4) on the dual graph via Potts (penalize equal colors on adjacent faces).
# Supports two input modes:
#   (1) Lambda term -> primal rotation system -> dual faces, Tutte embedding for plotting
#   (2) Adjacency matrix (0/1 square text file) of the dual graph for direct face K-coloring
# Includes:
#   * Block Gibbs with optional block partition via greedy vertex-coloring (--block-coloring)

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#!/usr/bin/env python
# -*- coding: utf-8 -*-

from sage.all import Graph, matrix, ZZ
import unittest

# ============================================================
# Data Representation and Helper Functions
# ============================================================