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slide tweaks
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digama0 committed Sep 9, 2024
1 parent 4c6919a commit acf7656
Showing 1 changed file with 17 additions and 15 deletions.
32 changes: 17 additions & 15 deletions ITP/slides.typ
Original file line number Diff line number Diff line change
Expand Up @@ -25,7 +25,7 @@
line((x, fly), (x, tly), ..style)
x += step
}

let y = fy
while y <= ty + eps {
line((flx, y), (tlx, y), ..style)
Expand All @@ -34,6 +34,7 @@
}

#let lean = "Lean"
#let thin = h(3em/18)

// Many slides adapted from https://www.cs.cmu.edu/~mheule/talks/6hole-TACAS.pdf

Expand All @@ -44,7 +45,7 @@
title: [Formal Verification of the Empty Hexagon Number],
author: [
Bernardo Subercaseaux¹, Wojciech Nawrocki¹, James Gallicchio¹,\
Cayden Codel¹, *Mario Carneiro*#h(0em)¹, Marijn J. H. Heule¹
Cayden Codel¹, #underline[Mario Carneiro]#h(0em)¹, Marijn J. H. Heule¹
],
date: [
_Interactive Theorem Proving_ | September 9th, 2024\
Expand Down Expand Up @@ -130,7 +131,7 @@ A *$bold(k)$-hole* is a convex $k$-gon with no point of $S$ in its interior.
#let (uncover,) = utils.methods(self)

*Theorem* (Klein 1932). // WN: I don't think a citation exists for this
Every 5 points in the plane contain a 4-hole. #pause
Every set of 5 points in the plane contains a 4-hole. #pause

_Proof._ By cases on the size of the convex hull.

Expand Down Expand Up @@ -348,7 +349,7 @@ _focus of our work_.
import cetz.draw: *
set-style(circle: (fill: config.colors.neutral-darkest, stroke: none, radius: 0.1))
scale(3.2)

on-layer(1, {
let pts = (
(0, 0, "p"), (1, 1, "s"), (2, 1, "q"), (1.2, 2, "r"), (1.8, 1.8, "t")
Expand All @@ -358,7 +359,7 @@ _focus of our work_.
content((x, y+0.015), [#set text(fill: config.colors.neutral-lightest, size: 20pt); $#n$])
}
})

let (cg, cb, cr) = (green, blue, red).map(c => c.desaturate(20%))
line("p", "r", "q", stroke: cg, mark: (end: "stealth", fill: cg))
line("p", "s", "t", stroke: cb, mark: (end: "stealth", fill: cb))
Expand Down Expand Up @@ -412,7 +413,7 @@ _focus of our work_.
)

scale(3.2)

// Grid and axes
let ((efx, efy), (etx, ety)) = extents.at(self.subslide - 1)
on-layer(-1, {
Expand Down Expand Up @@ -464,7 +465,7 @@ _focus of our work_.
line(..r, fill: c)
}
})

// Equal-x marker lines
if self.subslide == 1 {
let ((_, yf), (_, yt)) = extents.at(0)
Expand All @@ -475,7 +476,7 @@ _focus of our work_.
line((x6, yf), (x6, yt))
}
})

#let captions = (
[Starting set of points.],
[Rotation ensures distinct $x$.],
Expand Down Expand Up @@ -515,11 +516,11 @@ structure CanonicalPoints where
CNF formula produced directly from executable #lean definition. #pause

To verify $h(6) ≤ 30$:\ #pause
▸ CNF with 65092 variables and 436523 clauses\ #pause
▸ partitioned into 312 418 subproblems\ #pause
▸ CNF with 65#(thin)092 variables and 436#(thin)523 clauses\ #pause
▸ partitioned into 312#(thin)418 subproblems\ #pause
▸ each subproblem solved by CaDiCaL 1.9.5\ #pause
▸ unsatisfiability proofs checked on-the-fly by `cake_lpr`\ #pause
▸ 25 876.5 CPU hours on Bridges 2 cluster of Pittsburgh Supercomputing Center
▸ 25#(thin)876.5 CPU hours on Bridges 2 cluster of Pittsburgh Supercomputing Center

== Lower bounds

Expand All @@ -538,17 +539,18 @@ We verified it, and used it to check the lower bounds.
axiom unsat_6hole_cnf : (Geo.hexagonCNF 30).isUnsat
theorem holeNumber_6 : holeNumber 6 = 30 :=
le_antisymm (hole_6_theorem' unsat_6hole_cnf) (hole_lower_bound [
le_antisymm
(hole_6_theorem' unsat_6hole_cnf)
(hole_lower_bound [
(1, 1260), (16, 743), (22, 531), (37, 0), (306, 592),
(310, 531), (366, 552), (371, 487), (374, 525), (392, 575),
(396, 613), (410, 539), (416, 550), (426, 526), (434, 552),
(436, 535), (446, 565), (449, 518), (450, 498), (453, 542),
(458, 526), (489, 537), (492, 502), (496, 579), (516, 467),
(552, 502), (754, 697), (777, 194), (1259, 320)
])
(552, 502), (754, 697), (777, 194), (1259, 320)])
```
]

== Bibliography

#bibliography("main.bib", style: "chicago-author-date", title: none)
#bibliography("main.bib", style: "chicago-author-date", title: none)

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