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<!DOCTYPE html>
<!--
Vendored + adapted into posterly from ARIS (Auto-claude-code-research-in-sleep),
skill paper-poster-html. Origin: https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep
Upstream tokenization: MIT (c) 2026 wanshuiyin -- ../LICENSES/aris-MIT.txt
This is the tokenized form of posterly's own neutral template; the class names and
content are posterly's own (c) 2026 Ruishuo Chen. As an adapted derivative this file
ships as part of posterly under AGPL-3.0. See ../NOTICE.md.
-->
<!--
============================================================
TEMPLATE: landscape_4col (ARIS fork)
CANVAS: 60in × 36in landscape (ICML / NeurIPS / generic landscape)
LAYOUT: header → optional banner → 4 body columns → optional takeaways → footer
USE WHEN: standard ML conference poster with 3-5 content cards per column,
mix of figures + equations + small tables.
HOW TO USE:
1. Copy this file to your working directory as `poster.html`.
2. Edit the DESIGN TOKENS in `:root` to your lab/venue colors.
3. Replace TODO content placeholders (search for "TODO").
4. Run `python tools/run_gates.py poster.html --tokens design_tokens.json` (the default driver: preflight -> style -> measure -> polish; design_tokens.json is the design-direction pack written at lock time -- SKILL.md Step 2.5) to align columns and check style/structure.
5. Run `python tools/render_preview.py poster.html` to produce the PDF.
NOTE: as shipped, this scaffold passes `preflight` (structure) but is
EXPECTED to FAIL `measure`/`polish` -- figures are commented out and copy
is TODO stubs, so columns only fill the top of the canvas. Those two gates
judge a FILLED poster; balance them once you've added real content. See
templates/README.md ("Scaffolds, not finished posters").
MEASURE ROLES: every layout-critical element carries `data-measure-role`.
Generic measurement scripts depend on these — do not remove.
CANVAS RETARGETING: to print at another size, change the canvas in exactly
TWO places that must stay in sync -- the `@page { size: ... }` rule and the
`.poster { width/height }` (also the `@media print .poster { width/height }`).
Example: ICLR 2026 main conference uses 185cm 90cm landscape (official print
service spec) -- set @page to `185cm 90cm`, width to `1850 * var(--u)` and
height to `900 * var(--u)` (and the print-override .poster to `185cm`/`90cm`).
Adapted from posterly (MIT, © 2026 Ruishuo Chen) — see LICENSES/ & NOTICE.md;
ARIS modifications: flat de-gradient, --fs token scale, zero-inline-style
utilities, data-source/data-color-exempt contracts.
============================================================
-->
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Reproducing: On the Computational Complexity of Performative Prediction — ICML 2026</title>
<!-- MathJax v3 for inline equations. CDN by default when the file is
opened by hand; the posterly check tools (measure/polish/pack/…)
intercept this request and serve the skill's bundled copy
(assets/mathjax/tex-svg.js, MathJax 3.2.2), so gates render math
deterministically even offline. To make a hand-opened poster
offline too, copy that bundle next to the poster and point the
<script> `src` at it. -->
<script>
window.MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']],
displayMath: [['$$', '$$'], ['\\[', '\\]']],
packages: {'[+]': ['ams']}
},
svg: { fontCache: 'global' }
};
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
<style>
/* =========================================================
CANVAS — 60" × 36" landscape
========================================================= */
@page { size: 60in 36in; margin: 0; }
:root {
/* ===== DESIGN TOKENS ===== */
/* Primary accent (header underline, card-highlight bar, section nums, .keyword) */
--accent: #5B21B6; /* complexity-theory indigo/violet; white ink on it measures 8.98:1 (>= AAA) */
--accent-deep: #3B0764;
--accent-light: #EDE9FE;
--accent-soft: #C4B5FD;
--accent-ink: #FFFFFF; /* ink ON the accent (chips, callout, thead) */
/* Emphasis register for "ours / best" (table .ours row, "★" callouts).
Default is the warm gold; a redesign may choose any register that
keeps 4.5:1 with --emph-ink (see templates/THEMES.md Mechanism 1). */
--emph: #C9A24A;
--emph-soft: #FFF7E0;
--emph-ink: #14314A; /* ink ON the emphasis fill. NOT var(--accent-deep):
#1F4566 on the default gold measures 4.16:1 (< AA);
#14314A measures 5.58:1 (>= 4.5:1). */
/* Text */
--text-primary: #1A1A1A;
--text-secondary: #555555;
--text-muted: #888888;
/* Backgrounds */
--bg-page: #F5F6F9;
--bg-card: #FFFFFF;
--bg-card-tint: #FAFAFB;
--bg-emphasis: var(--accent-light);
/* Borders */
--border-soft: #D8D8D8;
--border-strong: var(--accent);
/* Screen-only dark mat behind the poster (the off-canvas viewport
background). Print resets html/body to white, so this never reaches
paper; kept as a token so no color literal lives outside this block. */
--bg-viewport: #2B2B2B;
/* Base unit. Print: 1mm; screen preview: 1.6px (~3.78px = 1mm at 96dpi). */
--u: 1.6px;
/* Font-size scale (9 archetypes). Every `font-size` in this template
references one of these. `calc(var(--fs-N) * k)` is permitted ONLY for
a COMPONENTS.md-defined variant (e.g. `.eqn--large`). */
--fs-1: calc(9 * var(--u)); /* micro label */
--fs-2: calc(10 * var(--u)); /* small caption */
--fs-3: calc(11 * var(--u)); /* caption / table */
--fs-4: calc(12 * var(--u)); /* body text */
--fs-5: calc(13 * var(--u)); /* equation / emphasis */
--fs-6: calc(15 * var(--u)); /* subtitle */
--fs-7: calc(16 * var(--u)); /* section title */
--fs-8: calc(22 * var(--u)); /* banner number */
--fs-9: calc(32 * var(--u)); /* main title */
/* Fonts. Override at :root if your venue mandates a specific family. */
--font-serif: "Charter", "Source Serif Pro", "Georgia", serif;
--font-sans: "Inter", "Helvetica Neue", sans-serif;
/* Shadows & watermark ink — tokenized so rules 1/3 stay literal-free
(the faint radial page tint is the ONE allowed literal outside this
block; rule 5 validates it WHEN ENABLED -- the style gate ships with rules 4-5 off). */
--shadow-screen: 0 0 60px rgba(0, 0, 0, 0.5);
--shadow-card: 0 calc(2 * var(--u)) calc(6 * var(--u)) rgba(91, 33, 182, 0.05);
--ornament-ink: rgba(91, 33, 182, 0.06);
/* Corner-radius scale. Every border-radius calc() multiplies by this;
1 = the shipped soft look, 0 = square/flat (see templates/THEMES.md). */
--rs: 1;
/* Figure mount: the ground behind paper figures (transparent PNGs sit on
it) and the keyline around them (.figure img / .ff-fig img). Re-theme
with the Axis 6 frame decision so figures sit mounted in the design
instead of pasted on it; --fig-frame: transparent = frameless mount.
QR backgrounds stay literal white -- that's scannability, not styling. */
--fig-bg: white;
--fig-frame: var(--border-soft);
/* ===== END DESIGN TOKENS ===== */
}
/* =========================================================
RESET + BASE
========================================================= */
* { box-sizing: border-box; margin: 0; padding: 0; }
/* =========================================================
BASE DEFENSES -- wrap & ink safety. KEEP this block in ANY
skeleton, including a fully custom one (copy it over and
EXTEND the selector lists with your own prose/display
classes -- a hand-rolled skeleton that drops it strands
single-word widows and ragged titles; polish warns as
TEXT-WRAP).
- pretty: fills each line, protects the last-line orphan
(single-word widow). Safe on all prose.
- balance: evens CENTERED display text only -- never pair
it with left-aligned multi-sentence prose (SKILL.md wrap
rules).
- Any inline class you add that paints a background (a
.mark highlight, a keyword chip) must declare its own
`color` (Gate G -- never inherit ink across a ground
change) plus `box-decoration-break: clone;
-webkit-box-decoration-break: clone;` so a wrapped
highlight keeps its padding on both fragments (then it
never needs &nbsp;-gluing to hold one line).
========================================================= */
p, li, dd, figcaption,
.body-text, .caption, .callout, .section-title { text-wrap: pretty; }
.title { text-wrap: balance; }
html, body {
background: var(--bg-viewport);
font-family: var(--font-serif);
color: var(--text-primary);
-webkit-font-smoothing: antialiased;
}
/* =========================================================
UTILITY CLASSES — replace inline `style=` in the body markup.
The template (and any finished poster) must carry ZERO `style=`
attributes. Use these classes instead. Two documented exceptions
exist ONLY as examples and may appear in comments, never live:
- a logo/seal SVG flagged data-color-exempt="logo"
- a paper figure `<img ... data-source="paper" style="width: NN%">`
(AR width tweak; prefer the .w-NN classes below where possible)
========================================================= */
/* Poster container — exact print dimensions; data-measure-role="poster" so poster_check.py
can verify the canvas size. */
.poster {
width: calc(1524 * var(--u));
height: calc(914 * var(--u));
background: var(--bg-page);
/* Page tint kept (radial only, all color stops alpha <= 0.06 per the
de-gradient policy: linear-gradient is banned, this low-alpha radial
wash is the single allowed exception). */
background-image:
radial-gradient(ellipse at top left, rgba(91, 33, 182, 0.06), transparent 40%),
radial-gradient(ellipse at bottom right, rgba(201, 162, 74, 0.05), transparent 50%);
margin: 20px auto;
padding: calc(10 * var(--u)) calc(14 * var(--u));
display: grid;
grid-template-columns: minmax(0, 1fr); /* column-axis twin of the minmax(0,1fr) body-row defense: without it the implicit `auto` column grows to a wide child's max-content and a full-width row overflows the canvas (measure's canvas-overflow gate). Keep on any custom skeleton. */
grid-template-rows: auto auto minmax(0, 1fr) auto; /* header | banner | body | footer. minmax(0,1fr) (not bare 1fr): an over-tall body compresses instead of pushing footer off-canvas */
gap: calc(6 * var(--u));
box-shadow: var(--shadow-screen);
position: relative;
overflow: hidden;
}
/* Decorative top bar — flat solid accent (de-gradient). */
.poster::before {
content: "";
position: absolute; top: 0; left: 0; right: 0;
height: calc(8 * var(--u));
background: var(--accent);
}
/* =========================================================
HEADER
========================================================= */
.header {
display: grid;
grid-template-columns: 1fr minmax(50%, auto) 1fr; /* equal side tracks (1fr) -> the title track is centred on the poster, not just between the side blocks; the centre track is floored at 50% so a one-line title still fills it (else a short title measures narrow and trips a false HEADER/TITLE-SQUEEZED). Best-effort: a side block wide enough to clamp its 1fr track can still pull the title off-centre. */
align-items: center;
gap: calc(16 * var(--u));
padding: calc(2 * var(--u)) calc(4 * var(--u)) calc(5 * var(--u));
border-bottom: calc(2 * var(--u)) solid var(--accent);
}
.venue-badge {
justify-self: start; /* anchor to the far-left margin so the centre track stays centred */
display: flex; flex-direction: column;
align-items: center; justify-content: center;
min-width: calc(95 * var(--u));
text-align: center;
border-right: calc(1 * var(--u)) solid var(--border-soft);
padding-right: calc(12 * var(--u));
}
.venue-badge .vb-venue {
font-family: var(--font-sans);
font-weight: 800;
font-size: var(--fs-9);
color: var(--accent-deep);
line-height: 1;
letter-spacing: -0.5px;
}
.venue-badge .vb-year {
font-family: var(--font-sans);
font-size: var(--fs-5);
color: var(--text-secondary);
margin-top: calc(3 * var(--u));
letter-spacing: 1.2px;
}
.venue-badge .vb-tag {
font-family: var(--font-sans);
font-size: var(--fs-2);
color: var(--accent);
font-weight: 700;
margin-top: calc(2 * var(--u));
letter-spacing: 1.2px;
}
.title-block { text-align: center; min-width: 0; }
.title {
font-family: var(--font-sans);
font-weight: 800;
font-size: var(--fs-9);
line-height: 1.05;
color: var(--accent-deep);
letter-spacing: -0.5px;
}
.title .accent { color: var(--accent); }
.subtitle {
font-family: var(--font-sans);
font-weight: 500;
font-size: var(--fs-6);
color: var(--text-secondary);
margin-top: calc(2 * var(--u));
font-style: italic;
}
.authors-line {
font-family: var(--font-sans);
font-size: var(--fs-4);
color: var(--accent);
font-weight: 600;
margin-top: calc(3 * var(--u));
}
.authors-line .author { margin: 0 calc(4 * var(--u)); }
.authors-line sup { font-size: 0.7em; color: var(--accent); }
.authors-line .aff {
color: var(--text-secondary);
font-weight: 400;
display: block;
margin-top: calc(2 * var(--u));
font-size: var(--fs-4);
}
.right-block {
justify-self: end; /* keep logo+QR in the far-right corner */
display: flex; align-items: center;
gap: calc(10 * var(--u));
}
.qr-block { display: flex; flex-direction: column; align-items: center; gap: calc(2 * var(--u)); }
.qr-block img {
width: calc(85 * var(--u));
height: calc(85 * var(--u));
border: calc(2 * var(--u)) solid var(--accent);
border-radius: calc(4 * var(--u) * var(--rs));
background: white;
padding: calc(2 * var(--u));
}
.qr-label {
font-family: var(--font-sans);
font-size: var(--fs-3);
color: var(--accent);
font-weight: 600;
}
/* Optional logo slot — drop your lab logo here. Keep its rendered height
close to the QR (~85u) so the header doesn't grow disproportionately.
A raster logo needs no exemption. An inline-SVG logo with brand colors
must carry data-color-exempt="logo" so style_check skips its fills, e.g.:
<svg data-color-exempt="logo" ...> ... </svg> */
.logo-slot img { height: calc(85 * var(--u)); width: auto; max-width: calc(360 * var(--u)); object-fit: contain; display: block; }
/* Logo size classes on .logo-slot -- pick from the file's aspect ratio (SKILL.md Gate E).
tall/square sit at the QR-matched slot height; wide is intentionally shorter (~68% of the
QR) and width-capped so a long wordmark doesn't out-mass the title. Do NOT combine these
with logo-stack (that row is width-normalized, below). */
.logo-slot.logo-tall img,
.logo-slot.logo-square img { height: calc(85 * var(--u)); }
.logo-slot.logo-wide img { height: calc(58 * var(--u)); max-width: calc(300 * var(--u)); }
/* Logo chip: a solid backing that keeps a transparent / white-bordered logo legible on a
colored/dark header (white chip) or a light header (.logo-chip-dark); the padding + radius
fold a stray white box into a deliberate rounded tile (SKILL.md Gate E, Background). */
.logo-chip {
display: inline-flex; align-items: center; justify-content: center;
background: var(--bg-card); border-radius: calc(3 * var(--u) * var(--rs));
padding: calc(3 * var(--u)) calc(5 * var(--u));
}
.logo-chip.logo-chip-dark { background: var(--text-primary); }
/* logo-row: institution logos in the header right block (REAL logos the
user provided — never fabricate a seal). Each img MUST carry
data-color-exempt="logo"; height pairs with the QR. */
.logo-row { display: flex; align-items: center; gap: calc(5 * var(--u)); }
.logo-row img { height: calc(68 * var(--u)); width: auto; display: block; }
/* --boxed variant: each logo in a labeled tile (logo + institution name) —
more presence at poster distance; white tile + soft border, no new hues. */
.logo-row .lr-item {
display: flex; flex-direction: column; align-items: center;
gap: calc(2 * var(--u));
background: var(--bg-card);
border: 1px solid var(--border-soft);
border-radius: calc(3 * var(--u) * var(--rs));
padding: calc(4 * var(--u)) calc(6 * var(--u));
}
.logo-row .lr-item img { height: calc(58 * var(--u)); }
.logo-row .lr-label {
font-family: var(--font-sans); font-weight: 600; font-size: var(--fs-1);
color: var(--text-secondary); text-align: center; line-height: 1.15;
}
/* logo-stack variant: WIDE WORDMARKS (AR >= ~2) normalized to EQUAL WIDTH
and stacked vertically, left-aligned. Use when two wide wordmarks of
different aspect ratio read unbalanced height-matched in a row (equal
width lets the less-wide mark grow taller and aligns a clean block).
NOT for a square seal or tall mark (equal width blows it up — keep those
height-matched). Do NOT also apply the logo-wide/tall/square classes. */
.logo-row.logo-stack { flex-direction: column; align-items: flex-start; gap: calc(8 * var(--u)); }
.logo-row.logo-stack img { width: calc(170 * var(--u)); height: auto; }
/* venue badge may carry the official venue logo above its text line */
.venue-badge img { height: calc(62 * var(--u)); width: auto; display: block; margin: 0 auto calc(2 * var(--u)); }
.venue-badge .vb-title { font-family: var(--font-sans); font-weight: 800; font-size: var(--fs-5); color: var(--accent-deep); letter-spacing: 0.5px; }
/* =========================================================
OPTIONAL FRAMEWORK BANNER (delete this whole section if you don't need it)
========================================================= */
.framework-banner {
display: flex;
align-items: center;
gap: calc(16 * var(--u));
/* Flat solid emphasis fill (de-gradient). */
background: var(--bg-emphasis);
border: calc(1 * var(--u)) solid var(--border-soft);
border-left: calc(6 * var(--u)) solid var(--accent);
border-radius: calc(6 * var(--u) * var(--rs));
padding: calc(6 * var(--u)) calc(14 * var(--u));
}
.framework-banner img { height: calc(120 * var(--u)); width: auto; display: block; }
.framework-banner .banner-stats {
flex: 1;
display: grid;
grid-template-columns: repeat(4, 1fr);
gap: calc(6 * var(--u));
}
.framework-banner .bs-item {
background: white;
border: calc(1 * var(--u)) solid var(--border-soft);
border-left: calc(3 * var(--u)) solid var(--accent);
border-radius: calc(3 * var(--u) * var(--rs));
padding: calc(2 * var(--u)) calc(8 * var(--u));
text-align: center;
}
.framework-banner .bs-num {
font-family: var(--font-sans);
font-weight: 800;
font-size: var(--fs-8);
color: var(--accent);
line-height: 1;
}
.framework-banner .bs-label {
font-family: var(--font-sans);
font-size: var(--fs-3);
color: var(--text-secondary);
margin-top: calc(2 * var(--u));
line-height: 1.2;
}
.framework-banner .fb-text {
flex: 1.6;
font-family: var(--font-serif);
font-size: var(--fs-6);
line-height: 1.5;
text-wrap: balance; /* centered banner headline: even the two lines so neither widows (Gate B) */
text-align: center;
}
.framework-banner .fb-text strong { color: var(--accent-deep); }
.framework-banner .fb-label {
display: inline-block;
background: var(--accent);
color: var(--accent-ink);
font-family: var(--font-sans);
font-size: var(--fs-5);
font-weight: 700;
padding: calc(2 * var(--u)) calc(8 * var(--u));
border-radius: calc(4 * var(--u) * var(--rs));
text-transform: uppercase;
letter-spacing: 1px;
vertical-align: middle;
line-height: 1;
position: relative;
top: calc(-1 * var(--u));
}
/* Method-overview figure for the banner (banner-figure component,
catalogued in COMPONENTS.md). Usually CAPTIONLESS -- the banner text
block beside it is the figure's explanation. width:min-content collapses
the slot to the IMAGE (a captionless figure's slot IS the image); if a
short caption is used it wraps at the image box and can NEVER set the
flex-item width; margin-inline centres a block image (text-align does
not); overflow-wrap guards a long unbreakable token. Do NOT hand-roll a
.fb-fig wrapper or a bare <img class="w-100"> here. */
.framework-banner .banner-figure {
flex: 0 0 auto;
width: min-content;
margin: 0;
text-align: center;
}
.framework-banner .banner-figure img {
height: calc(120 * var(--u));
width: auto;
display: block;
margin-inline: auto;
}
.framework-banner .banner-figure figcaption {
width: 100%;
margin-top: calc(2 * var(--u));
font-family: var(--font-sans);
font-size: var(--fs-2);
line-height: 1.2;
color: var(--text-secondary);
text-align: center;
text-wrap: pretty;
overflow-wrap: anywhere;
}
.framework-banner .banner-figure figcaption strong { color: var(--accent-deep); }
/* =========================================================
BODY: 4 columns, variable-width hint via fr values
========================================================= */
.body-grid {
display: grid;
grid-template-columns: 1fr 1.05fr 1.05fr 1fr;
gap: calc(10 * var(--u));
/* No overflow:hidden here — it would clip card shadows (pitfall #6).
.poster already clips at the page boundary; min-height:0 is the
grid-blowout guard. */
min-height: 0;
}
.column {
display: flex; flex-direction: column;
gap: calc(6 * var(--u));
min-height: 0;
height: 100%;
padding-bottom: calc(4 * var(--u)); /* shadow breathing room above takeaways */
}
/* =========================================================
CARDS
========================================================= */
.card {
background: var(--bg-card);
border-radius: calc(5 * var(--u) * var(--rs));
padding: calc(4 * var(--u)) calc(9 * var(--u));
border: calc(1 * var(--u)) solid var(--border-soft);
box-shadow: var(--shadow-card);
position: relative;
}
.card.tinted { background: var(--bg-card-tint); }
.card.card--compact { padding: calc(3 * var(--u)) calc(6 * var(--u)); } /* predefined variant: tighter padding (fix (f)) */
.card.highlight {
border-left: calc(6 * var(--u)) solid var(--accent);
/* Flat emphasis tint (de-gradient). */
background: var(--bg-emphasis);
}
.section-title {
font-family: var(--font-sans);
font-weight: 700;
font-size: var(--fs-7);
color: var(--accent-deep);
margin-bottom: calc(3 * var(--u));
display: flex; align-items: center;
gap: calc(5 * var(--u));
}
/* Title text + any ★ marker share ONE .st-text span, so the heading wraps as
natural text (hanging indent) instead of flex-wrapping atomic items: the
number badge is never stranded on its own line and the ★ never widows. */
.section-title .st-text { flex: 1; min-width: 0; line-height: 1.18; }
/* Graceful fallback if a title is NOT wrapped in .st-text: float the badge so
bare inline text still wraps beside it rather than dropping below it. */
.section-title:not(:has(.st-text)) { display: block; line-height: 1.18; }
.section-title:not(:has(.st-text)) .num { float: left; margin-right: calc(5 * var(--u)); }
.section-title .num {
display: inline-flex; align-items: center; justify-content: center;
width: calc(22 * var(--u)); height: calc(22 * var(--u));
background: var(--accent); color: var(--accent-ink);
border-radius: 50%;
font-size: var(--fs-5); font-weight: 700;
flex-shrink: 0;
}
/* Inline "★ KEY" / "★ Headline" marker beside a section title. */
.section-title .key-mark { color: var(--emph); font-size: var(--fs-3); }
.body-text, .card p, .card li {
font-family: var(--font-serif);
font-size: var(--fs-4);
line-height: 1.3;
color: var(--text-primary);
}
.card ul, .card ol { padding-left: calc(18 * var(--u)); }
.card li { margin-bottom: calc(2 * var(--u)); }
.keyword { color: var(--accent); font-weight: 700; }
.keyword-emph { color: var(--emph); font-weight: 700; }
.highlight-text {
background: var(--bg-emphasis);
padding: 0 calc(3 * var(--u));
border-radius: calc(2 * var(--u) * var(--rs));
}
/* Equation block */
.eqn {
background: var(--bg-emphasis);
border-left: calc(3 * var(--u)) solid var(--accent);
padding: calc(4 * var(--u)) calc(10 * var(--u));
margin: calc(4 * var(--u)) 0;
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/* =========================================================
PRINT OVERRIDE — KEEP LAST so it wins source-order ties.
========================================================= */
@media print {
html, body { background: white; }
.poster { margin: 0; box-shadow: none; width: 60in; height: 36in; page-break-after: avoid; }
:root { --u: 1mm; }
}
</style>
</head>
<body>
<div class="poster" data-measure-role="poster">
<!-- =========================== HEADER =========================== -->
<header class="header" data-measure-role="header">
<div class="venue-badge">
<div class="vb-venue">ICML</div>
<div class="vb-year">2026</div>
<div class="vb-tag">REPRO CHALLENGE</div>
</div>
<div class="title-block">
<h1 class="title">On the Computational Complexity of <span class="accent">Performative Prediction</span></h1>
<div class="subtitle">Independent reproduction &mdash; Anagnostides, Chauhan, Panageas, Sandholm, Yan (arXiv:2601.20180, ICML 2026) &mdash; reproduced by SabaPivot, CPU-only, $0</div>
<div class="authors-line">
<span class="author">6 claims &mdash; 5 verified, 1 falsified (published proof of Thm 4.4)</span>
<span class="aff">A pure-theory paper: no code, no experiments, 34 pages. Every reduction, constant, algorithm and proof step re-checked from scratch.</span>
</div>
</div>
<!-- RIGHT: paper identifiers, text only (no remote assets) -->
<div class="right-block">
<div class="qr-block">
<div class="qr-label">arXiv 2601.20180</div>
<div class="qr-label">5 verified &middot; 1 falsified</div>
<div class="qr-label">no official code exists</div>
</div>
</div>
</header>
<!-- ===================== VERDICT BANNER ===================== -->
<section class="framework-banner" data-measure-role="banner">
<div class="fb-text">
<span class="fb-label">Verdict</span>
&nbsp;Finding an $\varepsilon$-performatively stable point is <strong>PPAD-complete</strong> at $\rho = 1 + O(\varepsilon)$ yet <strong>poly$(d, \log 1/\varepsilon)$</strong> once $\rho \le 1 + O(\varepsilon^4)$. Five claims reproduce; the published <strong>PLS-hardness proof of Thm 4.4 does not</strong>.
</div>
<div class="banner-stats">
<div class="bs-item"><div class="bs-num">5/6</div><div class="bs-label">claims<br>verified</div></div>
<div class="bs-item"><div class="bs-num">1</div><div class="bs-label">published proof<br>falsified</div></div>
<div class="bs-item"><div class="bs-num">446,768</div><div class="bs-label">classifiers<br>enumerated</div></div>
<div class="bs-item"><div class="bs-num">$0</div><div class="bs-label">CPU only,<br>under 20 min</div></div>
</div>
</section>
<!-- ============================ BODY ============================ -->
<div class="body-grid" data-measure-role="body">
<!-- ============ COLUMN 1 : FRAMING, METHOD, FACTS ============ -->
<div class="column" data-measure-role="column">
<div class="card highlight card--fill3" data-measure-role="card">
<div class="section-title"><span class="num">1</span><span class="st-text">The Paper in One Line</span></div>
<p class="body-text">
In <span class="keyword">performative prediction</span> the deployed model $x$ shifts the data distribution it is
then scored on; $x$ is $\varepsilon$-performatively stable when it is $\varepsilon$-optimal for the distribution
it itself induces. The hardness dial is a single ratio, built from the shift's Lipschitz constant $L$, the loss
smoothness $\beta$ and its strong convexity $\alpha$.
</p>
<div class="eqn eqn--large text-center">
<span class="label">The single parameter that decides everything</span>
$$\rho = \frac{L\beta}{\alpha}$$
</div>
<div class="flow-strip">
<div class="step"><span class="step-name">$\rho = 1 + O(\varepsilon)$</span>PPAD-complete</div>
<div class="arrow">&rarr;</div>
<div class="step step--final"><span class="step-name">$\rho \le 1 + O(\varepsilon^4)$</span>poly$(d, \log 1/\varepsilon)$</div>
</div>
<p class="body-text mt-2">
A <span class="keyword">sharp phase transition</span>, and the whole paper lives on it: intractable on one side of
the dial, solvable in $d$ and $\log 1/\varepsilon$ on the other.
</p>
</div>
<div class="card" data-measure-role="card">
<div class="section-title"><span class="num">2</span><span class="st-text">How You Reproduce a Complexity Paper</span></div>
<p class="body-text">
You cannot run PPAD-completeness. But four things in a theory paper <span class="keyword">are</span> executable,
and we did all four:
</p>
<ol class="algo mt-2">
<li><strong>Every reduction</strong> &mdash; checked for solution preservation in <em>both</em> directions, exhaustively where the instances are small.</li>
<li><strong>Every explicit constant</strong> &mdash; recomputed symbolically, traced to its cited source.</li>
<li><strong>Every algorithm</strong> &mdash; implemented, then fitted against its claimed complexity.</li>
<li><strong>Every proof step's arithmetic</strong> &mdash; evaluated, not read.</li>
</ol>
<p class="body-text fs-3 mt-2">
Step 1 caught the defect in Thm 4.4. Step 2 caught the constant slips in Thm 3.4 and Thm 3.12.
</p>
</div>
<div class="card card--fill8" data-measure-role="card">
<div class="section-title"><span class="num">3</span><span class="st-text">Reproduction Facts</span></div>
<div class="keybox">
<div class="kb-item"><div class="kb-num">CPU</div><div class="kb-label">no GPU,<br>no API key</div></div>
<div class="kb-item"><div class="kb-num">11 min</div><div class="kb-label">total compute,<br>end to end</div></div>
<div class="kb-item"><div class="kb-num">$0</div><div class="kb-label">total<br>cost</div></div>
</div>
<ul class="fs-3 mt-4">
<li><span class="keyword">Stack:</span> numpy + sympy + scipy, seed 20260725 everywhere.</li>
<li><span class="keyword">Artifacts:</span> 6 scripts, 6 JSON result files, 3 figures.</li>
<li><span class="keyword">No official code exists</span> for this paper &mdash; arXiv, GitHub, Papers-with-Code, Semantic Scholar and alphaXiv all checked.</li>
</ul>
</div>
</div>
<!-- ============ COLUMN 2 : CLAIMS 1 & 2, ERRATA ============ -->
<div class="column" data-measure-role="column">
<div class="card highlight card--fill7" data-measure-role="card">
<div class="section-title"><span class="num">4</span><span class="st-text">Claim 1 &mdash; PPAD-Hardness</span></div>
<p class="body-text fs-3">
<span class="verdict-chip">Verified</span> Thm 3.4 holds at $\rho \le 1 + \varepsilon/\varepsilon'$ with
$\varepsilon' = 0.088/6$: the reduction is affine, its performative gap an exact rescaling of the VI gap.
</p>
<div class="eqn">
<span class="label">Reduction, $c = \varepsilon/\varepsilon'$</span>
$$g(x) = (I - cA)x - cb, \qquad \text{perf-gap}(x) = c \cdot \text{VI-gap}(x)$$
</div>
<table class="result-table">
<thead>
<tr><th class="method">check</th><th>scale</th><th class="derived">result</th></tr>
</thead>
<tbody>
<tr><td class="method">gap identity, random $x$</td><td>1600 checks</td><td class="derived">max rel. err $4.8 \cdot 10^{-12}$</td></tr>
<tr><td class="method">solution sets, $201 \times 201$ grid</td><td>30 inst., 1.2M pts</td><td class="derived">symmetric diff. <span class="best">0</span></td></tr>
<tr><td class="method">$\rho = \|I - cA\|_2 \le 1 + c$</td><td>1000 instances</td><td class="derived"><span class="best">1000 / 1000</span></td></tr>
<tr class="ours"><td class="method">tightness at $A = -I$</td><td>closed form</td><td class="derived">equality exactly</td></tr>
</tbody>
</table>
<p class="body-text fs-3 mt-2">
<span class="keyword">Constant chain re-derived.</span> Pure-Circuit gives $2\sqrt{73} - 17 = 0.0880075$;
Bernasconi et al. divide by 6 to force $\|A\|_1, \|A\|_\infty \le 1$. The printed $0.088$ clears it with
$7.5 \cdot 10^{-6}$ to spare.
</p>
</div>
<div class="card" data-measure-role="card">
<div class="section-title"><span class="num">5</span><span class="st-text">Claim 2 &mdash; Quadratic Loss, Affine Shift</span></div>
<p class="body-text fs-3">
<span class="verdict-chip">Verified</span> $\alpha = \beta = 1$ exactly (the Hessian is $I$), so
$\rho = \|I - cA\|_2$, and $x^\star = -A^{-1}b$ satisfies $x^\star = g(x^\star)$ to $1.5 \cdot 10^{-14}$.
<span class="keyword">The distribution is irrelevant:</span> swapping the point mass for
$\mathcal{N}(g(x), \sigma^2 I)$ leaves the argmin and the $W_1$ sensitivity unchanged, within 2.5 Monte-Carlo
standard errors at $n = 20{,}000$.
</p>
<table class="result-table">
<thead>
<tr><th class="method">predicted rate $\rho$</th><th class="derived">measured RRM contraction</th></tr>
</thead>
<tbody>
<tr><td class="method">0.50</td><td class="derived">0.5000</td></tr>
<tr><td class="method">0.90</td><td class="derived">0.9000</td></tr>
<tr><td class="method">0.99</td><td class="derived">0.9900</td></tr>
<tr class="ours"><td class="method">1.00</td><td class="derived">cycles forever (Ex. D.3)</td></tr>
</tbody>
</table>
<p class="body-text fs-3 mt-2">
RRM contracts at <strong>exactly</strong> the predicted rate for every $\rho &lt; 1$, and never converges at
$\rho = 1$ &mdash; the boundary the hardness result sits on.
</p>
</div>
<div class="card" data-measure-role="card">
<div class="section-title"><span class="num">6</span><span class="st-text">Also Found &mdash; Two Errata</span></div>
<ul class="fs-3">
<li><span class="keyword">Costs are not arbitrary.</span> Thm 4.4's metric property forces
$c_{\text{far}} \le 2 c_{\text{close}}$, so its costs are not free in $(0,1)$ and $(1,\infty)$: $0.5/1.5$
gives <strong>40 triangle violations</strong>.</li>
<li><span class="keyword">An uncitable constant.</span> $\varepsilon' = 0.088/6$ is in neither cited source; it
must be composed from Bernasconi et al. Thm 4.4.</li>
</ul>
</div>
</div>
<!-- ============ COLUMN 3 : CLAIMS 3 & 4 ============ -->
<div class="column" data-measure-role="column">
<div class="card highlight card--fill1" data-measure-role="card">
<div class="section-title"><span class="num">7</span><span class="st-text">Claim 3 &mdash; The Phase Transition</span></div>
<p class="body-text fs-3">
<span class="verdict-chip">Verified</span> Square-root-form ellipsoid method for the VI, fitted over
$d \in \{2,\dots,32\}$ and $\varepsilon \in \{10^{-2},\dots,10^{-8}\}$: 105 runs, all on target.
</p>
<div class="eqn">
<span class="label">Fitted, against the predicted $d^2 \log(1/\varepsilon)$</span>
$$\text{iters} = 2.03 \cdot d^{1.957} (\log 1/\varepsilon)^{0.993}, \quad R^2 = 0.992$$
</div>
<div class="figure">
<img src="claim3_ellipsoid_phase.png" data-source="paper" data-asset-id="claim3-ellipsoid-phase" class="w-85"
alt="Ellipsoid-method iteration scaling and the hypomonotonicity threshold at which the cut stops being valid">
<div class="caption fs-2">
The cut is valid in <strong>0%</strong> of iterations once the operator is hypomonotone, <strong>100%</strong>
when it is not; the fixed-point gap jumps from $10^{-17}$ to $1.4\sigma$ there.
</div>
</div>
<p class="body-text fs-3 mt-2">
The Prop D.5 / D.6 certificates hold <strong>40/40</strong> and scale as $\sigma^{0.51}$ (VI) and
$\sigma^{0.26}$ (fixed point) against the predicted $1/2$ and $1/4$ &mdash; inverting the latter gives
$\rho \le 1 + O(\varepsilon^4)$.
</p>
<div class="callout emph">
<strong>Sharper constant.</strong> $F = \mathrm{id} - T$ is exactly $\sigma$-hypomonotone, not
$\sigma + \sigma^2/2$: the identity reduces to $\langle u, u - w \rangle$, min $-\sigma\|u\|^2$.
</div>
</div>
<div class="card card--fill1" data-measure-role="card">
<div class="section-title"><span class="num">8</span><span class="st-text">Claim 4 &mdash; Exponential ERM Queries</span></div>
<p class="body-text fs-3">
<span class="verdict-chip">Verified</span> One ERM query returns $G(x) = (1-\lambda)x + \lambda T(x)$, and
$T(x)$ is recovered exactly from it (error $5.6 \cdot 10^{-15}$): the Hirsch&ndash;Papadimitriou&ndash;Vavasis
bound transfers to Cor 3.7 <strong>with no loss</strong>.
</p>
<div class="figure">
<img src="claim4_query_lb.png" data-source="paper" data-asset-id="claim4-query-lb" class="w-50"
alt="Median query count of a hidden-path Brouwer probe growing exponentially in the dimension">
<div class="caption fs-2">
<strong>Toy probe.</strong> A hidden-path Brouwer family at $m = 3$, $d = 2..9$ needs a median $1.737^d$
queries, against the predicted $\sqrt{m} = 1.732$, with $R^2 = 0.998$.
</div>
</div>
<p class="body-text fs-3 mt-2">
<span class="keyword">What "constant $\varepsilon$" means.</span> $c((1/\varepsilon - 10)L)^{d-2}$ beats
$c \cdot 2^{d-2}$ exactly when $\varepsilon \le 1/12$, and is vacuous for $\varepsilon &gt; 1/11$.
</p>
</div>
</div>
<!-- ============ COLUMN 4 : CLAIMS 5 & 6 ============ -->
<div class="column" data-measure-role="column">
<div class="card card--fill1" data-measure-role="card">
<div class="section-title"><span class="num">9</span><span class="st-text">Claim 5 &mdash; Any Convex Domain</span></div>
<p class="body-text fs-3">
<span class="verdict-chip">Verified with corrections</span> We ran the whole Appendix E construction of
Thm 3.12 &mdash; equilateral triangle, $\varepsilon$-ThickBrouwer colouring, bit-extraction circuit, $k = 16$
sampled colours &mdash; over four well-bounded domains (unit disk, larger disk, square, irregular 7-gon) on
$400 \times 400$ grids. <strong>Zero violations</strong> in any scan; Lemma E.4 holds at $L = 288$, $k = 16$,
$n = 3$, with at most 2 of the 16 samples poorly positioned &mdash; exactly its bound.
</p>
<p class="body-text fs-3 mt-2">
Two defects, <strong>neither affecting the theorem</strong>:
</p>
<ul class="fs-3 mt-1">
<li><span class="keyword">Arithmetic.</span> The proof sets $\varepsilon = 1/8$, then writes
$\varepsilon' \le \varepsilon/8 = 1/32$ &mdash; but $\varepsilon/8 = 1/64$, and its own second case yields
only 0.01953, clearing $1/64$ and <strong>not</strong> $1/32$.</li>
<li><span class="keyword">Coordinates.</span> $A_1 = (0,0)$ contradicts the Definition 3.11 convention
$B_{R_1}(0) \subset X$: the circumcentre then sits at $(\sqrt{3}/2, 1/2)$.</li>
</ul>
</div>
<div class="card highlight card--fill1" data-measure-role="card">
<div class="section-title"><span class="num">10</span><span class="st-text">Claim 6 &mdash; PLS-Hardness, Thm 4.4</span></div>
<p class="body-text fs-3">
<span class="verdict-chip verdict-chip--alt">Falsified as proved</span> Enumerating all $2^{|X|}$ classifiers
for 11 graphs &mdash; <strong>446,768 in total</strong> &mdash; shows the Appendix F reduction is
<span class="keyword">not solution-preserving</span>.
</p>
<div class="callout mt-1 mb-1">
The all-ones classifier $f \equiv 1$ is a strategic local optimum of <strong>every</strong> instance the reduction
produces. Its induced cut is the empty cut, which is not a local max cut.
</div>
<p class="body-text fs-3">
No point deviates when every label is 1, and flipping one to 0 makes that point deviate to a still-positive
close neighbour, leaving the Jury's utility unchanged.
</p>
<div class="eqn mt-1 mb-1">
<span class="label">Minimal witness &mdash; the single-edge graph</span>
$$M \cdot U = 2 \text{ at } f \equiv 1, \quad \text{all four single flips} = 2, \quad \text{optimum} = 6$$
</div>
<p class="body-text fs-3">
<span class="keyword">Where it breaks.</span> The proof's first claim &mdash; that a Jury with
$f(x_{(u,v)}^-) = 1$ gains $1/M$ by flipping it &mdash; silently assumes $f(x_{(u,v)}^+) = 0$. A guard-point
repair does not save it.
</p>
<p class="body-text fs-3 mt-2">
<span class="keyword">What survives.</span> The converse direction (every local max cut <em>does</em> lift to
a strategic local optimum), the metric property, $M \cdot U = \text{cut} + \text{const}$, Eq. (19)&ndash;(20),
(22), (24), and the global-optimum / NP-hardness remark.
</p>
<div class="callout emph">
<strong>Read this precisely.</strong> The theorem may still be true &mdash; another reduction could establish
it &mdash; but this proof does not.
</div>
</div>
</div>
</div>
<!-- ============================ FOOTER ============================ -->
<div class="footer" data-measure-role="footer">
<div>
<strong class="method-name">On the Computational Complexity of Performative Prediction</strong> &middot;
Independent reproduction, ICML 2026 Reproducibility Challenge &middot; 5 of 6 claims verified, 1 published proof falsified &middot; CPU only, $0.
</div>
<div>
Paper: <span class="repo">arXiv:2601.20180</span> &nbsp;&middot;&nbsp;
Official code: <span class="repo">none exists</span> &nbsp;&middot;&nbsp;
Reproduction: <span class="repo">SabaPivot</span>
</div>
</div>
</div>
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