| <!-- | |
| 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 -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; | |
| font-size: var(--fs-5); | |
| overflow-x: hidden; | |
| } | |
| /* Predefined variant for a larger / more legible display equation. | |
| `calc(var(--fs-N) * k)` is allowed here because this is a | |
| COMPONENTS.md-registered variant (DESIGN_FINAL §A / §10 f). */ | |
| .eqn--large { font-size: calc(var(--fs-5) * 1.25); } | |
| .eqn .label { | |
| display: block; | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-2); | |
| color: var(--accent); | |
| font-weight: 600; | |
| margin-bottom: calc(2 * var(--u)); | |
| text-transform: uppercase; | |
| letter-spacing: 1px; | |
| } | |
| /* Callout: solid accent for primary, solid emphasis fill for theorems / "★ key" strips */ | |
| .callout { | |
| background: var(--accent); | |
| color: var(--accent-ink); | |
| padding: calc(5 * var(--u)) calc(10 * var(--u)); | |
| border-radius: calc(4 * var(--u) * var(--rs)); | |
| font-size: var(--fs-4); | |
| margin: calc(4 * var(--u)) 0; | |
| } | |
| .callout strong { color: var(--emph-soft); } | |
| /* Flat solid emphasis fill (de-gradient). */ | |
| .callout.emph { | |
| background: var(--emph); | |
| color: var(--emph-ink); /* route through the token — accent-deep here would dodge the register swap AND fail AA on the default gold */ | |
| } | |
| .callout.emph strong { color: var(--emph-ink); } | |
| /* Figure container */ | |
| .figure { margin: calc(4 * var(--u)) 0; text-align: center; } | |
| .figure img:not([class*="w-"]) { width: 100%; } | |
| .figure--wide img { width: 100%; } /* predefined variant: force full card width over any .w-NN (fix (f)) */ | |
| .figure img { | |
| border-radius: calc(4 * var(--u) * var(--rs)); | |
| border: calc(1 * var(--u)) solid var(--fig-frame); | |
| background: var(--fig-bg); | |
| } | |
| .figure .caption { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-3); | |
| color: var(--text-secondary); | |
| margin-top: calc(3 * var(--u)); | |
| line-height: 1.3; | |
| text-align: left; | |
| } | |
| .figure .caption strong { color: var(--accent-deep); } | |
| /* Float a figure BESIDE text in a TEXT-RICH card: text wraps to its side | |
| and then below it. The clearfix grows the card to contain the float; | |
| mark the <img> data-fig-layout="beside-text" so the AR gates honour the | |
| intentionally small width. Use ONLY when there is enough text to fill the | |
| figure's height -- a text-sparse card should center .figure instead. A | |
| short-text float leaves an L-shaped void below the text, which polish's | |
| FIG/BESIDE-TEXT-VOID flags. */ | |
| .fig-wrap::after { content: ""; display: table; clear: both; } | |
| .ff-fig { | |
| float: right; | |
| width: 48%; max-width: 58%; min-width: 38%; | |
| margin: calc(1 * var(--u)) 0 calc(3 * var(--u)) calc(11 * var(--u)); | |
| text-align: center; | |
| } | |
| .ff-fig.left { | |
| float: left; | |
| margin: calc(1 * var(--u)) calc(11 * var(--u)) calc(3 * var(--u)) 0; | |
| } | |
| .ff-fig img { | |
| display: block; | |
| width: 100%; | |
| border-radius: calc(4 * var(--u) * var(--rs)); | |
| border: calc(1 * var(--u)) solid var(--fig-frame); | |
| background: var(--fig-bg); | |
| } | |
| .ff-fig .caption { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-3); | |
| color: var(--text-secondary); | |
| margin-top: calc(3 * var(--u)); | |
| line-height: 1.3; | |
| text-align: center; | |
| } | |
| /* Result table with .ours row highlighted with the emphasis tint */ | |
| .result-table { | |
| width: 100%; | |
| border-collapse: collapse; | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-3); | |
| margin-top: calc(3 * var(--u)); | |
| } | |
| .result-table th, .result-table td { | |
| padding: calc(2 * var(--u)) calc(4 * var(--u)); | |
| text-align: center; | |
| border-bottom: calc(1 * var(--u)) solid var(--border-soft); | |
| } | |
| .result-table thead th { | |
| background: var(--accent); color: var(--accent-ink); | |
| font-weight: 600; font-size: var(--fs-2); | |
| } | |
| .result-table tbody tr.group-row td { | |
| background: var(--bg-emphasis); font-weight: 700; | |
| text-align: left; | |
| color: var(--accent-deep); | |
| padding-left: calc(8 * var(--u)); | |
| border-bottom: calc(2 * var(--u)) solid var(--accent); | |
| } | |
| .result-table tbody tr.ours td { background: var(--emph-soft); font-weight: 700; } | |
| .result-table tbody tr.ours td:first-child { color: var(--accent-deep); } | |
| /* Greyed reference row (was inline color:#888). */ | |
| .result-table tbody tr.reference td { color: var(--text-muted); } | |
| .result-table .method { text-align: left; padding-left: calc(8 * var(--u)); } | |
| .result-table .best { color: var(--accent); font-weight: 700; } | |
| /* 3-up stat box */ | |
| .keybox { | |
| display: grid; | |
| grid-template-columns: repeat(3, 1fr); | |
| gap: calc(4 * var(--u)); | |
| margin: calc(4 * var(--u)) 0 0; | |
| } | |
| .keybox .kb-item { | |
| background: var(--bg-emphasis); | |
| border-top: calc(2 * var(--u)) solid var(--accent); | |
| padding: calc(3 * var(--u)); | |
| text-align: center; | |
| /* The grid stretches every tile to the tallest one; center the content | |
| vertically so a 1-line tile's number aligns with a 2-line neighbour's | |
| instead of top-ragged (SKILL Layout pitfall — stat-tile alignment). */ | |
| display: flex; flex-direction: column; justify-content: center; | |
| border-radius: 0 0 calc(3 * var(--u) * var(--rs)) calc(3 * var(--u) * var(--rs)); | |
| } | |
| .kb-item .kb-num { | |
| font-family: var(--font-sans); | |
| font-weight: 800; | |
| font-size: var(--fs-6); | |
| color: var(--accent); | |
| line-height: 1; | |
| } | |
| .kb-item .kb-label { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-1); | |
| color: var(--text-secondary); | |
| margin-top: calc(2 * var(--u)); | |
| line-height: 1.1; | |
| /* Reserve two label lines (2lh tracks this line-height) so 1-line | |
| and 2-line labels occupy the same height and the big numbers | |
| align across tiles. Keep labels <= 2 lines (COMPONENTS §keybox). */ | |
| min-height: 2lh; | |
| } | |
| /* Optional takeaways strip (delete the section if not needed) */ | |
| .takeaways-strip { | |
| display: grid; | |
| grid-template-columns: auto repeat(4, 1fr); | |
| align-items: center; | |
| gap: calc(10 * var(--u)); | |
| /* Flat solid emphasis fill (de-gradient). */ | |
| background: var(--bg-emphasis); | |
| border: calc(1 * var(--u)) solid var(--border-soft); | |
| border-radius: calc(5 * var(--u) * var(--rs)); | |
| padding: calc(8 * var(--u)) calc(12 * var(--u)); | |
| } | |
| .takeaways-strip .ts-title { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-6); | |
| font-weight: 800; | |
| color: var(--accent-deep); | |
| display: flex; align-items: center; gap: calc(6 * var(--u)); | |
| } | |
| .takeaways-strip .ts-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; | |
| } | |
| .takeaways-strip .ts-item { | |
| border-left: calc(3 * var(--u)) solid var(--accent); | |
| padding-left: calc(8 * var(--u)); | |
| line-height: 1.3; | |
| text-align: center; | |
| text-wrap: balance; | |
| } | |
| .takeaways-strip .ts-key { | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-3); | |
| font-weight: 700; | |
| color: var(--accent); | |
| text-transform: uppercase; | |
| letter-spacing: 1px; | |
| } | |
| .takeaways-strip .ts-text { | |
| font-family: var(--font-serif); | |
| font-size: var(--fs-4); | |
| margin-left: calc(4 * var(--u)); | |
| } | |
| /* Footer */ | |
| .footer { | |
| grid-column: 1 / -1; | |
| display: flex; justify-content: space-between; align-items: baseline; | |
| /* When the two blocks can't sit side by side they stack (wrap) instead of | |
| overflowing; row-gap keeps the stacked blocks legible. */ | |
| flex-wrap: wrap; gap: calc(2 * var(--u)) calc(10 * var(--u)); | |
| padding-top: calc(8 * var(--u)); | |
| border-top: calc(1 * var(--u)) solid var(--border-soft); | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-5); | |
| color: var(--text-muted); | |
| } | |
| .footer .method-name { color: var(--accent-deep); } | |
| /* Long repo URL / email breaks mid-token rather than overflowing the margin. */ | |
| .footer .repo { color: var(--accent); font-weight: 600; overflow-wrap: anywhere; } | |
| /* Optional watermark */ | |
| .ornament { | |
| position: absolute; | |
| right: calc(20 * var(--u)); | |
| bottom: calc(20 * var(--u)); | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-9); | |
| color: var(--ornament-ink); | |
| font-weight: 900; | |
| letter-spacing: 4px; | |
| pointer-events: none; | |
| user-select: none; | |
| } | |
| /* ========================================================= | |
| DENSITY COMPONENTS (catalogued — see COMPONENTS.md). | |
| Guardrail: no component-local color semantics. Distinction is | |
| carried by labels, order and typography — never by new hues. | |
| ========================================================= */ | |
| /* equation-stack: compact multi-row formula stack (denser than one big .eqn) */ | |
| .equation-stack { margin: calc(2 * var(--u)) 0; } | |
| .equation-stack .eqn { margin: calc(2 * var(--u)) 0; padding: calc(2 * var(--u)) calc(8 * var(--u)); } | |
| /* eqn-anatomy: term-by-term anatomy grid (2x2 default; --row variant = 1x4) */ | |
| .eqn-anatomy { | |
| display: grid; grid-template-columns: 1fr 1fr; | |
| gap: calc(2.5 * var(--u)); margin: calc(3 * var(--u)) 0; | |
| } | |
| .eqn-anatomy.eqn-anatomy--row { grid-template-columns: repeat(4, 1fr); } | |
| .eqn-anatomy .ea-item { | |
| background: var(--bg-card-tint); | |
| border: 1px solid var(--border-soft); | |
| border-left: calc(2 * var(--u)) solid var(--accent); | |
| border-radius: calc(2 * var(--u) * var(--rs)); | |
| padding: calc(2 * var(--u)) calc(4 * var(--u)); | |
| font-size: var(--fs-2); line-height: 1.3; | |
| } | |
| .eqn-anatomy .ea-tag { | |
| display: inline-block; font-family: var(--font-sans); font-weight: 700; | |
| font-size: var(--fs-1); color: var(--accent-deep); | |
| background: var(--accent-light); border-radius: calc(1.5 * var(--u) * var(--rs)); | |
| padding: calc(0.5 * var(--u)) calc(2.5 * var(--u)); | |
| margin-right: calc(1.5 * var(--u)); | |
| } | |
| /* flow-strip: labeled pipeline, ALL steps the same accent; ONLY the | |
| final step may carry the emphasis top bar. Not an "algorithm" unless the | |
| paper has one — see COMPONENTS.md. */ | |
| .flow-strip { display: flex; align-items: stretch; gap: calc(1.5 * var(--u)); margin: calc(3 * var(--u)) 0; } | |
| .flow-strip .step { | |
| flex: 1; background: var(--accent-light); | |
| border: 1px solid var(--accent-soft); border-radius: calc(2 * var(--u) * var(--rs)); | |
| padding: calc(2 * var(--u)) calc(2.5 * var(--u)); | |
| text-align: center; font-size: var(--fs-2); line-height: 1.25; | |
| } | |
| .flow-strip .step .step-name { | |
| display: block; font-family: var(--font-sans); font-weight: 700; | |
| font-size: var(--fs-1); color: var(--accent-deep); | |
| letter-spacing: 0.5px; text-transform: uppercase; | |
| margin-bottom: calc(1 * var(--u)); | |
| } | |
| .flow-strip .step--final { border-top: calc(1.5 * var(--u)) solid var(--emph); background: var(--emph-soft); } | |
| .flow-strip .arrow { | |
| align-self: center; color: var(--accent); | |
| font-family: var(--font-sans); font-weight: 700; font-size: var(--fs-4); | |
| flex: 0 0 auto; | |
| } | |
| /* figure--duo: two paper figures sharing one caption; each img MUST be | |
| a data-source="paper" asset and carry .w-45/.w-50 (42-48% each). */ | |
| .figure--duo { display: flex; gap: calc(3 * var(--u)); align-items: flex-start; justify-content: center; } | |
| .figure--duo img { max-width: 48%; min-width: 0; } /* hard cap: duo contract is 42-48% each; an oversized w-NN cannot overflow the card */ | |
| /* result-table derived column (emph-soft = DERIVED arithmetic; label it) */ | |
| .result-table th.derived, .result-table td.derived { | |
| background: var(--emph-soft); font-family: var(--font-sans); font-weight: 700; | |
| } | |
| /* Header cells keep the accent ink rule: on the emph-soft ground the white | |
| head ink would read 1.07:1, so route the header's derived cell through | |
| the emphasis ink token (Gate G -- never inherit ink across a ground change). */ | |
| .result-table thead th.derived { color: var(--emph-ink); } | |
| /* keybox 4-up variant */ | |
| .keybox.keybox--4 { grid-template-columns: repeat(4, 1fr); } | |
| /* algo: compact numbered procedure — ONLY when the paper itself states | |
| an explicit algorithm/procedure; never invent steps. */ | |
| ol.algo { padding-left: calc(16 * var(--u)); } | |
| ol.algo li { margin-bottom: calc(1.5 * var(--u)); font-size: var(--fs-3); line-height: 1.3; } | |
| /* claim-pills: provenance mini-table (numeric-heavy posters only) */ | |
| .claim-pills { width: 100%; border-collapse: collapse; font-family: var(--font-sans); font-size: var(--fs-2); } | |
| .claim-pills td { | |
| border-bottom: 1px solid var(--border-soft); | |
| padding: calc(1.5 * var(--u)) calc(3 * var(--u)); | |
| } | |
| .claim-pills .cp-id { | |
| font-weight: 700; color: var(--accent-deep); background: var(--accent-light); | |
| border-radius: calc(1.5 * var(--u) * var(--rs)); padding: 0 calc(2.5 * var(--u) * var(--rs)); white-space: nowrap; | |
| } | |
| .claim-pills .cp-fact { color: var(--accent-deep); font-weight: 700; } | |
| .claim-pills .cp-derived { color: var(--text-secondary); font-weight: 700; } | |
| /* Grid-blowout guards: (1) columns may shrink below min-content so a | |
| wide equation can never widen its track and squeeze siblings; | |
| (2) over-wide display math scales down to fit its box instead of | |
| blowing out the card (SVG keeps aspect via height:auto). */ | |
| .body-grid > .column { min-width: 0; } | |
| .card { min-width: 0; } | |
| .eqn mjx-container > svg { max-width: 100%; height: auto; } | |
| /* verdict-chip: an inline VERDICT badge that opens a claim card | |
| (VERIFIED / FALSIFIED). Paints a ground, so it declares its own ink | |
| (Gate G) and clones its box decoration so a wrapped chip keeps its | |
| padding on both fragments. --alt routes through the emphasis register | |
| for the one falsified claim; distinction is carried by the LABEL, the | |
| register swap only raises it to headline weight. */ | |
| .verdict-chip { | |
| display: inline-block; | |
| background: var(--accent); | |
| color: var(--accent-ink); | |
| font-family: var(--font-sans); | |
| font-size: var(--fs-2); | |
| font-weight: 700; | |
| line-height: 1.25; | |
| padding: calc(0.5 * var(--u)) calc(4 * var(--u)); | |
| margin-right: calc(2 * var(--u)); | |
| border-radius: calc(2 * var(--u) * var(--rs)); | |
| text-transform: uppercase; | |
| letter-spacing: 1px; | |
| box-decoration-break: clone; | |
| -webkit-box-decoration-break: clone; | |
| } | |
| .verdict-chip.verdict-chip--alt { background: var(--emph); color: var(--emph-ink); } | |
| /* card--fillN: column-balance ladder. Each variant REPLACES the base | |
| `.card` padding shorthand (never adds to it), so exactly one padding | |
| declaration ever applies to a card and the measure loop can tune a | |
| column's bottom edge in ~4px steps without touching the copy. The ladder | |
| runs tighter (fill1) and looser (fill12) than the base card. */ | |
| .card.card--fill1 { padding: calc(3 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill2 { padding: calc(3.5 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill3 { padding: calc(4.5 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill4 { padding: calc(5 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill5 { padding: calc(5.5 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill6 { padding: calc(6 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill7 { padding: calc(7 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill8 { padding: calc(8 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill9 { padding: calc(10 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill10 { padding: calc(12 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill11 { padding: calc(15 * var(--u)) calc(9 * var(--u)); } | |
| .card.card--fill12 { padding: calc(18 * var(--u)) calc(9 * var(--u)); } | |
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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> | |
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| <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 — Anagnostides, Chauhan, Panageas, Sandholm, Yan (arXiv:2601.20180, ICML 2026) — reproduced by SabaPivot, CPU-only, $0</div> | |
| <div class="authors-line"> | |
| <span class="author">6 claims — 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 · 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> | |
| 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">→</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> — checked for solution preservation in <em>both</em> directions, exhaustively where the instances are small.</li> | |
| <li><strong>Every explicit constant</strong> — recomputed symbolically, traced to its cited source.</li> | |
| <li><strong>Every algorithm</strong> — implemented, then fitted against its claimed complexity.</li> | |
| <li><strong>Every proof step's arithmetic</strong> — 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 — 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 — 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 — 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 $\rho < 1$, and never converges at | |
| $\rho = 1$ — 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 — 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 — 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 $1/4$ — 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 — 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–Papadimitriou–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 $\varepsilon > 1/11$. | |
| </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 — 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 — equilateral triangle, $\varepsilon$-ThickBrouwer colouring, bit-extraction circuit, $k = 16$ | |
| sampled colours — 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 — 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 | |
| $\varepsilon' \le \varepsilon/8 = 1/32$ — 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 — 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 — <strong>446,768 in total</strong> — 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 — 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 — that a Jury with | |
| $f(x_{(u,v)}^-) = 1$ gains $1/M$ by flipping it — 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)–(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 — another reduction could establish | |
| it — 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> · | |
| Independent reproduction, ICML 2026 Reproducibility Challenge · 5 of 6 claims verified, 1 published proof falsified · CPU only, $0. | |
| </div> | |
| <div> | |
| Paper: <span class="repo">arXiv:2601.20180</span> · | |
| Official code: <span class="repo">none exists</span> · | |
| Reproduction: <span class="repo">SabaPivot</span> | |
| </div> | |
| </div> | |
| </div> | |
| </body> | |
| </html> | |
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