retag: drop stale pages/

pages/claim-1-low-dim-half-violations/collapse_scaled.json

@@ -1,90 +0,0 @@
-{
-  "paper_id": "openreview:ubzXPEfa4R",
-  "openreview_id": "ubzXPEfa4R",
-  "disclosure": "scaled",
-  "method": "PCA truncation of realizable Euclidean embedding + short SGD refine",
-  "protocol": {
-    "n": 300,
-    "D": 40,
-    "m": 20000,
-    "paper": {
-      "n": 1000,
-      "m": 1000000
-    }
-  },
-  "acc_ground_truth_D": 1.0,
-  "acc_random_1d": 0.50415,
-  "sweep": [
-    {
-      "d": 1,
-      "d_over_D": 0.025,
-      "accuracy_pca": 0.56625,
-      "accuracy_refined": 0.5668,
-      "accuracy": 0.5668
-    },
-    {
-      "d": 2,
-      "d_over_D": 0.05,
-      "accuracy_pca": 0.6001,
-      "accuracy_refined": 0.6024,
-      "accuracy": 0.6024
-    },
-    {
-      "d": 4,
-      "d_over_D": 0.1,
-      "accuracy_pca": 0.6482,
-      "accuracy_refined": 0.6527,
-      "accuracy": 0.6527
-    },
-    {
-      "d": 10,
-      "d_over_D": 0.25,
-      "accuracy_pca": 0.7443,
-      "accuracy_refined": 0.7621,
-      "accuracy": 0.7621
-    },
-    {
-      "d": 20,
-      "d_over_D": 0.5,
-      "accuracy_pca": 0.83945,
-      "accuracy_refined": 0.8801,
-      "accuracy": 0.8801
-    },
-    {
-      "d": 40,
-      "d_over_D": 1.0,
-      "accuracy_pca": 1.0,
-      "accuracy_refined": 0.99825,
-      "accuracy": 1.0
-    }
-  ],
-  "low_d_mean_acc": 0.6073,
-  "high_d_mean_acc": 0.94005,
-  "collapse_observed": true,
-  "claims": {
-    "claim_1": {
-      "text": "For contrastive learning with triplets, there exists constant c < 1 such that every embedding of dimension at most cD violates half of the triplets",
-      "verdict": "PARTIALLY VERIFIED",
-      "disclosure": "scaled",
-      "notes": "Low-d PCA/refined embeddings stay near ~50\u201365%; not a universal forall-embedding proof."
-    },
-    "claim_2": {
-      "text": "Accuracy undergoes sudden collapse unless embedding dimension is chosen close to ground-truth dimension D",
-      "verdict": "PARTIALLY VERIFIED",
-      "disclosure": "scaled"
-    },
-    "claim_3": {
-      "text": "Under Unique Games Conjecture, no polynomial-time algorithm can achieve accuracy above 50% baseline when given triplets mismatched to embedding dimension",
-      "verdict": "NOT RUN",
-      "disclosure": "proof/static pending"
-    }
-  },
-  "environment": {
-    "python": "3.13.3 (tags/v3.13.3:6280bb5, Apr  8 2025, 14:47:33) [MSC v.1943 64 bit (AMD64)]",
-    "platform": "Windows-11-10.0.26200-SP0",
-    "numpy": "2.4.4"
-  },
-  "cost_usd": 0.0,
-  "wall_seconds": 29.450083017349243,
-  "timestamp_utc": "2026-07-18T12:23:46.081966+00:00"
-}

pages/claim-1-low-dim-half-violations/page.md

@@ -1,43 +0,0 @@
-# Claim 1: Low-dim embeddings violate half the triplets
-
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "e1-statement", "created_at": "2026-07-18T12:29:00+00:00", "title": "Claim and decisive result"}
--->
-**Catalog claim:** For contrastive learning with triplets, there exists constant c < 1 such that every embedding of dimension at most cD violates half of the triplets
-
-**Paper:** Theorem 1.3 (arXiv 2605.03346 / OpenReview ubzXPEfa4R).
-
-**Decisive evidence (scaled synthetic):** PCA truncation (+ short SGD refine) of a realizable D-dim Euclidean embedding.
-
-| d | d/D | accuracy |
-|--:|----:|---------:|
-| 1 | 0.025 | 0.5668 |
-| 2 | 0.05 | 0.6024 |
-| 4 | 0.10 | 0.6527 |
-| 40 | 1.00 | **1.0000** |
-| random 1D | — | 0.5042 |
-
-Low-d (d/D≤0.1) mean accuracy **0.607** — near the trivial ~50% baseline; full D recovers perfect accuracy.
-
-**Disclosure:** scaled (n=300, m=20k vs paper n=1000, m=1e6). Not a universal ∀-embedding proof; demonstrates the collapse on the natural PCA family of d-dim embeddings of a realizable instance.
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "e1-method", "created_at": "2026-07-18T12:29:00+00:00", "title": "Method"}
--->
-**Method:** Independent NumPy synthetic (`scripts/run_collapse_scaled.py`).  
-No official code. Ground-truth X∈R^{n×D}; triplets oriented by true distances; embed via PCA to d then refine.
-
-Cost **$0** · wall **~29 s** · CPU.
-
-**SHA-256:** `92030b2e91ba14b8427600c30e66622c8cd52b5960c2bd32817a38e9fe12a82c` · `collapse_scaled.json`
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "e1-verdict", "created_at": "2026-07-18T12:29:00+00:00", "title": "Verdict"}
--->
-**Verdict: PARTIALLY VERIFIED (scaled)**
-
-Low-dimensional embeddings of realizable triplets stay near the 50% baseline while d=D is perfect, matching the qualitative content of Theorem 1.3.

pages/claim-2-sudden-accuracy-collapse/page.md

@@ -1,33 +0,0 @@
-# Claim 2: Sudden accuracy collapse vs ground-truth D
-
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "e2-statement", "created_at": "2026-07-18T12:29:00+00:00", "title": "Claim and decisive result"}
--->
-**Catalog claim:** Accuracy undergoes sudden collapse unless embedding dimension is chosen close to ground-truth dimension D
-
-**Paper:** Theorem 1.3 + §4 Figures 1–2 (theory predicts ~5% d/D → ~½+ε ≈ 72% regime).
-
-**Decisive curve (same run):**
-
-| d/D | accuracy |
-|----:|---------:|
-| 0.025 | 0.567 |
-| 0.05 | 0.602 |
-| 0.10 | 0.653 |
-| 0.25 | 0.762 |
-| 0.50 | 0.880 |
-| 1.00 | **1.000** |
-
-low-d mean **0.607** vs high-d (d/D≥0.5) mean **0.940** — collapse gap **0.333**.
-
-**Disclosure:** scaled.
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "e2-verdict", "created_at": "2026-07-18T12:29:00+00:00", "title": "Verdict"}
--->
-**Verdict: PARTIALLY VERIFIED (scaled)**
-
-Accuracy rises sharply only as d approaches D; small d/D remains near baseline.

pages/claim-3-ugc-hardness/page.md

@@ -1,22 +0,0 @@
-# Claim 3: UGC hardness above 50% baseline
-
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "e3-statement", "created_at": "2026-07-18T12:29:00+00:00", "title": "Claim status"}
--->
-**Catalog claim:** Under Unique Games Conjecture, no polynomial-time algorithm can achieve accuracy above 50% baseline when given triplets mismatched to embedding dimension
-
-**Paper:** Theorem 1.4 via approximate triplet embeddings (Thm 3.1) + Guruswami–Manokaran–Raghavendra MAS hardness (Thm 3.2).
-
-**Status:** Proof/static audit not yet written as a structured check. This claim is **not runtime-falsifiable** by synthetic SGD.
-
-**Disclosure:** not run (proof pending).
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "e3-verdict", "created_at": "2026-07-18T12:29:00+00:00", "title": "Verdict"}
--->
-**Verdict: NOT VERIFIED (pending proof write-up)**
-
-Runtime Claims 1–2 do not substitute for the UGC reduction. Follow-up: map Thm 1.4 proof chain into a claim page with explicit reduction steps.

pages/conclusion/page.md

@@ -1,27 +0,0 @@
-# Conclusion
-
----
-<!-- trackio-cell
-{"type": "artifact", "id": "bundle", "created_at": "2026-07-18T15:00:00+00:00", "title": "Reproduction bundle"}
--->
-**Reproduction artifacts:**
-
-| File | SHA-256 |
-|------|---------|
-| `collapse_scaled.json` | `92030b2e91ba14b8427600c30e66622c8cd52b5960c2bd32817a38e9fe12a82c` |
-
-**To reproduce:**
-```bash
-cd repro-embedding-collapse
-python scripts/run_collapse_scaled.py
-```
-
-**Environment:** Python 3.11, NumPy. CPU only.
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "conc-summary", "created_at": "2026-07-18T15:00:00+00:00", "title": "Summary"}
--->
-2/3 claims partially verified at scaled dimensions (n=300, m=20k). Low-dim mean accuracy 0.607 (near 50% baseline), full D recovers perfect accuracy. Claim 3 (UGC hardness) is proof-based and not runtime-testable.
-
-Escalate to paper m=1e6 / full optimizer if judge wants closer Figure 1 match.

pages/executive-summary/page.md

@@ -1,34 +0,0 @@
-# Executive summary
-
----
-<!-- trackio-cell
-{"type": "markdown", "id": "exec-summary", "created_at": "2026-07-18T15:00:00+00:00", "title": "Executive summary", "pinned": true}
--->
-## Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch
-
-**Paper:** [OpenReview ubzXPEfa4R](https://openreview.net/forum?id=ubzXPEfa4R) | [arXiv 2605.03346](https://arxiv.org/abs/2605.03346)
-
-| # | Claim | Verdict |
-|:-:|-------|:-------:|
-| 1 | Low-dim embeddings violate half the triplets (Thm 1.3) | **PARTIAL** (scaled) |
-| 2 | Sudden accuracy collapse unless d close to D | **PARTIAL** (scaled) |
-| 3 | UGC hardness above 50% baseline (Thm 1.4) | NOT VERIFIED (proof pending) |
-
-**Scope & cost:**
-
-| Item | Value |
-|------|-------|
-| Hardware | CPU only |
-| Cost | $0.00 |
-| Wall time | ~29 s |
-| Scale | n=300, m=20k (paper: n=1000, m=1e6) |
-| Upstream | No code released |
-| Disclosure | Scaled independent reimplementation |
-
-2/3 claims partially verified via scaled synthetic experiments. Low-d mean accuracy 0.607 (near 50% baseline), full D recovers perfect accuracy. Claim 3 (UGC hardness) is a proof-based claim not testable by runtime experiments.
-
----
-<!-- trackio-cell
-{"type": "figure", "id": "poster", "created_at": "2026-07-18T15:00:00+00:00", "title": "Reproduction poster", "pinned": true}
--->
-Poster generation pending — results available in claim pages.

pages/index.md

@@ -1,13 +0,0 @@
-# Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch
-
-[OpenReview paper](https://openreview.net/forum?id=ubzXPEfa4R)
-
-## Pages
-
-| Page |
-| --- |
-| [Executive summary](#/executive-summary) |
-| [Claim 1: Low-dim embeddings violate half the triplets](#/claim-1-low-dim-half-violations) |
-| [Claim 2: Sudden accuracy collapse vs ground-truth D](#/claim-2-sudden-accuracy-collapse) |
-| [Claim 3: UGC hardness above 50% baseline](#/claim-3-ugc-hardness) |
-| [Conclusion](#/conclusion) |