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README.md

@@ -40,9 +40,9 @@ per-geometry finite-element (FEM) solve for fast design-space exploration.
 Verified node-by-node against FEM: pooled **R² = 0.99986**, test relative-L2 **0.00597** on the shipped
 checkpoint. **Interactive demo:** https://huggingface.co/spaces/Efradeca/elastic-stress-surrogate
 
-> **Honesty note.** This card reports the model's limitations as prominently as its strengths. The
-> deployed value is *accuracy + speed*. The equilibrium regularizer is a well-characterized **trade-off**
-> (a prior-art idea in a new meshfree instantiation), not a free win — see *Evaluation* and *Findings*.
+> **At a glance.** The deployed value is *accuracy + speed*: **R² = 0.99986** vs FEM, milliseconds on CPU.
+> The equilibrium regularizer is a physical-consistency component with a well-characterized
+> accuracy/consistency **trade-off** (see *Evaluation*).
 
 ## Model Details
 
@@ -66,7 +66,7 @@ connectivity.
   attention block is reused verbatim) and an independent, from-equations reimplementation of the
   **LinearNO** attention block (Hu et al., AAAI 2026).
 
-### What is and isn't novel (read this)
+### Novelty and prior work
 
 The soft equilibrium-residual penalty `λ‖∇·σ‖²` on a predicted stress field is **established prior art**
 (PI-UNet 2022; PiFNO 2024; and especially **P-DivGNN 2025**, which uses essentially the same
@@ -75,7 +75,7 @@ periodic micro-RVE). We do **not** claim the idea. This
 repository's actual contribution is (1) a specific, previously-unattested **instantiation** — the penalty
 on a *transformer* operator with a *meshfree, connectivity-free* MLS divergence (exact on affine fields by
 the degree-1 GMLS reproduction property), distinct from the FE / FFT / finite-difference operators of all
-prior work — and (2) a **cross-operator honesty analysis** of when that penalty actually helps.
+prior work — and (2) a **cross-operator analysis** that quantifies when that penalty actually helps.
 
 ### Model Sources
 
@@ -192,21 +192,21 @@ committed per-seed distributions are in the repository (`docs/RESULTS.md`, `resu
 | LinearNO, M=256 (this work) | 0.00635 | 0.00622 ± 0.00071 | 3 | 765,313 |
 | **+ equilibrium regularizer (this model)** | 0.00653 | 0.00668 ± 0.00065 | 3 | 582,275 |
 
-**Comparable, not "beats."** In this sample LinearNO's median (0.00606) is lower than our reproduced
-baseline's (0.00766) at fewer parameters, and it reaches the published ~0.0050 level on good seeds. But
-both models have **high run-to-run variance** (`torch.compile` non-determinism on 1000 samples), and the
-baseline's higher mean is driven by 2 outlier seeds. We do **not** claim LinearNO beats or is more robust
-than the baseline; an attempted mechanistic explanation (slice-attention instability) was **empirically
-tested and refuted**. Honest reading: LinearNO is **comparable** to the baseline at ≤ its parameters, both
-reproducing ~0.0064 on good seeds. As a cross-check, we re-evaluated the authors' released official
-checkpoint on our data with their code and reproduced **0.005007** — confirming the dataset, split, and
-metric are identical, so the table is mutually comparable.
+**Accuracy: comparable to the baseline.** In this sample LinearNO's median (0.00606) is lower than our
+reproduced baseline's (0.00766) at fewer parameters, and it reaches the published ~0.0050 level on good
+seeds. Both models show **high run-to-run variance** (`torch.compile` non-determinism on 1000 samples),
+with the baseline's higher mean driven by 2 outlier seeds; an attempted mechanistic explanation
+(slice-attention instability) was tested and **not supported** by the evidence. LinearNO is therefore best
+read as **statistically comparable** to the baseline at ≤ its parameters, both reaching ~0.0064 on good
+seeds, without claiming an accuracy improvement. As a cross-check, we re-evaluated the authors' released
+official checkpoint on our data with their code and reproduced **0.005007**, confirming the dataset, split,
+and metric are identical, so the table is mutually comparable.
 
 **Verification against FEM ground truth** (200 test meshes; shipped checkpoint = best of 3 eqreg seeds):
 per-sample relative-L2 mean **0.00597** (median 0.00533), pooled Pearson **r = 0.99993**, **R² = 0.99986**,
 peak-stress relative error **0.27%** — reproducible via `scripts/verify_model.py` → `results/verify_model.json`.
 
-### Findings (the honest part)
+### Research findings
 
 **1. The meshfree MLS operator is rigorously grounded.** It is a degree-1 GMLS derivative: *exact on
 affine fields* (~1e-14 in float64) and *O(h)-convergent* on smooth fields (fitted slope 1.01), validated
@@ -219,7 +219,7 @@ same-architecture, epoch-matched ablation the regularizer cuts the residual **~3
 model's own (MLS) operator**, but an **independent FE operator** sees only **~6–53×** — at a **measured
 accuracy cost** (test rel-L2 0.00479 → 0.00621, +30%). A model-free control on exactly-divergence-free
 analytic fields confirms the FE operator is *comparable* to MLS off the void-rim slivers (the large raw
-gap is a sliver artifact), so the honest operator-agnostic reduction (~53×) still sits **an order of
+gap is a sliver artifact), so the operator-agnostic reduction (~53×) still sits **an order of
 magnitude below** the trained-operator 325×. The gaming reproduces on the *literal* official LinearNO
 block (gap ~25×), so it is a property of the soft-penalty objective, not our implementation.
 
@@ -237,8 +237,8 @@ equilibrium residual low OOD (+7%), but on an orthogonal field-smoothness proxy
 from the unregularized models.
 
 **Takeaway:** the soft equilibrium penalty looks most impressive exactly where it is least physical (an
-unsupervised latent tensor). We report this rather than paper over it. The deployed model's value is its
-accuracy (R² = 0.99986) and millisecond CPU speed.
+unsupervised latent tensor), and its benefit largely disappears under direct tensor supervision. The
+deployed model's value is its accuracy (R² = 0.99986) and millisecond CPU speed.
 
 ## Technical Specifications