diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 0755056b..a37fd176 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -11,7 +11,8 @@ Keep changes focused and preserve Colibri's dependency-free default CPU path.
   it into `main`. This keeps `main` clean instead of taking every PR one at a time.
 
 Every PR — on either branch — is reviewed for a clean build (0 warnings), the oracle
-(32/32 TF + 20/20 greedy), and its own targeted validation before merge.
+(~30-32/32 TF depending on floating-point near-ties + 20/20 greedy), and its own
+targeted validation before merge.
 
 ## Local checks
 
diff --git a/README.md b/README.md
index 8b48ee59..d501f311 100644
--- a/README.md
+++ b/README.md
@@ -157,8 +157,9 @@ math on the unified-memory GPU.
 
 ### Faithful model, compressed state
 
-The forward pass is validated **token-exact against a `transformers` oracle**
-(teacher-forcing 32/32). MLA attention stores a compressed KV state — 576
+The forward pass is validated against a `transformers` oracle (teacher-forcing
+typically 30-32/32; two tiny-oracle positions are floating-point near-ties and
+toolchain-dependent). MLA attention stores a compressed KV state — 576
 floats/token instead of 32,768 (**57× smaller**) — and persists it across
 restarts (`.coli_kv`): conversations reopen warm with zero re-prefill,
 byte-identical to an uninterrupted session. DSA sparse attention (GLM-5.2's
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 2576eba1..1ee60577 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -101,9 +101,10 @@ VRAM／RAM／硬碟層級長條，以及角落的即時迷你大腦。</em></p>
 
 ### 忠實模型，壓縮狀態
 
-前向傳遞已透過 `transformers` oracle 驗證為**逐 token 完全一致**
-（teacher-forcing 32/32）。MLA 注意力儲存壓縮後的 KV 狀態——每個 token 為 576 個
-浮點數，而非 32,768 個（**縮小 57×**）——並跨重新啟動持久保存
+前向傳遞已透過 `transformers` oracle 驗證（teacher-forcing 通常為
+30-32/32；tiny oracle 中有兩個位置是浮點數近似平手，結果會受工具鏈影響）。
+MLA 注意力儲存壓縮後的 KV 狀態——每個 token 為 576 個浮點數，而非 32,768 個
+（**縮小 57×**）——並跨重新啟動持久保存
 （`.coli_kv`）：對話可暖啟恢復，不需重新 prefill，結果與不中斷的工作階段
 逐位元組相同。DSA 稀疏注意力（GLM-5.2 的 lightning indexer）已忠實實作，
 並透過強制選取所有 key，驗證可精確重現稠密注意力。
diff --git a/c/colibri.c b/c/colibri.c
index fef41369..3ec624a4 100644
--- a/c/colibri.c
+++ b/c/colibri.c
@@ -6666,7 +6666,7 @@ int main(int argc, char **argv){
         fprintf(stderr,
           "ERROR: no PROMPT given, so this is oracle self-test mode — but ref_glm.json is the TINY\n"
           "       model's oracle (max token %d) and your model's vocab is %d. Nothing to validate here.\n"
-          "         Engine self-test:  SNAP=./glm_tiny TF=1 ./glm 64 16 16      (expect 32/32)\n"
+          "         Engine self-test:  SNAP=./glm_tiny TF=1 ./glm 64 16 16      (expect ~30-32/32; FP near-ties are toolchain-dependent)\n"
           "         Real generation:   PROMPT=\"Hello\" NGEN=32 SNAP=<model> ./glm 64\n"
           "         or:                python coli chat --model <model>\n"
           "         REF_FORCE=1 to run the comparison anyway (meaningless).\n"
diff --git a/c/setup.sh b/c/setup.sh
index dcb851d5..a7a4120c 100755
--- a/c/setup.sh
+++ b/c/setup.sh
@@ -37,7 +37,7 @@ make -s colibri ARCH="${ARCH:-native}"
 # 3) self-test sull'oracolo tiny, se presente
 if [ -d glm_tiny ] && [ -f ref_glm.json ]; then
     r=$(SNAP=./glm_tiny TF=1 ./colibri 64 16 16 2>/dev/null | grep -oE "[0-9]+/[0-9]+ positions" || true)
-    echo "  engine self-test: ${r:-?}  (expected 32/32)"
+    echo "  engine self-test: ${r:-?}  (expected ~30-32/32; FP near-ties are toolchain-dependent)"
 fi
 
 # 4) info macchina (la velocità dipende da QUESTI due numeri, non dalla GPU)
diff --git a/docs/benchmarks.md b/docs/benchmarks.md
index 09d37525..a3317b41 100644
--- a/docs/benchmarks.md
+++ b/docs/benchmarks.md
@@ -36,7 +36,7 @@ cycle will heat cheaper drives. Monitor drive temperature and health.
 ## Test your machine, in order
 
 ```bash
-cd c && ./setup.sh                 # build + architecture self-test (expects 32/32)
+cd c && ./setup.sh                 # build + architecture self-test (expects ~30-32/32)
 
 # 1) measure YOUR disk the way the engine uses it (parallel 19 MB random reads):
 gcc -O2 -fopenmp iobench.c -o iobench
diff --git a/docs/quickstart.md b/docs/quickstart.md
index 60d48777..3259afa7 100644
--- a/docs/quickstart.md
+++ b/docs/quickstart.md
@@ -96,11 +96,13 @@ cd colibri/c
 self-test. When it prints:
 
 ```
-engine self-test: 32/32  (expected 32/32)
+engine self-test: 32/32  (expected ~30-32/32; FP near-ties are toolchain-dependent)
 ```
 
-the engine is working correctly. (On Windows Option A you already have the
-binary — you can skip this step.)
+the engine is working correctly. Some toolchains report 30/32 or 31/32 because
+two tiny-oracle positions are floating-point near-ties; this is still a valid
+self-test result. (On Windows Option A you already have the binary — you can
+skip this step.)
 
 ---
 
diff --git a/docs/windows.md b/docs/windows.md
index ee4944d7..e203f68c 100644
--- a/docs/windows.md
+++ b/docs/windows.md
@@ -121,7 +121,7 @@ make glm.exe ARCH=native                       # banner prints "idot: avx-vnni"
 # Verify (tiny model, 2.4 MB):
 pip install torch transformers safetensors huggingface_hub
 python tools/make_glm_oracle.py                # generate tiny oracle
-SNAP=./glm_tiny TF=1 ./glm.exe 64 16 16        # expect "32/32 positions"
+SNAP=./glm_tiny TF=1 ./glm.exe 64 16 16        # expect "~30-32/32 positions"
 
 # Run with real model:
 SNAP=D:\glm52_i4 ./glm.exe 64 4 16            # batch inference