The ladder is TNF, and the four families now have their vectors (Refs #2001)

ERRATA_2026-06-14.md

@@ -157,3 +157,59 @@ number, which is what lets the two drift. The gate warns rather than fails on
 that axis by design, and this amendment is the second time the warning has been
 acted on. The recommendation from 2026-06-14 stands: quote the live SSOT count
 with the commit that produced it, not a number frozen into a title.
+
+---
+
+# Amendment 2 -- 2026-08-09: 92 -> 109, and why the count moved twice in one day
+
+Amendment 1 set the count at 92 after a whole family, the ternary-exponent ladder,
+turned out to have zero rows. It moved again the same day, and the reason is the
+opposite of a miscount: **two families were conflated into one.**
+
+The ladder was renamed twice on 2026-08-09 -- GF-T to TEF, then TEF to TNF -- on
+the assumption that these were the same object under successive names. They are
+not. **GF-T and TNF are different families on different rules**, and a control
+family, **BNF**, was then added to measure what separates them.
+
+Four families on two axes:
+
+| | phi-derived | theorem-derived |
+|---|---|---|
+| binary | GF | **BNF** (new) |
+| ternary | **GF-T** (restored) | TNF |
+
+GF-T carries a mantissa from the phi lineage and leaves positions unspent -- 2 at
+16 bits, 4 at 64 through 512, 6 at 1024. TNF derives its mantissa from the width
+rule and spends every position. By the precision law the difference is exactly
+2^k, and the reference oracle confirms it at 4.03x, 15.43x, 15.99x and 15.24x
+against predictions of 4, 16, 16 and 16.
+
+BNF differs from TNF in exactly one thing -- the radix the exponent field is
+encoded in -- so the pair measures the ternary encoding rather than asserting it.
+
+**Canonical count going forward: 109.** 84, 83 and 92 are superseded.
+
+## Cluster breakdown at 109
+
+| Cluster | Count |
+|---|---|
+| GoldenFloat | 48 |
+| HistoricalVendor | 10 |
+| PositUnumIII | 8 |
+| IntegerFixed | 8 |
+| MlLowPrecision | 7 |
+| Ieee754Binary | 5 |
+| Lns | 4 |
+| Theoretical | 4 |
+| CompressionTrick | 4 |
+| Ieee754Decimal | 3 |
+| ExtendedFloat | 3 |
+| Microscaling | 3 |
+| QuantTuned | 2 |
+| **TOTAL** | **109** |
+
+## What did not change
+
+No conformance pack, SHA-256 or bit-exact vector from the 92 is affected. GF-T's
+nine rungs are restored with their historical parameters, exactly as they were
+before the rename; BNF's eight are new.