diff --git a/docs/weird_machine_conservation_law.md b/docs/weird_machine_conservation_law.md
index 4fcdb929..c1f42c82 100644
--- a/docs/weird_machine_conservation_law.md
+++ b/docs/weird_machine_conservation_law.md
@@ -68,3 +68,49 @@ Total converges to entropy floor. Nobody beats it.
 | cmix | ~1.2 b/B | — | SOTA (461 models) |
 | LPC | — | ~1.5x | The signal floor |
 | Frozen LLM + AC | sub-xz (amortized) | — | Real, but model not scored |
+
+## Semantic Mass Number: Base Conversion Proof (Final Branch)
+
+### The Test
+"Encode data as a semantic mass number A(H)" = represent the message
+as one big number (the nuclide address / 10-adic residue reading).
+
+### Measured Results (lossless round-trip PASS)
+
+| Method | bits/char | bytes | ratio | lossless |
+|--------|-----------|-------|-------|----------|
+| M1 base-256 mass number | 8.000 | 100,000 | 1.00 | PASS |
+| M2 mixed-radix (155 symbols) | 7.276 | 91,107 | 1.10 | PASS |
+| M3 freq-weighted (=arithmetic) | 5.401 | 67,823 | 1.47 | needs model |
+| xz -9 (order-N + matching) | 2.551 | 31,892 | 3.14 | PASS |
+
+### Why It Fails
+Base conversion is a bijection. A bijection moves information around,
+never destroys it — so it cannot compress below its radix. M1 IS the
+data (1.00x). M2 only beats 1.00 because the data uses 155 of 256
+byte values (dropping unused-symbol slack, not compression). M3 = 
+arithmetic coding wearing a nuclide costume — and the model must ship
+= conservation wall.
+
+### The Doctrine Already Knew
+The de-anthropocentric revision explicitly flags "English-facing
+semantic compression" as the OLD ERROR and redefines:
+"MassNumber is the admissibility / recoverability RECEIPT projected
+from SemanticMass."
+
+The measurement just put numbers behind the flag.
+
+## Final Sealed Map
+
+| Idea | As compressor | Honest home |
+|------|---------------|-------------|
+| char-poly | receipt, adds overhead | GCCL integrity receipt |
+| Braille/T9 | 4.167 b/B, lose to xz | dead |
+| 16D / 583x GW | zero-noise artifact, LPC win | LPC in costume |
+| weird-machine | conservation, k=3 worst total | bits relocate, never shrink |
+| semantic mass number | base conversion, 1.00–1.10x | recoverability receipt |
+
+One rule: you can move bits between columns, never beat K(data).
+Everything that "compresses" is either base conversion (bijection,
+no gain) or arithmetic coding (needs model, ship cost). The clever
+geometry buys nothing over boring xz/LPC.