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+# TLM Quantum Number Generator
+
+Recursive vacuum / black-hole gravity input layer — Free Pascal implementation.
+
+Authors: Ahmad Ali Parr, Jessica L. Williams (SNAPKITTYWEST)
+
+---
+
+## Architecture
+
+```
+P4 ALGOL (source boundary)
+    │
+    ▼
+Quantum Event Generator
+    │  VacuumSample { SourceWord, GravityWord, EventWord, ModeWord }
+    ▼
+Pascal Recursive Generator
+    │  RecursiveVacuumStep + QuantumState (16 × 32-bit words)
+    ▼
+32-bit Quantum Number
+    │  RecursiveP3 feedback (depth 4)
+    ▼
+P3 Round  (QuantumP3Round)
+    │
+    ▼
+P2 GF(2^8)  (MixColumn / XTime)
+    │
+    ▼
+P1 Boolean  (XOR32, AND32, ROTL32, ROTR32)
+```
+
+The VacuumSample interface does not prescribe how values are obtained.
+Any external vacuum / gravity mechanism can supply them directly.
+
+**All internal operations are integer, modular, recursive, and deterministic.**
+No floating point is used.
+
+---
+
+## Key Properties
+
+| Property | Value |
+|----------|-------|
+| State size | 16 × 32-bit words |
+| Max recursion depth | 64 |
+| Output word size | 32 bits |
+| Arithmetic | Modular integer (mod 2³²) |
+| GF field | GF(2⁸), irreducible poly x⁸+x⁴+x³+x+1 (AES) |
+| P3 test vector | D4 BF 5D 30 → 04 66 81 E5 (canonical AES MixColumns) |
+
+---
+
+## Build
+
+```bash
+# Requires Free Pascal Compiler (fpc)
+fpc tlm_quantum_generator.pas
+./tlm_quantum_generator
+```
+
+Expected output:
+```
+TLM QUANTUM NUMBER GENERATOR
+BEGIN VERIFICATION
+XTIME TEST PASSED
+MIXCOLUMN D4 BF 5D 30 TEST PASSED
+ZERO COLUMN TEST PASSED
+REPEATED COLUMN TEST PASSED
+STATE INITIALIZATION TEST PASSED
+RECURSION TEST PASSED
+SOURCE FUSION TEST PASSED
+ALL VERIFICATION TESTS PASSED
+
+RECURSIVE QUANTUM GENERATION
+-----------------------------
+EVENT   0 SOURCE=...  GRAVITY=...  QUANTUM=...
+...
+GENERATOR COMPLETE
+```
+
+---
+
+## Verification Tests
+
+| Test | What it checks |
+|------|---------------|
+| `TestXTime` | GF(2⁸) multiply-by-x at key boundary values ($00,$01,$40,$80,$FF) |
+| `TestMixColumn` | AES canonical vector: D4 BF 5D 30 → 04 66 81 E5 |
+| `TestZeroColumn` | Zero input → zero output (linearity) |
+| `TestRepeatedColumn` | Constant column is its own fixed point |
+| `TestStateInitialization` | Same seed → identical 16-word state (determinism) |
+| `TestRecursion` | `RecursiveSeed` is pure / referentially transparent |
+| `TestSampleFusion` | `FuseVacuumSample` is deterministic |
+
+---
+
+## Source Boundary
+
+```
+VacuumSample
+    ├── SourceWord   (vacuum field)
+    ├── GravityWord  (gravity field)
+    ├── EventWord    (quantum event)
+    └── ModeWord     (mode selector)
+            │
+            ▼
+     FuseVacuumSample → RecursiveVacuumStep → QuantumState → QN → P3 → GF(2⁸) → Boolean
+```
+
+---
+
+## License
+
+MIT