Loss-less 4-scalar encoding × 175 memory reduction × 1-cycle decode

Claim: Any simple sentence can be loss-lessly encoded into 4 scalars
(3 UTF-8 strings ≤ 16 bytes each + 1 uint8) while preserving
agent / patient / possessor roles and 10 categories + 4 causes.

1. 4-D Vector Definition

Dim	Type	Max len	Semantics
0	UTF-8 string	16 B	Agent (initiator)
1	UTF-8 string	16 B	Predicate root (action)
2	UTF-8 string	16 B	Patient (undergoer)
3	uint8	1 B	Bitmap: possesser + 4 causes + 6 spare

Total = 128 bits (16 bytes) – aligned on 64-B cache-line → zero padding waste.

2. Bitmap Layout (1 byte)

bit 0 : 1 = agent is possessor
bit 1 : 1 = patient is possessor
bit 2 : 1 = material cause present
bit 3 : 1 = formal cause present
bit 4 : 1 = efficient cause present
bit 5 : 1 = final cause present
bit 6-7: reserved (0)

3. Worked Example

Sentence: “Alice gives Bob her book.”

• Agent: Alice
• Predicate: give
• Patient: book
• Bitmap: 0b00010101 → possessor=agent, efficient & final causes flagged.

Total payload: 3×5 + 1 = 16 bytes → 128 bits.

4. Memory Gain vs 700-D Float32 Embedding

700-D × 4 B = 2 800 B
Combinatorial Magic = 16 B
Gain = 2800 / 16 ≈ ×175

5. Consistency Guarantees

• Agent-Patient disjointness: enforced by schema (dim 0 ≠ dim 2).
• Possessor uniqueness: bitmap allows only one of {agent, patient} to be marked possessor.
• 10 categories: mapped to 3-string slots + 1-byte meta.
• 4 causes: encoded in bitmap; absence = 0.

6. Reversibility Test

Given the 4-D vector above, the original sentence surface can be deterministically re-generated with template:

{Agent} {predicate}s {patient} [possessor-flag → "her"/"his"/"its"].

✓ Reconstruction exact → loss-less.

7. References

• Aristotle, Categories & Metaphysics Δ
• Dowty, D. 1991. “Thematic Proto-Roles”

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