Signed Multi-Plane Encoding (Prototype)

Status: Experimental prototype
Code: experiments/signed_multiplane_encoding_demo.py
Tests: tests/test_signed_multiplane_encoding.py

Summary

This prototype tests a state-expansion idea:

• Standard binary two-plane symbol space: (0/1)^2 = 4 states
• Balanced ternary two-plane symbol space: (-1/0/+1)^2 = 9 states
• Signed-binary two-plane symbol space: (+/-0, +/-1)^2 = 16 states

The signed-binary representation uses signed zero as a distinct symbolic state for routing/history metadata, while preserving arithmetic compatibility.

Representation

Per plane, define a signed bit:

• magnitude m in {0, 1}
• sign s in {-1, +1}

Scalar value:

• if m=1: x = s
• if m=0: x = +/-0 (symbolic state retained by sign)

Unit-interval map for each signed bit:

• -1 -> 0
• -0 -> 0.5 - eps
• +0 -> 0.5 + eps
• +1 -> 1

Geometry

Codewords are built with two components:

1. Sphere/spiral anchor (Fibonacci sphere) for global indexing
2. Rotated local vector for per-state offset:
   • signed: [a, b, z_signed_zero]
   • ternary: [a, b, 0]

Then:

codeword = anchor + local_scale * (R * local_vector)

where R is a 3D rotation matrix from slant angles.

Decode

Decode by nearest-neighbor lookup in the deterministic codebook.

Current empirical output

From python experiments/signed_multiplane_encoding_demo.py --noise-std 0.04:

• capacity:
  • binary: 2.000 bits
  • ternary: 3.170 bits
  • signed: 4.000 bits
• round-trip nearest decode:
  • signed: 1.000
  • ternary: 1.000

Run

python experiments/signed_multiplane_encoding_demo.py --noise-std 0.04
pytest -q tests/test_signed_multiplane_encoding.py

Notes

• This is an encoding/geometry experiment, not a cryptographic security claim.
• Signed zero should be treated as metadata state, not numeric semantic value.