B13 Processor – Residual-to-Bias Feedback with Stability Constraints (Work in Progress)

Abstract

This note describes an experimental architectural concept called the B13 Processor.

Unlike classical FFT-based processing, which performs linear basis decomposition,

the B13 architecture treats internal residual energy ("heat", H) not as waste,

but as a structured control signal.

This document focuses on one specific mechanism:

Error-to-Bias Feedback (H-Carrier)

with explicit stability constraints.

This is an engineering-oriented draft (Ver 0.9).

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1. Motivation

In most signal processing pipelines:

• Residual error is discarded.
• Noise is suppressed or filtered out.
• Adaptation requires explicit learning.

The B13 approach proposes a different viewpoint:

Residual energy (H) may contain unresolved structural information.

Instead of discarding it,

we convert it into a bounded adaptive bias for the next stage.

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2. H-Carrier Concept

Each unit produces:

• Primary signal outputs (I/Q or equivalent)
• Residual outputs:
  • H_s (signed residual)
  • H_m (residual magnitude)

The residual is processed through:

1. Threshold gating
2. Leaky integration
3. Loop-gain constraint

Only after satisfying these conditions is it reinjected.

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3. Stability Constraints

3.1 Threshold Gate

Small residuals (noise floor level) must not circulate.

Let:

• τ = noise floor threshold
• κ = soft-gate slope

Gate coefficient: