Abstract
Every number is centric. In SSM a value is a pair (m, a), where m is the classical magnitude and a ∈ [-1, +1] is a bounded alignment factor indicating stability vs drift. When a = +1, SSM collapses to classical arithmetic; otherwise, the alignment channel makes hidden drifts explicit and auditable across domains.
🔍 Why another axis for numbers?
Classical mathematics treats numbers as absolute magnitudes on a line—context-free. A “10” is the same on Earth, the Moon, or in abstraction. This scalar view has powered centuries of progress, but it hides a limitation: size is recorded; stability is not.
SSM adds a second axis. Each value becomes (m, a) with:
m— classical size (magnitude).a— alignment in[-1, +1], signalling centred/stable vs drifting/unstable.
🧭 What changes in practice?
- Preservation (collapse): classical results remain intact when you apply
phi(m, a) = m. - Visibility: two equal magnitudes can differ in stability; the alignment channel makes this explicit.
- Predictive leverage: centre–drift structure exposes early warning and earned calm, improving interpretability for physics, biology, economics, telecom, and more.
🧩 Interpretability — Pearo / Zearo / Nearo at a glance
- Pearo — stability-leaning; think systems where perturbations decay.
- Nearo — drift-leaning; think systems where perturbations amplify.
- Zearo — neutral/undecided; neither force dominates.
In all cases,ais unitless, bounded, and comparable across domains, enabling a single symbolic language for diverse fields.
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Disclaimer
Observation only. Reproducible math; domain claims require independent peer review. Defaults: gamma=1, mult_mode=M2, clamp_eps=1e-6, |a|<1.
Explore further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematics
Disclaimer
Observation-only; not for safety-critical decisions.