Abstract
Shunyaya Symbolic Mathematics (SSM) extends scalars to pairs (m, a) where m is magnitude and a ∈ [-1, +1] encodes centre vs drift. Classical arithmetic is preserved under the collapse phi(m,a) = m.
🔭 Positioning & universality
- ✅ Conservative extension: SSM augments numbers; it does not replace them.
- 🔁 Collapse guarantee (for all operations defined herein):
phi(x oplus y) = phi(x) + phi(y) phi(x otimes y) = phi(x) * phi(y) - 🔒 Backward-compatibility: all classical identities hold under
phi. - 🎯 Added resolution: two equal magnitudes can differ in stability (alignment).
- 🧭 Practical leverage: forecasts, signals, and risks gain a centre–drift axis.
🧩 What this framework is
- A symbolic numeral is a pair
(m, a), withma classical real magnitude andaa bounded, dimensionless alignment factor in[-1, +1]. - Interpretation:
anear+1⇒ centred, robust;anear−1⇒ drift/instability. - Test oracle: if all
a = +1, results match classical arithmetic to machine precision.
🛡️ Guarantees (scope of correctness)
- Collapse preserves sums and products exactly as shown above.
- Alignment remains bounded by design; edge cases at
|a| = 1are treated as limits. - Defaults are declared explicitly elsewhere; any deviation must be stated in-page.
📏 Tone of claims
Mathematics-first and observation-grade only. Domain claims require independent peer review before operational use.
Navigation
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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.
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