Shunyaya
Symbolic Mathematics

A New Axis of Numbers

What if every equation you already use could reveal hidden stability or fragility β€” without changing a single line of code, instrument, or infrastructure? That is the promise of Shunyaya Symbolic Mathematics (SSM) β€” a universal upgrade to arithmetic that delivers earlier signals, clearer stability, and cross-domain gains with zero infrastructure change.

Instead of representing numbers as single magnitudes, SSM represents each value as a pair:

  • m = magnitude (the classical real number you already use)
  • a = alignment factor (bounded between βˆ’1 and +1, capturing stability vs. drift)

This alignment channel instantly exposes whether a system is centred and robust (Pearo), neutral (Zearo), or drifting toward collapse (Nearo).

Classical results are always preserved under collapse:

phi(m, a) = m

This means you gain predictive depth without losing backward compatibility.

All Shunyaya standards include real scripts, deterministic demos, CI-validated POCs, and fully reproducible examples β€” this is a working symbolic system, not a theoretical concept.

Explore the Shunyaya Framework

Proof of Concept β€” Bounded Classical Laws β€” Shunyaya Symbolic Mathematics (SSM)

Why This Changes Everything

Across diverse domains, the shift from scalars to symbolic numerals (m, a) yields measurable improvements β€” with no new infrastructure required:

  • πŸŒͺ Cyclones: SSM signaled weakening up to 100+ hours earlier than wind-only categories
  • ❀️ ECG: ~18–22% earlier anomaly visibility compared to entropy/variance methods
  • πŸ“‘ Telecom: Instability flagged one or more windows before jitter thresholds
  • πŸ”‹ Batteries: SSM avoided premature β€œrecovery” unlocks by requiring earned calm
  • πŸ“Š Audit Risk: Stable vs. fraudulent firms separated more cleanly on the stability axis

Observation only. Results are reproducible but require peer review before operational use.

βœ… Proof of Concept: 10 real-life scenarios (scripts + β€œGetting Started” guides + CI workflow) β€” Symbolic-Mathematics-POC (Check repository at GitHub)

Core Idea at a Glance

  • Addition (βŠ•): (m1, a1) oplus (m2, a2) = (m1 + m2, tanh((w1atanh(a1) + w2atanh(a2)) / (w1 + w2)))
  • Subtraction (βŠ–): (m1, a1) ominus (m2, a2) = (m1, a1) oplus (βˆ’m2, a2)
  • Multiplication (βŠ—, M2 default): (m1, a1) otimes (m2, a2) = (m1*m2, tanh(atanh(a1) + atanh(a2)))
  • Division (⊘, M2 default): (m1, a1) odiv (m2, a2) = (m1/m2, tanh(atanh(a1) βˆ’ atanh(a2)))
  • Identities: additive identity = (0, +1); multiplicative identity = (1, +1)

Example:
Classical: 10 βˆ’ 4 = 6
Symbolic: (10, +0.2) ominus (4, βˆ’0.3) = (6, βˆ’0.1) β†’ reveals the result leans toward 9, a hidden drift in classical math.

Conservative yet Expansive

  • Conservative: All existing theorems still hold under collapse.
  • Expansive: Now every number carries two dimensions β€” size and stability.
  • Universal: Same rules work across physics, biology, finance, telecom, climate, and more.

Future work will redefine not just arithmetic but the foundational laws of mathematics and physics in SSM form.
Additional subsections will expand beyond what the 200-page white paper could cover β€” bringing calculus, geometry, probability, and even symbolic law redefinitions into this unified framework.

Quickstart

Minimal Python demo:

# Minimal, correct SSM quickstart (M2 defaults; gamma = 1)
from math import atanh, tanh

EPS_A = 1e-6  # tiny clamp to keep |a| < 1
GAMMA = 1.0   # weights w(m) = |m|^gamma

def clamp_a(a):
    hi = 1.0 - EPS_A
    lo = -hi
    return max(lo, min(hi, a))

def oplus(x, y, gamma=GAMMA):
    m1, a1 = x; m2, a2 = y
    a1 = clamp_a(a1); a2 = clamp_a(a2)
    m = m1 + m2
    w1 = abs(m1)**gamma
    w2 = abs(m2)**gamma
    u = (w1*atanh(a1) + w2*atanh(a2)) / (w1 + w2) if (w1 + w2) > 0 else 0.0
    return (m, tanh(u))

def otimes(x, y):
    m1, a1 = x; m2, a2 = y
    a1 = clamp_a(a1); a2 = clamp_a(a2)
    return (m1*m2, tanh(atanh(a1) + atanh(a2)))  # M2 (rapidity-additive)

def odiv(x, y):
    m1, a1 = x; m2, a2 = y
    a1 = clamp_a(a1); a2 = clamp_a(a2)
    return (m1/m2, tanh(atanh(a1) - atanh(a2)))  # M2 division

# Reproduce your example exactly:
print(oplus((10, 0.6), (5, -0.2)))
# -> (15, 0.3752508431504078)

Note: Result uses weighted rapidity averaging (Ξ³ = 1). Observation only, requires peer review before operational use.

Scope & Licensing

  • Scope: mathematics-first, reproducible, domain-agnostic. Observation-grade only (not operational or clinical).
  • License: Β© The Authors of Shunyaya Framework. Released under CC BY-NC 4.0 (non-commercial, with attribution).
  • External data: all case studies rely on public datasets, used strictly under their respective licences. Detailed dataset references will be provided in results sections.

Navigation

Next β†’ Introduction (1)

Explore Repositories on Github

1. Shunyaya Symbolic Mathematics (SSM)
https://github.com/OMPSHUNYAYA/Symbolic-Mathematics

2. Proof of Concept: 10 real-life scenarios (scripts + β€œGetting Started” guides + CI workflow)
https://github.com/OMPSHUNYAYA/Symbolic-Mathematics-POC

3. Field proof. Bounded versions of 10 familiar textbook laws (Ohm, Newton, Bernoulli, Snell, Faraday, etc.) show that the scalar m stays identical, while the lane a surfaces β€œsame value, different reality” behaviour across runs
https://github.com/OMPSHUNYAYA/Symbolic-Mathematics-Bounded-Classical-Laws-PO

4. Shunyaya Symbolic Mathematics (SSM) Ecosystem
https://github.com/OMPSHUNYAYA/Shunyaya-Symbolic-Mathematics-Master-Docs

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Disclaimer
Observation-only; not for safety-critical decisions.

OMP