Shunyaya Symbolic Mathematical Symbols – What SSMS is; Canonical Object and Collapse (1.1, 1.2)

What this page covers
A crisp foundation for the operator layer: what Shunyaya Symbolic Mathematical Symbols is, the symbolic numeral, the collapse map, and the safe rapidity path that keeps alignment bounded. Goal: a minimal, portable canon that preserves classical results under phi while enabling stability-aware operations through a bounded alignment channel.

What SSMS is (1.1)
Shunyaya Symbolic Mathematical Symbols defines portable, alignment-aware versions of everyday operations that act on symbolic numerals while preserving classical results under collapse.

  • Operators: s_add, s_sub, s_mul, s_div, s_pow, s_gt, s_eq, plus helpers min, max, abs, round.
  • Collapse parity: every result reduces exactly to the classical value under phi.
  • Bounded alignment: the alignment channel remains strictly within (-1, +1) and never alters classical magnitudes.
  • Streaming-safe addition: summation uses explicit accumulators so associativity holds in streaming and batch.
  • Decision readiness: comparisons yield numeric scores that support banded "true" / "false" / "undecided" reporting.
  • Environment hook (optional): a calm gate may attenuate only the alignment channel at the operator boundary.
  • Portability: the same operators compose for scalars, vectors, matrices, and polynomials.

Scope: Shunyaya Symbolic Mathematical Symbols provides the verbs and guards. The numeral and the collapse map are defined below and referenced by all operators.

Canonical object and collapse (1.2)

Symbolic numeral and collapse:

x = (m, a)
m in R                 # classical magnitude
a in (-1, +1)          # bounded alignment

phi(x) = m             # collapse is observation-only

Rapidity path (linearize alignment safely):

sign(z) =  1 if z >= 0 else -1

clamp_a(a, eps_a):
  if abs(a) >= 1 - eps_a: return sign(a) * (1 - eps_a)
  else: return a

u = atanh( clamp_a(a, eps_a) )
a = tanh(u)

Invariants:

  • |a| < 1 at all times (by clamp_a and tanh).
  • u is real-valued and unconstrained.
  • Collapse never changes classical results ( phi forgets alignment ).

Navigation
Previous: Continuity and Micro Examples with Banded Comparisons (0.3)
Next: Identities, Inverses, and Zero-Class Display (1.3)

Explore further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-Symbols

Disclaimer (observation only)
SSMS provides stability-aware arithmetic for analysis and decision support; it does not replace domain models, operational controls, or safety processes.