What if every ambiguous 0/0 moment came with a clear headline and a built-in confidence signal?
What if we could keep the classical answer intact and still know how well we approached it?
That is exactly what this note delivers.
Shunyaya Symbolic Mathematics (SSM) pairs every value with a bounded alignment channel so that results carry both the classical magnitude and a composable “how confident/stable” trace.
Shunyaya Symbolic Mathematical Symbols (SSMS) is the operator canon that combines these alignments safely and prints compact, auditable one-liners.
Scope. This note does not replace classical limits; it packages 0/0 behavior in a deterministic, conservative form <m,a> and prints an alignment signal via SSMS. When classical limits exist, phi(<m,a>) = m matches them; when multiple behaviors are possible, SSM makes the dominant rate and quality explicit.
0) SSM/SSMS Primer (quickstart)
Symbolic numeral (core idea).
x := <m, a>
m = classical magnitude (extended real allowed: 0, finite, +inf, -inf)
a in (-1, +1) = alignment (bounded "quality/centering" tag)
Collapse to classical (conservative).
phi(<m,a>) = m
Why alignment exists.
Classical limits discard how you approach a value. Alignment keeps a bounded summary of path/quality/stability that composes cleanly and never changes the classical magnitude after collapse.
Composing alignments (ASCII).
u := atanh(a)
many influences: a = tanh( sum_i atanh(a_i) )
quotient (division): a_div = tanh( atanh(a_f) - atanh(a_g) )
Clamps & guards (always-on).
clamp alignment before any atanh:
a := clamp(a, -1+eps_a, +1-eps_a)
recommended: eps_a = 1e-6
Picking alignment priors.
no prior -> use a_f = 0, a_g = 0
from data fit quality R2 in [0,1]:
linear map (default): a := 2*R2 - 1
contrast map (optional): a := tanh(c*(R2 - 0.5)) # choose c in [0.5, 2.0], default c = 1.0
micro-calibration (3-point): choose low/med/high R2 exemplars; target bands ~ A- (~-0.6), A0 (~0.0), A+ (~+0.6); record in manifest
for a reference channel (e.g., time), avoid saturating at +1; practical default: a_g = +0.80 (then clamp)
Calibration note — reference channel prior (a_g).
Rationale.
Set a_g := +0.80 to preserve headroom (avoid saturation at +1) and to keep the reference rapidity finite:
u_g = 0.5*log( (1+a_g)/(1-a_g) )
for a_g = 0.80, u_g ~ 1.0986
This stabilizes a_div = tanh( atanh(a_f) - u_g ) against small changes in a_f (always clamp before any atanh).
Domain presets (publish which one you chose).
low reliability reference -> a_g := +0.60 (u_g ~ 0.6931)
default / mixed reference -> a_g := +0.80 (u_g ~ 1.0986)
high reliability reference -> a_g := +0.90 (u_g ~ 1.4722)
Quick protocol (tier selection).
1) Run a one-pass sensitivity on your chosen windows (keep K and the grid fixed).
2) Choose the smallest tier whose a_div bands do not saturate (A++/A--) on >80% of accepted windows.
3) Record the a_g tier and your a-mapping in the manifest.
Mapping reminder.
Declare and publish the a-mapping parameters you used (linear or contrast); examples above: a := 2*R2 - 1 or a := tanh( c*(R2 - 0.5) ).
Zero-class display.
Any <0, a> is “zero-class.” You may canonicalize to <0, +1> if you want a strict center, but keeping the actual a is often informative.
Navigation
Next: P2 — SSMS Alignment Symbols (0A) and Print Grammar (0B)
Explore further:
https://github.com/OMPSHUNYAYA/Symbolic-Mathematics-0over0-Limits
Disclaimer (observation only)
This page informs analysis and decision support; it does not replace domain models, operational controls, or safety processes.
Explore further
https://github.com/OMPSHUNYAYA/Shunyaya-Symbolic-Mathematics-Master-Docs
Explore Shunyaya Projects:
Introduction to Shunyaya Framework
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Disclaimer
Observation-only; not for safety-critical decisions.
Explore Shunyaya Projects:
https://github.com/OMPSHUNYAYA/Shunyaya-Symbolic-Mathematics-Master-Docs
Disclaimer
Observation-only; not for safety-critical decisions.
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