SSM-JTK – Concept & Guarantees (1)

1.1 Two-channel object (headline + alignment)
We separate what you report from how well it holds.
x := (m, a) with m in R, a in (-1, +1)
phi((m, a)) = m (collapse; alignment never distorts m)
Note: m is an ordinary scalar. For displayed longitudes we use wrap360 so angles fall in [0, 360).

Guarantees (channeling).

  • Separation: m is always the reported value; a is metadata about confidence/clarity.
  • Non-interference: arithmetic on a cannot change m (collapse commutes with the arithmetic below).

1.2 Bounded arithmetic via rapidity (no blow-ups)
All alignment composition happens in rapidity (atanh/tanh) space; pooled sums stay bounded and stable.

  • Constants and clamp: eps_a = 1e-6, eps_w = 1e-12, clamp_a(z) = max(-1+eps_a, min(+1-eps_a, z)).
  • Single value -> rapidity: u = atanh( clamp_a(a) ).
  • Pooling (weighted mean in rapidity space), with 0 <= w_i <= 1:
    U = sum_i [ w_i * atanh( clamp_a(a_i) ) ], W = sum_i w_i, a_sum = tanh( U / max(W, eps_w) ).
  • Binary ops (M2 rapidity combine):
    a_mul = tanh( atanh(clamp_a(a1)) + atanh(clamp_a(a2)) )
    a_div = tanh( atanh(clamp_a(a_f)) - atanh(clamp_a(a_g)) )
  • Guarantees (alignment math):
    Boundedness: if each input a_i in (-1, +1), outputs remain in (-1, +1).
    Antisymmetry: a_div(f, g) = -a_div(g, f).
    Composable pooling: associative as a weighted mean in rapidity space (stable for many sources).

Why this matters. The alignment channel lets SSM-JTK report a clear scalar while carrying bounded evidence about stability; rapidity-space composition prevents numeric blow-ups and keeps long aggregations stable.

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Disclaimer
The contents in the Shunyaya Symbolic Mathematics Jyotish Transit Kernel (SSM-JTK) materials are research/observation material. They are not astrological advice, not a scientific ephemeris, and not operational guidance. Do not use for safety-critical, medical, legal, or financial decisions. Use at your own discretion; no warranties are provided; results depend on correct implementation and inputs.

Explore Further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematics-Jyotish-Transit-Kernel