What if every species carried a second, bounded coordinate that tells you, mathematically, how stable it wants to be right now?
Shunyaya Symbolic Mathematical Chemistry represents each species as a pair:
x = (m, a)
m = classical magnitude (count / concentration / stoichiometric coefficient)
a in (-1, +1) = alignment (stability vs drift)
Collapse (backward-compatibility):
phi(m, a) = m
Classical stoichiometry is preserved exactly (balances, plant mass accounting).
Primer — Shunyaya Symbolic Mathematics (SSM)
SSM is a collapse-safe extension of arithmetic: a classical scalar becomes (m, a). The alignment channel a propagates through operations while leaving classical results intact under collapse.
Combine policies reused here:
- M1 (simple or “ionic” combine): a’ = a1 * a2
- M2 (rapidity or “covalent” combine): a’ = tanh(atanh(a1) + atanh(a2))
Both keep |a| < 1 and commute with collapse: phi(f(m, a)) = f(m).
Directionality as algebra (table-light)
Declare a study-specific, dimensionless contrast and assign bounded alignments:
e = (E_formed – E_broken) / E_unit
a_r = tanh(-c * e)
a_p = tanh(+c * e)
Pool in rapidity space (u = atanh(a)) with weights w = |m|^gamma to obtain a bounded Reaction Stability Index (RSI):
U_r = sum_r( w_r * atanh(a_r) )
V_p = sum_p( w_p * atanh(a_p) )
W_r = sum_r( w_r )
RSI = tanh( (V_p – U_r) / max(W_r, eps_w) )
By monotonicity of tanh and atanh (and W_r > 0), the sign lemma holds:
sign(RSI) = sign(e)
Hence direction follows E_formed > E_broken without lookup tables. RSI magnitudes depend on (E_unit, c, gamma), but ordering and sign do not.
Conditions via a single calm gate (unified framework)
Realization is gated by a bounded environment factor:
RSI_env = g_t * RSI
g_t = ( 1 / (1 + Z_t + kappaDelta_t) ) * ( 1 – exp(-muQ_t) )
Delta_t = |Z_t – A_t|
Q_t = rho*Q_prev + (1 – rho)*clip(A_t – Z_t, 0, 1)
Z_t is a bounded drift fuse; A_t is a slow alignment track. Low g_t (edge or stress such as poor mixing) can lift non-ground branches; high g_t restores ground outcomes. This blog uses the unified gate (ZEOZO-Core + SYASYS-Core) for all condition effects.
What this delivers (beyond theory)
- Reproducible worked sets and benches. Direction-only validations across canonical reactions, with per-run records and a minimal JSON snapshot.
- Mainstream-compatible contrast. e may derive from thermodynamic tables, electrochemistry, bond-energy baselines, or (when cited) DFT/transition-state estimates; always normalized by E_unit and declared in the manifest.
- Sensitivity windows, not hidden knobs. (E_unit, c, gamma) and (kappa, mu, rho) are declared once and swept on a small grid; signs/orderings remain stable.
- Failure-mode clarity. If e is ill-defined (multi-step paths, mixed phases, incomplete data): accumulate at the lens level; publish “unknown/withheld” when inputs are not defensible; or run the 3-Test with priors = 0. Guardrails and clamps are explicit.
- Transparent priors. Rapidity-space nudges (bounded by alpha_max) can encode lattice/solvation, site-match, sustainability indices, etc.; all revert to baseline at zero.
- Observation-only scope. RSI/RSI_env express qualitative stability preference and direction, not kinetics, hazards, or scale-up. Lab confirmation is mandatory (3-Test: Ground / Edge / Prior). All formulas are plain ASCII.
- Diverse empirical coverage. Selected inorganic, organic, catalysis, biochemistry, and materials exemplars share the same manifest and gate protocol.
Shunyaya Symbolic Mathematical Chemistry — What is covered in this blog?
- Core pipeline & invariants: contrast -> bounded alignments -> rapidity pooling -> RSI and RSI_env.
- Empirical validations: direction-only checks across representative reactions, with transparent manifests.
- Reproducibility assets: JSON/CSV schema samples, unit tests, and robustness grids suitable for independent verification.
- Canon & worked examples: consolidated tables and step-by-step cases spanning inorganic, organic, catalysis, biochemistry, and materials.
- Dataset notes: clear attributions and licence references wherever public datasets are used.
- Integration pointers: how the SSM core and Symbols layer generalize across domains while remaining collapse-safe.
License and external data
License: © The Authors of Shunyaya Framework. Released under CC BY-NC 4.0 (non-commercial, with attribution).
External datasets: Used strictly under their respective licences. Attributions appear with each dataset where used. No endorsement is implied.
Scope notice: Observation-only; not operational, clinical, or industrial advice.
Navigation
Next: Global defaults & consistency checklist (1.1)
Explore further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-Chemistry
Parts of this release
Part 1 covers the core pipeline, invariants, empirical validations, and the reproducibility manifest; Part 2 contains canon tables, worked sets, software benches, CSV and JSON schemas, and detailed datasets.
Disclaimer (observation only)
This is an observation only, symbolic framework that provides bounded, table-free mappings for directionality and ranking. It is not a kinetics, safety, or hazard model and does not constitute operational guidance. Always follow lab safety protocols and regulatory requirements.
SHUNYAYA 