SSM-AI – Domain Adapters (R1–R9)

Extends the bounded alignment lane into any vertical — from chemistry to finance — without ever touching classical magnitudes.

Purpose.
Offer a minimal, copy-pasteable interface that adapts any domain to the same symbolic math core.
Every integration is observation-only: phi((m,a)) = m.
Fusion and gating remain identical everywhere:
a_c := clamp(a, -1+eps_a, +1-eps_a) ; u := atanh(a_c) ;
U += w*u ; W += w ; a_out := tanh( U / max(W, eps_w) ).
Chooser: RSI := tanh( (V_out - U_in) / max(W_in, eps_w) ).
Optional calm gate: RSI_env := g_t * RSI or RSI_env := tanh( g_t * atanh(RSI) ).

R1) Domain adapter contract

Inputs.
Dimensionless contrasts P_i (supports) and N_j (penalties) with optional weights m.
No personally identifiable data allowed.

Lens.

• Single-channel: e := (Σ α_i*P_i − Σ β_j*N_j) / Unit, a := tanh(c*e)
• Two-channel:
  • a_in := tanh(−c*e_in)
  • a_out := tanh(+c*e_out)

Chooser.
RSI := tanh( (Σ w*atanh(a_out) − Σ w*atanh(a_in)) / max(Σ w, eps_w) )

Gate.
Alignment-only: RSI_env := g_t * RSI or RSI_env := tanh( g_t * atanh(RSI) ).

Invariants.
phi((m,a)) = m, |a|<1, |RSI|<1, |RSI_env|<1, order/shard invariance via (U,W).
Zero-evidence guard: if Σ w == 0, set RSI := 0, band "A0".

R2) Example domain — SSM-Chem (reaction stability)

Goal.
Score chemical candidates using a bounded Reaction Stability Index while leaving all energies and rates unchanged.

Normalized features.

• formation_margin := (E_broken − E_formed)/max(E_unit, eps)
• tox_penalty := clamp(toxicity_idx, 0, 1)
• license_penalty := clamp(license_risk, 0, 1)
• evidence := clamp(citation_strength, 0, 1)

Lens (two-channel).

e_out := (α_f*formation_margin + α_ev*evidence) / Unit_out
e_in  := (β_t*tox_penalty + β_l*license_penalty) / Unit_in
a_out := tanh(+c*e_out)
a_in  := tanh(−c*e_in)
RSI   := tanh( (atanh(a_out) − atanh(a_in)) / max(W, eps_w) )
RSI_env := g_t * RSI

Example results.

All values bounded and dimensionless.

R3) Worked minis (calculator-fast)

Parameters: Unit_out = Unit_in = 1, c = 1, w = 1.
Round to 6 decimals.

formation_margin = 0.50, evidence = 0.30 → e_out = 0.80 → a_out = 0.664037
tox_penalty = 0.20, license_penalty = 0.10 → e_in = 0.30 → a_in = −0.291313
RSI = tanh(atanh(0.664037) − atanh(−0.291313)) = tanh(1.10) = 0.800499
g_t = 0.81 → RSI_env = 0.648404 → band A+

All steps reproducible with any language supporting tanh/atanh.

R4) Minimal manifest stub

{
  "schema_version": "1.0",
  "dtype": "float64",
  "lens": {
    "Unit": 1.0, "c": 1.0, "weights": "abs_m_pow", "gamma": 1.0, "channels": "two",
    "terms": {
      "support": ["formation_margin", "evidence"],
      "penalty": ["tox_penalty", "license_penalty"]
    }
  },
  "policy": {"division_policy": "strict","eps_a":1e-6,"eps_w":1e-12},
  "gate": {
    "mode":"mul","rho":0.20,"g_min":0.00,"eps_g":1e-12,
    "weights":{"F":1,"D":1,"L":1,"E":1,"V":1,"Q":0},
    "safety_notch":{"enabled":false,"s_thr":0.80}
  },
  "bands":{"A++":0.90,"A+":0.60,"A0":−0.60,"A−":−0.90,"A−−":−1.00},
  "band_on":"RSI_env"
}

R5) API sketch

def chem_lens(feat, c=1.0, Unit_out=1.0, Unit_in=1.0, eps_a=1e-6):
    from math import tanh
    e_out = (feat["formation_margin"] + feat["evidence"]) / max(Unit_out, 1e-12)
    e_in  = (feat["tox_penalty"] + feat["license_penalty"]) / max(Unit_in, 1e-12)
    a_out = max(-1+eps_a, min(1-eps_a, tanh(c*e_out)))
    a_in  = max(-1+eps_a, min(1-eps_a, tanh(-c*e_in)))
    return a_in, a_out

def chem_score(item, g_t=1.0, eps_w=1e-12, eps_a=1e-6, gate_mode="mul"):
    from math import atanh, tanh
    a_in, a_out = chem_lens(item["feat"], eps_a=eps_a)
    U_in, V_out, W = atanh(a_in), atanh(a_out), 1.0
    RSI = tanh((V_out - U_in) / max(W, eps_w))
    RSI_e = tanh(g_t * atanh(RSI)) if gate_mode=="u_scale" else g_t * RSI
    RSI_e = max(-1+eps_a, min(1-eps_a, RSI_e))
    return {"m": item["m"], "RSI": RSI, "RSI_env": RSI_e}

R6) Wire envelope (JSON)

{
  "v": "SSM-LANE/1",
  "svc": "chem-check",
  "iso_utc": "2025-10-27T12:00:00Z",
  "knobs_hash": "sha256:...",
  "m": 2.000000, "phi_m": 2.000000,
  "a_in_items":[[-0.291313,1.0]], "a_out_items":[[0.664037,1.0]],
  "U":0.800000, "W":1.000000, "RSI":0.800499, "g_t":0.810000,
  "RSI_env":0.648404, "band":"A+",
  "stamp":"SSMCLOCK1|iso_utc|rasi_idx|theta_deg|sha256(file)|chain"
}

R7) Governance hooks

• Parity: phi((m,a)) = m before/after gating.
• Dimensionless: publish Unit, c, and scalers.
• Privacy: aggregate inputs only.
• Determinism: identical manifest + inputs ⇒ identical RSI.
• Order/shard invariance: merge via (U,W) only.
• Zero-evidence: W==0 → RSI=0, band "A0".

R8) Acceptance checklist

R9) Stamp example

SSMCLOCK1|2025-10-27T12:00:00Z|k=chem|U=0.800000|W=1.000000|RSI=0.800499|g=0.810000|RSI_env=0.648404|band=A+|knobs_hash=sha256:...

One-line takeaway.
Domains need only declare a dimensionless contrast and manifest.
The symbolic lane handles all bounded fusion, gating, and banding — keeping every classical number intact under phi((m,a)) = m.

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