Clamps & guards (declare once)
eps_a = 1e-6 # alignment clamp; enforce |a| <= 1 – eps_a
eps_w = 1e-12 # denominator guard; set W_r_safe = max(W_r, eps_w)
eps_fuse = 1e-6 # lane-weight renorm guard (fusion)
Units & scales (per study; publish)
E_unit > 0 # energy scale for e = (E_formed – E_broken) / E_unit
(optional) G_unit, B_unit if Gibbs/barrier lenses are used
Declare F, R, T if a redox/thermo variant is used (Faraday, gas constant, temperature).
Contrast -> alignment (symmetric map)
c > 0 # default 0.5
a_r = tanh( -c * e ) # reactants
a_p = tanh( +c * e ) # products
a = clamp( a, -1 + eps_a, 1 – eps_a )
u = atanh_safe( a, eps_a ) # rapidity for pooling; see atanh_safe below
atanh_safe(a, eps) = atanh( clamp( a, -1 + eps, 1 – eps ) )
clamp(x, lo, hi) = min( max( x, lo ), hi )
Weights (stoichiometric pooling)
gamma >= 0 # default 1
w = abs(m)^gamma
W_r_safe = max( sum_r w_r , eps_w )
RSI (publish formula and guard)
U_r = sum_r w_r * atanh_safe( a_r , eps_a )
V_p = sum_p w_p * atanh_safe( a_p , eps_a )
RSI = tanh( ( V_p – U_r ) / W_r_safe )
Unified calm gate (ranking uses RSI_env)
RSI_env = g_t * RSI
g_t = ( 1 / ( 1 + Z_t + kappa * Delta_t ) ) * ( 1 – exp( -mu * Q_t ) )
Delta_t = abs( Z_t – A_t )
Q_t = rho * Q_prev + ( 1 – rho ) * clip( A_t – Z_t , 0 , 1 )
A_t = 1 / ( 1 + Z_t ) # default A lane; publish if using a different A_recipe
clip(x, lo, hi) = min( max( x, lo ), hi )
Gate defaults (publish if changed)
kappa = 0.5, mu = 0.8, rho = 0.9, Q0 = 0
Z_t recipe (declare)
Var_EMA(beta) or Rolling(L) — publish which recipe is used, and the chosen beta or L.
Lane fusion (declare)
S_t = sum_i w_i * lane_i
If renormalizing: S_t = S_t / max( sum_i w_i , eps_fuse )
Determinism knobs (solver/logging)
seed, time_limit, mip_gap, threads, deterministic_mode
Rounding / export policy
Bankers’ rounding (half-to-even), >= 6 decimals, at export only. Keep full precision internally.
Ranking & publish policy
• Rank by RSI_env (primary). If no gate is used, rank by RSI.
• Always publish: { E_unit, c, gamma, eps_a, eps_w, kappa, mu, rho, Z_recipe, A_recipe, Q0, beta_or_L, eps_fuse, seed, time_limit, mip_gap, threads, deterministic_mode }
• One-line note: “RSI bounded; sign follows contrast e; gate is observation-only; priors are rapidity shifts.”
Priors (scope, bounds, idempotence)
Rapidity-only: delta_u = alpha * Index, with Index in [0, 1], alpha in [0, alpha_max].
Idempotence: Index = 0 => identical outputs within rounding. Priors never modify e.
Publish alpha_max.
Invariants (must hold everywhere)
phi(m, a) = m # collapse
|a| < 1 # with clamp
|RSI| < 1 # bounded index
sign(RSI) = sign(e) # under fixed stoichiometry and c > 0
JSON/YAML key canon (use verbatim across manifests)
Unit (E_unit), scale (c), weights_gamma (gamma),
guards { eps_a, eps_w, eps_fuse },
gate { kappa, mu, rho, Z_recipe, A_recipe, Q0 },
determinism { seed, time_limit, mip_gap, threads, deterministic_mode },
priors { alpha_max },
ranking_policy: “RSI_env”,
rounding { mode: “bankers”, decimals: 6, when: “export” }.
Minimal manifest stub (example, copy-ready)
{
"Unit": 100,
"scale": 0.5,
"weights_gamma": 1,
"guards": { "eps_a": 1e-6, "eps_w": 1e-12, "eps_fuse": 1e-6 },
"gate": {
"kappa": 0.5, "mu": 0.8, "rho": 0.9,
"Z_recipe": "Var_EMA_beta", "A_recipe": "1_over_1_plus_Z", "Q0": 0.0
},
"determinism": {
"seed": 42, "time_limit": 60, "mip_gap": 1e-6,
"threads": 1, "deterministic_mode": true
},
"priors": { "alpha_max": 0.05 },
"ranking_policy": "RSI_env",
"rounding": { "mode": "bankers", "decimals": 6, "when": "export" }
}
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