What this page covers
An optional, bounded gate that attenuates the alignment channel only (never magnitudes). We define a practical lane recipe, list properties (collapse parity, bounds, monotone calming), and provide guards, manifest keys, and QA checks.
Definition (alignment-only attenuator)
Given an operator output (m_op, a_op), apply a gate g_t in [0,1] to alignment only:
a_env = clamp_a( g_t * a_op , eps_a )
m_env = m_op
g_t may be a scalar or a field broadcastable to the shape of a_op.
Example lane recipe (bounded, with memory)
clip(x, lo, hi) = min( max(x, lo), hi )
# inputs (each in [0,1])
Z_t in [0,1] # lane stress
A_t = 1 / (1 + Z_t) # instantaneous calm (in [0,1])
# memory accumulator (in [0,1])
Q_t = rho * Q_prev + (1 - rho) * clip( A_t - Z_t , 0 , 1 )
# gate (pre-clamp)
g_t = ( 1 / ( 1 + Z_t + kappa * abs(Z_t - A_t) ) ) * ( 1 - exp(-mu * Q_t) )
# clamp to [0,1]
g_t = clip( g_t , 0 , 1 )
Parameters: rho in [0,1], kappa >= 0, mu >= 0, with published initial Q0 in [0,1].
Properties
- Collapse parity
phi( (m_op, a_env) ) = m_op - Bounds (if
|a_op| <= 1 - eps_aandg_t in [0,1])|a_env| <= 1 - eps_a - Monotone calming
g_t = 1 -> a_env = a_op g_t = 0 -> a_env = 0 # for fixed a_op, |a_env| is nondecreasing in g_t - Stateless vs stateful
Setmu = 0(orrho = 0) for a memoryless gate. Positivemuandrhoproduce history-aware calming viaQ_t. - Composability (pointwise)
Gate after each operator; repeated gates are safe. With clamping, effective gain is bounded by the product of gains.
Guards and manifest keys
gate_used in {"on","off"} # if "off": set g_t = 1 everywhere
lane_recipe : <string> # e.g., "ZE-lane-v1" (publish the recipe name)
kappa, mu : floats >= 0
rho : float in [0,1]
Q0 : float in [0,1] # initial memory
Z_t_source : <declared> # how Z_t is computed
Operational rules
- Apply the gate after each operator’s alignment is computed; never change magnitudes.
- Publish that
Z_t, A_t, Q_t, g_tare clamped to [0,1]. - Ensure final clamp:
a_env = clamp_a( g_t * a_op , eps_a ) - For tensors,
g_tmust be broadcast-compatible witha_op.
Tiny examples (illustrative)
eps_a = 1e-6
a_op = +0.80, g_t = 0.50 -> a_env = clamp_a( 0.40 , eps_a ) = +0.40
a_op = -0.60, g_t = 0.25 -> a_env = clamp_a( -0.15, eps_a ) = -0.15
Minimal QA invariants (L0–L1 for gating)
# L0 collapse parity
assert phi( (m_op, clamp_a(g_t*a_op, eps_a)) ) == m_op
# L0 bounds
assert abs( clamp_a(g_t*a_op, eps_a) ) <= 1 - eps_a
# L1 gate OFF equals identity on alignment (within numeric tolerance)
if gate_used == "off":
assert clamp_a(1*a_op, eps_a) == a_op
# L1 monotonic calming (sampled)
if g1 <= g2:
assert abs( clamp_a(g1*a_op, eps_a) ) <= abs( clamp_a(g2*a_op, eps_a) )
Navigation
Previous: Collapse-Safety Contract (1.5)
Next: Minimal Manifest (1.7)
SHUNYAYA 