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Result · DS-OKN-BOUND

Profiled stability implies approximate geometry

Proved herepublication: internal

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Meaning

The first-order violation bound scales with observation weight relative to the affected cell masses.

Statement

At a one-point exchange-stable Ds state, relative first-order violation is bounded by w_i(1/W_a+1/W_b); for equal weights and balanced cells this is O(K/N).

finite-to-population bridge candidate

Relationships

Rests on

The full chain beneath it

Enables

Open next door

Local graph
Local map of Approximate finite Ds efficient-Voronoi necessity bound1 prerequisites to the left, 1 results it enables or questions it raises to the right, 0 boundary cases below.Exact finite Ds one-point objective oracleExact finite Ds one-p…Conditional finite-to-population Ds bridgeConditional finite-to…Approximate finite Ds efficient-Voronoi necessity boundApproximate finite Ds…
Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

DS6. Approximate finite efficient-Voronoi bound

At a DsD_s one-point exchange-stable state, the relative first-order violation obeys a bound of the form

saa−sbbqaa≤wi(1Wa+1Wb).\boxed{ \frac{s_{aa}-s_{bb}}{q_{aa}} \le w_i\left(\frac1{W_a}+\frac1{W_b}\right). }

For equal weights and balanced cells this is O(K/N)O(K/N).

Measured suite: the observed maximum violation shrank from roughly 0.18 to 0.029 as NN increased from 8 to 64 in the reported experiment.

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