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    "Known initial state x0=0; unrestricted one-dimensional state at every stage.",
    "Both transitions are exactly x[t+1]=x[t]+u[t], with zero offsets and no external channels.",
    "Independent closed control intervals u0,u1 in [0,1].",
    "Nominal open-loop information; no observations, temporal constraints, or other constraints.",
    "Terminal quadratic objective has Q=2, linear coefficient -2, and offset 1: J(x2)=x2^2-2*x2+1.",
    "Requested target is exact_optimal_relation, representation csl.polyhedron.h, numerical assurance, no materialization limit, and empty transformation lineage."
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    "equalities": [
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        0,
        0,
        0,
        0
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        1,
        0,
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        0
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    "proof_summary": "x2=u0+u1 and J=(x2-1)^2>=0. Equality holds iff u0+u1=1; the control bounds then yield exactly the displayed closed segment.",
    "representation": "csl.polyhedron.h"
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  "coordinates": [
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  "evidence_limits": [
    "The complete relation is established analytically only for the strict profile listed above; admission rejects mutations outside that profile.",
    "The outer API labels assurance numerical. Validated assurance is unavailable in the shared registry contract.",
    "The proof capability is internally issued and non-forgeable by clients; serialized decoding creates an untrusted capability which publication rejects until a reviewed proof replay/exporter exists.",
    "This does not establish completeness for any generic synthesis strategy, another profile, or a decoded artifact.",
    "This report records the profile theorem and exact membership examples; it is not an independent mathematical review of the source implementation."
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