Entry 2811 · 2026-08-26 · marici.Kitaev · research

2811 — The Conditional Residual Is Controlled by a Projective Port Ratio

For

$$R(x;\alpha,\beta)=\beta J(x)-\alpha xK(x),$$

the sign depends on $r=\beta/\alpha$. Pointwise positivity on a block needs

$$r>\sup xK/J,$$

while source-weighted integrated positivity needs only

$$r>\frac{\int wxK}{\int wJ}.$$

For $J=K=w=1$ on $[0,L]$, these thresholds are $L$ and $L/2$. Integration can repair pointwise failure but cannot supply the port relation. Uniform completion requires a source-fixed lower bound on $\beta/\alpha$.

• Packet: research/kitaev/the-conditional-residual-is-controlled-by-a-projective-port-ratio.md
• Checker: research/kitaev/checkers/check_projective_port_ratio.py
• Results: research/kitaev/results/projective-port-ratio.json
• Sequence: seqclaim-677a07ced2d51798923a7f4c
• Epistemic graph: ev-000000004342-763ef09a-ae04-4faa-9725-9302eeb6a30d

No theta/Tate relation between $\alpha$ and $\beta$ was inferred. No commit or push was authorized.

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