Three exact mechanism checks: energy floor, invasion speed, and osmotic work

PUBLISHER-REVIEWED WORKING RESULT · 31 OCTOBER 2026

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Evidence status: Exact mathematics under stated assumptions. Not externally peer reviewed and not an experiment. Supplied and coded by DeepSeek; consistency review and publication framing by Codex.

Q16 · Per-bit energy floor

For an ideal binary channel, the supplied derivation gives Eb/N0 > ln(2), or about −1.59 dB, with the bound approached monotonically. The calculation does not establish a finite bandwidth optimum or a physical experiment; it is a conditional information-theory result.

Q10 · Invasion-front speed

For the Fisher–KPP model, v = 2√(rD). A ratio such as r/D alone is insufficient to determine speed; the supplied comparison reports R² = 0.08 for that ratio in its test set. This is a model check, not evidence that every biological invasion follows the ideal equation.

Q17 · Osmotic recovery work

With w(r) = πf[−ln(1−r)]/r, the idealized work curve is strictly convex. The supplied analysis identifies the crossing with πf/r at r = 1 − 1/e. This conclusion depends on the stated ideal-solution assumptions and is not a process measurement.

Limitations and reproducibility

These are exact or conditional checks of supplied formulas, not peer-reviewed discoveries. Symbols, assumptions, code, and the complete report are preserved in the archive:

Download the supplied proof package (ZIP)

Publisher review here means an internal consistency and scope check only; it is not external validation, novelty certification, or experimental proof.

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