A partial correctness claim connecting a precondition $P$, a program $C$ and a postcondition $Q$: every terminating execution begun with $P$ ends with $Q$. State separately whether total correctness is intended.

The Practical Biology protocol uses cold sucrose in buffer solution, ground green leaves, muslin filtration, centrifugation and cold pellet resuspension. A $100\mathrm{W}$ lamp illuminates extract plus DCPIP from $12$–$15\mathrm{cm}$; a red-filter colorimeter monitors blue-color loss.^[ref]

Compare extract plus dye in darkness, illuminated dye without extract, extract without dye, and supernatant plus dye: controls for light, extract dependence, background color and incomplete separation. Green supernatant can remain active; a centrifugation pellet establishes neither purity nor intact chloroplasts.^[ref]

Here is an original logical check of the controls. Suppose only the illuminated extract-plus-dye condition loses blue color, while the dark mixture and illuminated dye-only mixture retain it. Removing light or removing extract each removes the effect in those comparisons. That supports a joint requirement under the tested conditions. If the dye-only mixture also loses blue color, the proposed attribution to extract has failed its control; a faster change in the extract mixture would require a quantitative comparison before attribution. These are conditional cases, not experimental results.

Even the favorable case leaves three distinct questions. Dye reduction demonstrates delivery of electrons to an artificial electron acceptor. An independently calibrated molecular oxygen readout is needed to measure molecular oxygen evolution. Demonstrating carbon fixation additionally requires evidence that carbon dioxide becomes incorporated into organic material. None of the latter quantities is supplied by a blue-color endpoint alone. An absorbance change also needs background and scattering controls before it can be treated as dye concentration; Beer-Lambert law states the relevant assumptions.

In particular, two hypothetical preparations can give the same dye endpoint while differing in whether their stromal Calvin cycle is functional. Observing only the dye discards that distinction. The counterexample establishes why dye decolorization cannot alone prove complete photosynthesis, carbon fixation, or an intact chloroplast. Temperature, extract loading and illumination must also be matched when comparing rates: a lamp can alter both light exposure and heating.

A type-I band alignment confines electrons and electron holes together: its inner conduction band edge is lower, its valence band edge higher.^[ref]

In the chosen band offset example, the electron barrier is $0.6$, while the electron hole barrier is $0.4$. A hole's excitation energy is measured downward from a valence band maximum: reversing that convention would incorrectly make the two barriers appear to repel opposite carriers. An electrostatic shift $-q\varphi$ moves both electron energy band edges together; changing the band gap also changes their separation. Thus material composition supplies a control beyond the electric potential $\varphi$ alone.

A band offset is an interface discontinuity in a conduction band or valence band edge.^[ref]

For a chosen two-material example, let the central material A have $E_{c,A}=1$ and $E_{v,A}=0$, and the surrounding material B have $E_{c,B}=1.6$ and $E_{v,B}=-0.4$, in stipulated energy units. Define positive confinement barriers by $\Delta E_c=E_{c,B}-E_{c,A}$ and $\Delta E_v=E_{v,A}-E_{v,B}$. Then $\Delta E_c=0.6$, $\Delta E_v=0.4$, and the band gaps obeyThis identity determines the sum of the band offsets; a band gap difference alone cannot determine their partition. The chosen numbers illustrate the definition and do not specify a measured material pair.

For a lossless ideal Hertzian dipole driven by an incident wave, use its induced open-circuit voltage and its feed impedance $R_{\mathrm{rad}}+iX$. A conjugately matched load has impedance $R_{\mathrm{rad}}-iX$. The same induced current therefore delivers equal power to the load and to radiation resistance: $P_{\mathrm{sca}}=P_{\mathrm{load}}$. The scattered wave has the usual dipole angular pattern. In direction of gain $G$, its scattering cross-section is $G{A}_{\mathrm{eff}}$, since the load receives $S_{\mathrm{inc}}{A}_{\mathrm{eff}}$.

This ideal single-mode scattering is not the same as a signal that travels through an already matched antenna port, reflects from a mismatched terminating load, and returns. A zero port reflection coefficient removes that latter echo but does not make the physical dipole invisible to the incident field. Additional structural scattering, ohmic loss or a different load changes the result.