surface-ledgers-share-one-gamma-source - Surface Tension and Capillarity Step by Step

A shared gamma claim must be source identity, not same-valued text. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The line ledger owns the gamma source

The energy ledger may reuse gamma only by pointing to this source identity, not by copying the same number.

\gamma_{\text{line}}=3\ \text{N/m}\qquad F=12\ \text{N}

Shared values are listed with their bound source

The table is deliberately a source ledger. It keeps value and source identity visible at the same time.

\begin{array}{c|c|c}\text{ledger}&\text{value}&\text{source}\\\text{force}&12\ \text{N}&\text{bound}\\\text{energy}&24\ \text{J}&\text{bound}\\\text{gamma}&3\ \text{N/m}&\text{bound}\\\end{array}

A shared gamma claim needs source identity

The force and energy values can share gamma because the energy check points back to the exact line-force source.

12\ \text{N}\quad\text{and}\quad24\ \text{J}\quad\text{both cite}\quad3\ \text{N/m}