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    "year": 1847,
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        "description": "The graph-based solution concerns the stated linear electrical network, resistances and circuit constraints. Connectivity/uniqueness and exceptional parameter choices matter. It does not model arbitrary nonlinear/time-varying circuits or give a universal numerical conditioning guarantee. The 1845 current/loop laws and later general graph theorems remain separate contributions.",
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      "statement": "# Kirchhoff: solving a network through its cycles and trees\n\nKirchhoff gives a combinatorial solution of steady linear wire-network currents using independent cycles, resistance products and sums of electromotive forces around the remaining cycles.\n\nThe shape of a network helps organize its equations. Kirchhoff removes just enough wires to leave no closed route, then restores individual wires to obtain independent cycles. Products of resistances on the removed wires build a common denominator; source sums on the remaining cycles determine the currents. This links a physical circuit to a reusable combinatorial structure. It is the exact historical network solution, with modern tree terminology used only to explain its structure.\n\n## Scientific scope\n\nThe graph-based solution concerns the stated linear electrical network, resistances and circuit constraints. Connectivity/uniqueness and exceptional parameter choices matter. It does not model arbitrary nonlinear/time-varying circuits or give a universal numerical conditioning guarantee. The 1845 current/loop laws and later general graph theorems remain separate contributions.\n\n## People and systems\n\nGustav Robert Kirchhoff\n\n\n\n## Original sources\n\n- [G. Kirchhoff, Ueber die Aufloesung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Stroeme gefuehrt wird (1847), original facsimile](https://zenodo.org/records/2242265/files/article.pdf?download=1)\n- [Wikisource author and work index for Gustav Robert Kirchhoff: the 1845, 1846 and 1847 electrical papers](https://de.wikisource.org/wiki/Gustav_Robert_Kirchhoff)\n",
      "summary": "Kirchhoff gives a combinatorial solution of steady linear wire-network currents using independent cycles, resistance products and sums of electromotive forces around the remaining cycles.\n\nThe shape of a network helps organize its equations. Kirchhoff removes just enough wires to leave no closed route, then restores individual wires to obtain independent cycles. Products of resistances on the removed wires build a common denominator; source sums on the remaining cycles determine the currents. This links a physical circuit to a reusable combinatorial structure. It is the exact historical network solution, with modern tree terminology used only to explain its structure.",
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      {
        "title": "G. Kirchhoff, Ueber die Aufloesung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Stroeme gefuehrt wird (1847), original facsimile",
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