LemmaStatement: Literature-sourcedProof: AI-generatedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Charpit contact compatibility is preserved

Statement

Let $(X, Z, P) (s, y)$ be a $C^{1}$ Charpit strip lying in $F = 0$ . If $Z_{y} (0, y) = P (0, y) \cdot X_{y} (0, y)$ , then

$Z_{y} (s, y) = P (s, y) \cdot X_{y} (s, y)$

while the strip exists.

Facts & Assumptions

Given: A $C^{1}$ Charpit strip, its initial contact identity, and the constraint $F (X, Z, P) = 0$ .

Proof

technique · direct

1.1

Set $D : = Z_{y} - P \cdot X_{y}$ . Differentiate the Charpit equations in $y$ and apply the product and chain rules to obtain $D_{s} = F_{y} - F_{z} D$ .

givenalgebra

2.1

Differentiating $F (X, Z, P) = 0$ in $y$ gives $F_{y} = 0$ , so $D_{s} = - F_{z} D$ and $D (0, y) = 0$ .

step 1.1givenalgebra

3.1

Multiplication by the integrating factor $\exp (\int_{0}^{s} F_{z} (r, y) d r)$ makes $D$ constant; its initial value is zero, hence $D = 0$ .

step 2.1algebra∎

Depends on

Used by

Local fully nonlinear Charpit graph construction Theorem

Dependency tree · two levels

12 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Part I: Explicit methods — Lecture notes for MA342H (standard reference, not scraped)