Source: https://guthlabs.ai/docs/instruments/slope-field-direction-field-plotter/
instrument / verified-clean
# Slope Field / Direction Field Plotter
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)
**Tranche**: tranche-8
**Evidence ID**: t8-030
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The stated slope-field method is mathematically standard, and RK4 is the standard fourth-order explicit Runge-Kutta method, but the specification is incomplete for deterministic verification. Exact ambiguities requiring resolution are: plot x/y bounds, grid-point placement, segment length, segment normalization, RK4 step size, integration direction, trajectory stopping/clipping rules, and non-finite-expression handling.
### Formula and scope findings
- The core direction-field formula, slope=f(x,y), is standard and correct.
- The RK4 claim is standard but underspecified: the four stage equations, step size, integration direction, domain limits, and handling of failed evaluations are not defined.
- Grid density alone does not define a grid; x/y bounds and grid-point placement are missing.
- Line-segment normalization and segment length are unspecified. A slope field may use (1,f), a normalized vector, or another scaling convention, producing different plots.
- Initial-condition overlays require explicit initial x/y coordinates, integration direction, step size, stopping criteria, and whether trajectories are clipped to the plot domain.
- The implementation must reject or handle non-finite f(x,y) values, discontinuities, poles, and expressions outside their domains.
### Unit assumptions
- x and y are treated as numerical coordinates; no physical units are specified.
- For dy/dx=f(x,y), f has units of y-units per x-unit when x and y carry physical units.
- The test vectors use dimensionless x and y, so slopes are dimensionless.
- If x and y use different physical units, the plotting implementation must preserve the resulting slope units; no unit-conversion behavior is specified.
- Reference calculations below use centered field segments of total geometric length 0.2 and the normalized tangent (1,m)/sqrt(1+m^2). This convention is an explicit test assumption, not defined by the instrument spec.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The input f(x,y)=1/(x-y) with an initial or grid point at (0,0) produces division by zero. The plotter must detect the singularity and reject or omit that point rather than emitting a finite slope or attempting an RK4 step.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"f": "x+y",
"grid_point": {
"x": 1,
"y": 2
},
"segment_total_length": 0.2,
"render_mode": "direction_field_only"
},
"expected_outputs": {
"slope": 3,
"normalized_tangent": {
"dx": 0.31622776601683794,
"dy": 0.9486832980505138
},
"segment_endpoints": [
{
"x": 0.9683772233983162,
"y": 1.9051316701949486
},
{
"x": 1.0316227766016839,
"y": 2.094868329805051
}
]
},
"reference_data": {
"segment_rule": "centered endpoints p - 0.1*(1,m)/sqrt(1+m^2) and p + 0.1*(1,m)/sqrt(1+m^2)"
},
"working": "At (x,y)=(1,2), m=f(1,2)=1+2=3. Compute sqrt(1+m^2)=sqrt(10)=3.1622776601683793. The unit tangent is (1/sqrt(10),3/sqrt(10))=(0.31622776601683794,0.9486832980505138). Half the segment length is 0.2/2=0.1. The offset is (0.0316227766016838,0.0948683298050514). Subtracting from (1,2) gives (0.9683772233983162,1.9051316701949486); adding gives (1.0316227766016838,2.0948683298050514)."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche8/tranche8-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`