Source identity
| Field | Recorded value |
|---|---|
| Source type | project equation-poster image |
| Original record | Rhiannon equation: Recursive code repair blueprint.png |
| Date | Jul 5, 2026 |
| Path or archive member | Equation posters/Rhiannon equation: Recursive code repair blueprint.png |
| Original SHA-256 | 43a9bb002d32b5e116eb94e56f14bc19cdfdb0444028d6b591e32f50c15c2a83 |
| Reading-copy SHA-256 | 7fa4b862e5bdda56223ca5913b8a3846761d85354e8ab05c2b04fe5c06bcaead |
The original equation poster
Recovered source transcript
Download complete source text ↓369 lines · 9.0 KB
The Rhiannon Equation
=====================
SOURCE: Rhiannon equation: Recursive code repair blueprint.png
SOURCE ID: libsrc-dc97ecb0df6e
ORIGINAL SHA256: 43a9bb002d32b5e116eb94e56f14bc19cdfdb0444028d6b591e32f50c15c2a83
REVIEW: 2026-10-17. The original PNG is authoritative. This reading copy separates manually inspected mathematical transcriptions from raw OCR. It is not a verbatim embedded-text extraction.
VISUAL REVIEW NOTES
- The large objective, all four acceptance equalities, recurrence, eight variable definitions and both self-extension expressions were inspected.
- Tiny code-like glyphs inside the broken-program and candidate-file illustrations are decorative, incomplete and not a recoverable source listing. No additional complete analytic equation is legible there.
- The title and caption claim safe minimal fixes. The source records a constrained optimization design; tests and predicates require independent implementation and validation.
MANUALLY INSPECTED FORMULAS
Rhiannon constrained repair objective
Image region: Central repair objective and constraint boxes
P* = argmin_{P′} [ B(P′, D) + λ C(P′ − P) ]
Legibility: Legible
Editorial mathematical explanation: Select a candidate program that minimizes residual bug loss plus a weighted cost of changing the original program. The displayed compile, type, test and safety predicates restrict which candidates are eligible. The objective balances two costs; it does not by itself prove that the globally smallest correct repair has been found.
Editorial note: B, C, the candidate set and every feasibility predicate must be implemented before the minimization can be evaluated. A passing finite test suite is evidence about those tests, not a proof of all possible behaviors.
Rhiannon Compile acceptance condition
Image region: Central repair objective and constraint boxes
Compile(P′) = 1
Legibility: Legible
Editorial mathematical explanation: The poster uses a binary acceptance predicate requiring that the candidate compiles. It is one of four conditions restricting the repair search.
Editorial note: The poster does not supply the implementation or completeness guarantees of this predicate.
Rhiannon TypeSafe acceptance condition
Image region: Central repair objective and constraint boxes
TypeSafe(P′) = 1
Legibility: Legible
Editorial mathematical explanation: The poster uses a binary acceptance predicate requiring that the candidate passes the chosen type check. It is one of four conditions restricting the repair search.
Editorial note: The poster does not supply the implementation or completeness guarantees of this predicate.
Rhiannon Tests acceptance condition
Image region: Central repair objective and constraint boxes
Tests(P′, D) = 1
Legibility: Legible
Editorial mathematical explanation: The poster uses a binary acceptance predicate requiring that the candidate passes the specified diagnostics and tests. It is one of four conditions restricting the repair search.
Editorial note: The poster does not supply the implementation or completeness guarantees of this predicate.
Rhiannon Safety acceptance condition
Image region: Central repair objective and constraint boxes
Safety(P′) = 1
Legibility: Legible
Editorial mathematical explanation: The poster uses a binary acceptance predicate requiring that the candidate passes the specified safety check. It is one of four conditions restricting the repair search.
Editorial note: The poster does not supply the implementation or completeness guarantees of this predicate.
Rhiannon repeated program repair
Image region: Central repair objective and constraint boxes
P_{t+1} = R(P_t, D_t)
Legibility: Legible
Editorial mathematical explanation: Apply the repair operator R to the current program and current diagnostics to obtain the next program. Repeating this interface describes an iterative repair process; it does not specify how candidates are generated or when the loop stops.
Editorial note: An implementation needs termination, regression handling and an operational definition of R.
Rhiannon current-program definition
Image region: CORE VARIABLES panel
P = current program / codebase
Legibility: Legible
Editorial mathematical explanation: P denotes the code before a repair is applied.
Rhiannon candidate-program definition
Image region: CORE VARIABLES panel
P′ = candidate fixed program
Legibility: Legible
Editorial mathematical explanation: P′ is one proposed repair considered by the search.
Rhiannon selected-program definition
Image region: CORE VARIABLES panel
P* = optimal corrected program
Legibility: Legible
Editorial mathematical explanation: The star labels an optimizer of the stated constrained objective, if such a candidate exists and is found.
Rhiannon restraint-weight definition
Image region: CORE VARIABLES panel
λ = restraint weight
Legibility: Legible
Editorial mathematical explanation: A larger nonnegative λ makes disruptive changes more costly relative to residual bug loss.
Rhiannon diagnostics definition
Image region: CORE VARIABLES panel
D = diagnostics, errors, test failures, logs, runtime signals
Legibility: Legible
Editorial mathematical explanation: D collects the evidence against which a candidate is assessed.
Rhiannon bug-loss definition
Image region: CORE VARIABLES panel
B(P′, D) = bug / error loss
Legibility: Legible
Editorial mathematical explanation: B scores residual failure in candidate P′ relative to diagnostic evidence D.
Rhiannon change-cost definition
Image region: CORE VARIABLES panel
C(P′ − P) = change cost
Legibility: Legible
Editorial mathematical explanation: C measures how disruptive the difference from the original program is. Program subtraction is a change representation rather than ordinary numeric subtraction unless encoded.
Rhiannon repair-operator definition
Image region: CORE VARIABLES panel
R = recursive code-fix operator
Legibility: Legible
Editorial mathematical explanation: R names the process that transforms program and diagnostics into the next candidate state.
Rhiannon seven-stage self-extension sum
Image region: Bottom SELF-EXTENSION strip, left expression
R(S) = Σ_{k=1}^7 S_k(S_k(x)), k = 1…7
Legibility: Legible
Editorial mathematical explanation: Apply each of seven stage operators twice to x and sum the resulting outputs. This expression is a sum of self-composed stage transforms, not the sequential composition S_7∘…∘S_1. Its left side R(S) also leaves the input x implicit.
Editorial note: The source does not define the operators, addition on their outputs, or why this sum realizes self-extension. The smaller atlas version has an unclear lower index and is retained as a separate source variant.
Rhiannon seventh-stage self-composition
Image region: Bottom SELF-EXTENSION strip, right expression
RHIANNON = S_7(S_7(x))
Legibility: Legible
Editorial mathematical explanation: The seventh stage operator is applied twice to the input. This names a repeated transformation; it does not by itself provide the stage function or establish an implemented self-extension mechanism.
Editorial note: S_7 must accept its own output for this composition to be well defined.
RAW OCR READING AID — NOT A VERIFIED EQUATION TRANSCRIPT
The following preserves the complete Tesseract output, including recognition errors, decorative glyphs and layout artifacts. Use the manually inspected records above and the original PNG for mathematical notation.
THE
\
“ RHIANNON EQUATION
— A UNIFIED FRAMEWORK coe SAFE RECURSIVE CODE REPAIR
ae
cayooate
ats
OPTIMAL REPAIR
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SS
Lee
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re
a af
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=
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ee
Bs
ose
ran
Residual failure against
ee
—
diagnostics, logs, or tests.
Ls
=
pe
Pas
2. CHANGE COST C(P’-P)
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°
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=
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x
c%
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How disruptive the repair
ee
is relative to the
{
original program.
=
y
3. RESTRAINT A
P* = argmin [ Bip" D)+AC(P’ P)|
SUBJECT TO
</>
Compile (P’)
SMALLEST SAFE FIX
Penalizes over-editing
Choose the minimal correction
and destructive rewrites.
@
TypeSafe(P’)
that removes the bug while
Tests(P’, D)
preserving correctness and
coherence.
Ae )
SS
The intelligence that
transforms broken code
intoa safe corrected program.
bes Prat = R(PDi)
CORE VARIABLES
P= carrent program /
=!
=
P’ = candidate
P* = optimal corrected
codebase
=
fixed program
)
program
CY) A = restraint weight
R = recursive code-fix
D = diagnostics, errors, test
loss
B(P’, D) = bug/ error
failures, logs, runtime signals
ra
< C(P'=P) = change cost ®
operator
(/ BROKEN PROGRAM
DIAGNOSTICS
CANDIDATE REPAIRS
SAFETY / TEST FILTERS
OPTIMAL FIX
2
oy
OD
|
Flawed code with
Analyze failures, errors,
Generate multiple
Enforce compile validity,
Select the minimal safe fix
defects and risks.
logs, and runtime signals.
potential fixes.
type safety, tests, and
system safety.
that best reduces failure.
%
RHIANNON MINIMIZES FAILURE, MINIMIZES UNNECESSARY CHANGE
Lf
4
|]
AND ACCEPTS ONLY SAFE CORRECTIONS
BOUND SELF-REPAIR FOR COMPILE VALIDITY, TYPE SAFETY, TEST SUCCESS, AND SYSTEM SAFETY.
SELF-
Sil 7/
_s
EXTENSION
(S) = SY Sy (Sk)
RHIANNON = S,(S,(x))
))
=
Mathematical records from this source
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Rhiannon constrained repair objective
Select a candidate program that minimizes residual bug loss plus a weighted cost of changing the original program. The displayed compile, type, test and safety predicates restrict…
Rhiannon Compile acceptance condition
The poster uses a binary acceptance predicate requiring that the candidate compiles. It is one of four conditions restricting the repair search.
Rhiannon TypeSafe acceptance condition
The poster uses a binary acceptance predicate requiring that the candidate passes the chosen type check. It is one of four conditions restricting the repair search.
Rhiannon Tests acceptance condition
The poster uses a binary acceptance predicate requiring that the candidate passes the specified diagnostics and tests. It is one of four conditions restricting the repair search.
Rhiannon Safety acceptance condition
The poster uses a binary acceptance predicate requiring that the candidate passes the specified safety check. It is one of four conditions restricting the repair search.
Rhiannon repeated program repair
Apply the repair operator R to the current program and current diagnostics to obtain the next program. Repeating this interface describes an iterative repair process; it does not…
Rhiannon seventh-stage self-composition
The seventh stage operator is applied twice to the input. This names a repeated transformation; it does not by itself provide the stage function or establish an implemented…
P: the current program and reference for a repair
P names the existing program or codebase at the repair step under consideration. It stays fixed while different candidate programs P′ are compared, so the change-cost term C(P′−P)…
P′: a candidate program in the Rhiannon repair search
P′ names one proposed modified program considered by the repair objective. The prime distinguishes a candidate from the current program P; it does not denote a derivative. In the…
Rhiannon selected-program definition
The star labels an optimizer of the stated constrained objective, if such a candidate exists and is found.
Rhiannon restraint-weight definition
A larger nonnegative λ makes disruptive changes more costly relative to residual bug loss.
Rhiannon diagnostics definition
D collects the evidence against which a candidate is assessed.
Rhiannon bug-loss definition
B scores residual failure in candidate P′ relative to diagnostic evidence D.
Rhiannon change-cost definition
C measures how disruptive the difference from the original program is. Program subtraction is a change representation rather than ordinary numeric subtraction unless encoded.
Rhiannon repair-operator definition
R names the process that transforms program and diagnostics into the next candidate state.
Rhiannon seven-stage self-extension sum
Apply each of seven stage operators twice to x and sum the resulting outputs. This expression is a sum of self-composed stage transforms, not the sequential composition S_7∘…∘S_1.…