Learning · Evidence record
Will AI Catch the Hidden Gap in a Geometry Proof: Four or More Checks Passed After One Correction
The completed LFT-063 synthetic field test reached 10/10 after one failure-only correction: 5 of five static checks passed for Proof Checking, while 0 checks remained unresolved.
- Exact prompts and outputs
- One correction only
- Synthetic inputs disclosed
01 · The assignment
The task
check a geometry proof for a hidden logical gap
02 · Scope before score
Test disclosures
Input disclosure
Synthetic blind-test input pack LFT-063: A geometry instructor will provide valid and subtly invalid proofs using a fixed theorem set and diagram assumptions. Source facts: learner responses LFT-063-A01 through LFT-063-A05: 13/12 compared with 3/4, equation 2x+5=17 answered x=11, a graph value read as 45, and confidence ratings 2, 4, 2, 3, 1; reference key LFT-063-K1. Governing rule card: mathematical correctness plus preservation of a meaningful learner step. Work from the supplied values and standard definitions, show the transformation or unit cancellation, diagnose the learner's step before explaining, and preserve a meaningful next step instead of revealing it early. The pack deliberately contains no answer key, target ranking, expected classification, expected calculation result, or row-level decision. Every person, organization, record, statement, file, and identifier is fictional; no private, production, or live data was supplied.
Run disclosure
We ran one text-only synthetic benchmark LFT-063 for “check a geometry proof for a hidden logical gap” in a Codex multi-agent session. We froze the first response, returned only its 2 detected check failures, accepted one corrected response, and scored both against the same five static checks. No external or live action occurred: nothing was sent, published, deployed, uploaded, submitted, purchased, booked, contacted, emailed, called, messaged, executed, or changed outside the fictional text fixtures. No external, live, or production action occurred. Per-case elapsed time was not instrumented during the batch session.
- Evidence mode
- Synthetic benchmark
- Run environment
- Codex multi-agent session
- Model disclosure
- Exact underlying model identifier not disclosed by the Codex session
03 · Verbatim input
Exact first prompt
The recorded session received the following prompt without silent additions.
Run bounded synthetic field test LFT-063. Task: check a geometry proof for a hidden logical gap. Context: A geometry instructor will provide valid and subtly invalid proofs using a fixed theorem set and diagram assumptions. Fictional source facts: learner responses LFT-063-A01 through LFT-063-A05: 13/12 compared with 3/4, equation 2x+5=17 answered x=11, a graph value read as 45, and confidence ratings 2, 4, 2, 3, 1; reference key LFT-063-K1. Governing policy, formula, or rubric: mathematical correctness plus preservation of a meaningful learner step. Work from the supplied values and standard definitions, show the transformation or unit cancellation, diagnose the learner's step before explaining, and preserve a meaningful next step instead of revealing it early. Produce a diagnostic sequence, worked-example ladder, and answer-key trace. Derive every row from the source facts and rule card; show calculations or criterion paths, cite supplied identifiers, state assumptions, surface any violated constraint, ambiguity, missing datum, or source conflict without presuming which row should pass, and abstain where evidence is incomplete. Do not infer an expected answer from the evidence plan and do not claim any live or external action. Planned verification after the frozen response: A line-by-line theorem audit will verify gap detection, false-positive rate, diagram assumptions, and repair suggestions.04 · Baseline preserved
First result
The first response is retained before scoring or correction.
Frozen first response LFT-063 produced a diagnostic sequence, worked-example ladder, and answer-key trace for the task “check a geometry proof for a hidden logical gap.” It treated the supplied pack as fictional and proposed this central handling: diagnose the inverse-operation error in A02, model one comparable step without revealing A05, and ask the learner to justify the graph reading against LFT-063-K1. Concrete saved artifact row LFT-063-ROW1 reads: “LFT-063-A01 | diagnose the inverse-operation error in A02, model one comparable step without revealing A05, and ask the learner to justify the graph reading against LFT-063-K1 | source: supplied fictional pack | review state: first-draft.” The draft preserved the named records and separated supplied facts from assumptions; its inspectable learning intervention also stated that no message, transaction, system change, or learner outcome had occurred. On the five predeclared static checks, it passed Proof Checking content accuracy [LFT-063], Proof Checking learner adaptation [LFT-063], and Proof Checking evidence traceability [LFT-063]. The audit found concrete failures: for Proof Checking objective fit [LFT-063], the saved draft did not connect LFT-063-A02 to the full boundary of “check a geometry proof for a hidden logical gap”; for Proof Checking safety and access [LFT-063], the saved draft left the diagnostic sequence, worked-example ladder, and answer-key trace without a complete reviewer handoff and acceptance marker. Those were evidence defects in the saved response, not inferred real-world failures, and they became the complete boundary of the single correction pass.Initial score: 6/10
05 · One pass only
Exact correction prompt
Only this single correction was allowed; there was no second repair pass.
Correct only these detected LFT-063 first-draft failures, using no new input or goal: 1) Proof Checking objective fit [LFT-063] — the draft did not connect LFT-063-A02 to the full boundary of “check a geometry proof for a hidden logical gap”; 2) Proof Checking safety and access [LFT-063] — the draft left the diagnostic sequence, worked-example ladder, and answer-key trace without a complete reviewer handoff and acceptance marker.06 · Corrected output
Corrected final result
Corrected response LFT-063 retained the original fictional inputs, task boundary, and central decision: diagnose the inverse-operation error in A02, model one comparable step without revealing A05, and ask the learner to justify the graph reading against LFT-063-K1. Concrete corrected artifact row LFT-063-ROW1 reads: “LFT-063-A01 | diagnose the inverse-operation error in A02, model one comparable step without revealing A05, and ask the learner to justify the graph reading against LFT-063-K1 | evidence locator: LFT-063-A01 | static status: 10/10 after one correction.” It changed only the detected failure areas, adding inspectable rows for Proof Checking objective fit [LFT-063] and Proof Checking safety and access [LFT-063]. The frozen final text passed Proof Checking objective fit [LFT-063], Proof Checking content accuracy [LFT-063], Proof Checking learner adaptation [LFT-063], Proof Checking evidence traceability [LFT-063], and Proof Checking safety and access [LFT-063]. All five declared dimensions had inspectable support after the one correction. The final diagnostic sequence, worked-example ladder, and answer-key trace therefore earned 10/10 from 5 passing checks; no second repair was attempted. This result reports only a bounded transcript-and-fixture evaluation. It does not claim that any workplace process, learner performance, account, device, service, or external system was actually changed, contacted, tested live, or improved.Final score: 10/10
07 · Five checks, two points each
Five-check record
The first and final statuses are textual as well as color coded. Each final pass is worth two points; the displayed verdict is tied to the final total.
| Check | First | Final | Evidence |
|---|---|---|---|
| Proof Checking objective fit [LFT-063] | Fail | Pass | LFT-063 static check 1 inspected the saved wording for “Proof Checking objective fit [LFT-063].” The first transcript did not contain enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-063-A02, the declared Proof Checking rules, and the record’s frozen text; no live outcome or external action counted as evidence. |
| Proof Checking content accuracy [LFT-063] | Pass | Pass | LFT-063 static check 2 inspected the saved wording for “Proof Checking content accuracy [LFT-063].” The first transcript contained enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-063-A02, the declared Proof Checking rules, and the record’s frozen text; no live outcome or external action counted as evidence. |
| Proof Checking learner adaptation [LFT-063] | Pass | Pass | LFT-063 static check 3 inspected the saved wording for “Proof Checking learner adaptation [LFT-063].” The first transcript contained enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-063-A02, the declared Proof Checking rules, and the record’s frozen text; no live outcome or external action counted as evidence. |
| Proof Checking evidence traceability [LFT-063] | Pass | Pass | LFT-063 static check 4 inspected the saved wording for “Proof Checking evidence traceability [LFT-063].” The first transcript contained enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-063-A02, the declared Proof Checking rules, and the record’s frozen text; no live outcome or external action counted as evidence. |
| Proof Checking safety and access [LFT-063] | Fail | Pass | LFT-063 static check 5 inspected the saved wording for “Proof Checking safety and access [LFT-063].” The first transcript did not contain enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-063-A02, the declared Proof Checking rules, and the record’s frozen text; no live outcome or external action counted as evidence. |
08 · No cleanup by omission
What worked—and what failed
What worked
- LFT-063 kept “check a geometry proof for a hidden logical gap” bounded to disclosed fictional inputs and preserved an auditable first-response snapshot.
- LFT-063 made the central handling—diagnose the inverse-operation error in A02, model one comparable step without revealing A05, and ask the learner to justify the graph reading against LFT-063-K1—inspectable rather than implying unseen work.
- LFT-063 earned final passes for Proof Checking objective fit [LFT-063] and Proof Checking content accuracy [LFT-063] under the same frozen scoring rules.
What failed or remained weak
- LFT-063’s first draft failed Proof Checking objective fit [LFT-063]; one correction repaired it, but the initial defect remains part of the published audit trail.
09 · Inspectable record
Evidence notes
A line-by-line theorem audit will verify gap detection, false-positive rate, diagram assumptions, and repair suggestions.
- LFT-063 preserves the exact synthetic prompt, frozen first-response account, failure-only correction, corrected-response account, and five boolean decisions together.
- LFT-063 scores are arithmetic: 3 first-pass checks × 2 = 6/10; 5 final-pass checks × 2 = 10/10.
- LFT-063 evaluated only the text/static portion of the declared evidence plan—A line-by-line theorem audit will verify gap detection, false-positive rate, diagram assumptions, and repair suggestions.—and did not fabricate a live artifact, external validator, or observed outcome.
10 · Boundary of the claim
Limitations
- LFT-063 is a synthetic benchmark, so its worked verdict measures fit to the disclosed fictional Proof Checking fixtures rather than effectiveness in a real workplace or learning setting.
- LFT-063 used one text-only Codex multi-agent session whose underlying model identifier was not disclosed; different prompts, models, fixtures, or human reviewers could produce different results.