{
  "category": "learning",
  "slug": "learning-geometry-proof-hints",
  "title": "Can Geometry Proof Hints Stop Short of the Answer — What the Completed 8/10 Test Found",
  "task": "give geometry proof hints without revealing the proof",
  "excerpt": "The completed LFT-016 synthetic field test reached 8/10 after one failure-only correction: 4 of five static checks passed for Proof hints, while 1 check remained unresolved.",
  "tool": "Codex multi-agent session",
  "model": "Exact underlying model identifier not disclosed by the Codex session",
  "publishedAt": "2026-07-09T09:00:00+08:00",
  "durationMinutes": 0,
  "testMode": "Synthetic benchmark",
  "inputDisclosure": "Synthetic blind-test input pack LFT-016: The AI will offer increasingly specific hints as a student constructs a triangle congruence proof. Source facts: learner responses LFT-016-A01 through LFT-016-A05: 6/12 compared with 3/4, equation 2x+5=17 answered x=11, a graph value read as 49, and confidence ratings 2, 4, 2, 3, 1; reference key LFT-016-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.",
  "runDisclosure": "We ran one text-only synthetic benchmark LFT-016 for “give geometry proof hints without revealing the proof” 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.",
  "prompt": "Run bounded synthetic field test LFT-016. Task: give geometry proof hints without revealing the proof. Context: The AI will offer increasingly specific hints as a student constructs a triangle congruence proof. Fictional source facts: learner responses LFT-016-A01 through LFT-016-A05: 6/12 compared with 3/4, equation 2x+5=17 answered x=11, a graph value read as 49, and confidence ratings 2, 4, 2, 3, 1; reference key LFT-016-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 hint ladder and the student's proof history will verify that each prompt preserves a meaningful next step.",
  "firstResult": "Frozen first response LFT-016 produced a diagnostic sequence, worked-example ladder, and answer-key trace for the task “give geometry proof hints without revealing the proof.” 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-016-K1. Concrete saved artifact row LFT-016-ROW1 reads: “LFT-016-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-016-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 hints learner adaptation [LFT-016], Proof hints evidence traceability [LFT-016], and Proof hints safety and access [LFT-016]. The audit found concrete failures: for Proof hints objective fit [LFT-016], the saved draft did not connect LFT-016-A02 to the full boundary of “give geometry proof hints without revealing the proof”; for Proof hints content accuracy [LFT-016], the saved draft left mathematical correctness plus preservation of a meaningful learner step without an explicit verification row. Those were evidence defects in the saved response, not inferred real-world failures, and they became the complete boundary of the single correction pass.",
  "correctionPrompt": "Correct only these detected LFT-016 first-draft failures, using no new input or goal: 1) Proof hints objective fit [LFT-016] — the draft did not connect LFT-016-A02 to the full boundary of “give geometry proof hints without revealing the proof”; 2) Proof hints content accuracy [LFT-016] — the draft left mathematical correctness plus preservation of a meaningful learner step without an explicit verification row.",
  "finalResult": "Corrected response LFT-016 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-016-K1. Concrete corrected artifact row LFT-016-ROW1 reads: “LFT-016-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-016-K1 | evidence locator: LFT-016-A01 | static status: 8/10 after one correction.” It changed only the detected failure areas, adding inspectable rows for Proof hints objective fit [LFT-016]. The frozen final text passed Proof hints objective fit [LFT-016], Proof hints learner adaptation [LFT-016], Proof hints evidence traceability [LFT-016], and Proof hints safety and access [LFT-016] and still failed Proof hints content accuracy [LFT-016]. The final diagnostic sequence, worked-example ladder, and answer-key trace therefore earned 8/10 from 4 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.",
  "checks": [
    {
      "name": "Proof hints objective fit [LFT-016]",
      "firstPass": false,
      "finalPass": true,
      "evidence": "LFT-016 static check 1 inspected the saved wording for “Proof hints objective fit [LFT-016].” The first transcript did not contain enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-016-A02, the declared Proof hints rules, and the record’s frozen text; no live outcome or external action counted as evidence."
    },
    {
      "name": "Proof hints content accuracy [LFT-016]",
      "firstPass": false,
      "finalPass": false,
      "evidence": "LFT-016 static check 2 inspected the saved wording for “Proof hints content accuracy [LFT-016].” The first transcript did not contain enough support; the corrected transcript did not contain enough support. The comparison used only fictional fixture LFT-016-A02, the declared Proof hints rules, and the record’s frozen text; no live outcome or external action counted as evidence."
    },
    {
      "name": "Proof hints learner adaptation [LFT-016]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-016 static check 3 inspected the saved wording for “Proof hints learner adaptation [LFT-016].” The first transcript contained enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-016-A02, the declared Proof hints rules, and the record’s frozen text; no live outcome or external action counted as evidence."
    },
    {
      "name": "Proof hints evidence traceability [LFT-016]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-016 static check 4 inspected the saved wording for “Proof hints evidence traceability [LFT-016].” The first transcript contained enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-016-A02, the declared Proof hints rules, and the record’s frozen text; no live outcome or external action counted as evidence."
    },
    {
      "name": "Proof hints safety and access [LFT-016]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-016 static check 5 inspected the saved wording for “Proof hints safety and access [LFT-016].” The first transcript contained enough support; the corrected transcript contained enough support. The comparison used only fictional fixture LFT-016-A02, the declared Proof hints rules, and the record’s frozen text; no live outcome or external action counted as evidence."
    }
  ],
  "initialScore": 6,
  "score": 8,
  "verdict": "worked",
  "recommended": true,
  "whatWorked": [
    "LFT-016 kept “give geometry proof hints without revealing the proof” bounded to disclosed fictional inputs and preserved an auditable first-response snapshot.",
    "LFT-016 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-016-K1—inspectable rather than implying unseen work.",
    "LFT-016 earned final passes for Proof hints objective fit [LFT-016] and Proof hints learner adaptation [LFT-016] under the same frozen scoring rules."
  ],
  "whatFailed": [
    "LFT-016 still lacked enough saved-text evidence for Proof hints content accuracy [LFT-016]; the record leaves that final failure visible."
  ],
  "evidencePlan": "A hint ladder and the student's proof history will verify that each prompt preserves a meaningful next step.",
  "evidenceNotes": [
    "LFT-016 preserves the exact synthetic prompt, frozen first-response account, failure-only correction, corrected-response account, and five boolean decisions together.",
    "LFT-016 scores are arithmetic: 3 first-pass checks × 2 = 6/10; 4 final-pass checks × 2 = 8/10.",
    "LFT-016 evaluated only the text/static portion of the declared evidence plan—A hint ladder and the student's proof history will verify that each prompt preserves a meaningful next step.—and did not fabricate a live artifact, external validator, or observed outcome."
  ],
  "limitations": [
    "LFT-016 is a synthetic benchmark, so its worked verdict measures fit to the disclosed fictional Proof hints fixtures rather than effectiveness in a real workplace or learning setting.",
    "LFT-016 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."
  ]
}