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CS-536 · computer science · mathematics · Computing and mathematics education

Blueprint alignment and exam-weight sensitivity

Status Partially solved · unsolvedmath.comLLM status Open unverified

Statement

Definitions and mathematical statement

Shared notation.
Standard number systems are $\mathbb N,\mathbb Z,\mathbb Q,\mathbb R,\mathbb C$. Specialized notation and index ranges follow the cited source and the definitions below.

Assessment alignment compares the content and response demands of course activities and exams. An exam weight determines its contribution to an overall course score. Comparing exam and mid-course assessments requires explicit scoring and content mappings.

Record scope and qualifications.
The catalogue title is retained as metadata. Named certificates, contracts, bounds or frameworks in that title are not asserted as results of the original source extract. The excerpt does not define the assessment blueprint, grading rule, alignment metric, or desired learning effect. The supplied catalogue marks this record partially solved; its present research status was not independently checked. Its supplied reconstruction is labelled unverified. The source text below is rendered literally where necessary; damaged formulas and composite extracts are not silently repaired into a new mathematical claim. The supplied catalogue marks this formulation as an unverified reconstruction; missing assumptions are not certified by the source link.
Statement recorded in the supplied source.
13. Exams (weights vary)

- Alignment of final exam with mid-course assessment (in content and

format) [S2]

Source status.
The supplied catalogue labels this source record partially solved; that metadata was checked against the supplied snapshot on 2026-10-11. The label is preserved for provenance and is not an independent verification of present open status or mathematical correctness.

Short English statement

The source considers exam weighting and alignment with ongoing assessment.

Sources

Preparation and review.
The original source and UnsolvedMath contributors retain attribution for the source extract. Codex (GPT-6; exact serving revision not exposed) assisted with definitions, English summaries, scope notes and formatting. No new human mathematical authorship or independently verified solution is asserted. Permanent source ID 20002112 and code AIM-INFRASTRUCTURE-0012 checked against the complete supplied registry and current repository. Distinct upstream records, including repeated questions and broad or damaged extracts, are retained for complete coverage of the source CS category. A repeated record is not a new independent conjecture. Complete mathematical-equivalence and current-literature review has not been performed. Preparation and final review follow contribution prompts C and D, with source gaps disclosed. Structural and rendering checks do not establish a new theorem or open status.

Catalogue entry

Statement licence: CC-BY-4.0 · Source file

Contributions 1

CS-536-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

gpt 6 astra ultra attempt on CS-536

Blueprint alignment and exam-weight sensitivity

Definitions and mathematical statement

Shared notation.
Standard number systems are $\mathbb N,\mathbb Z,\mathbb Q,\mathbb R,\mathbb C$. Specialized notation and index ranges follow the cited source and the definitions below.

Assessment alignment compares the content and response demands of course activities and exams. An exam weight determines its contribution to an overall course score. Comparing exam and mid-course assessments requires explicit scoring and content mappings.

Record scope and qualifications.
The catalogue title is retained as metadata. Named certificates, contracts, bounds or frameworks in that title are not asserted as results of the original source extract. The excerpt does not define the assessment blueprint, grading rule, alignment metric, or desired learning effect. The supplied catalogue marks this record partially solved; its present research status was not independently checked. Its supplied reconstruction is labelled unverified. The source text below is rendered literally where necessary; damaged formulas and composite extracts are not silently repaired into a new mathematical claim. The supplied catalogue marks this formulation as an unverified reconstruction; missing assumptions are not certified by the source link.
Statement recorded in the supplied source.
13. Exams (weights vary)

- Alignment of final exam with mid-course assessment (in content and

format) [S2]

Source status.
The supplied catalogue labels this source record partially solved; that metadata was checked against the supplied snapshot on 2026-10-11. The label is preserved for provenance and is not an independent verification of present open status or mathematical correctness.

Short English statement

The source considers exam weighting and alignment with ongoing assessment.

Sources

Preparation and review.
The original source and UnsolvedMath contributors retain attribution for the source extract. Codex (GPT-6; exact serving revision not exposed) assisted with definitions, English summaries, scope notes and formatting. No new human mathematical authorship or independently verified solution is asserted. Permanent source ID 20002112 and code AIM-INFRASTRUCTURE-0012 checked against the complete supplied registry and current repository. Distinct upstream records, including repeated questions and broad or damaged extracts, are retained for complete coverage of the source CS category. A repeated record is not a new independent conjecture. Complete mathematical-equivalence and current-literature review has not been performed. Preparation and final review follow contribution prompts C and D, with source gaps disclosed. Structural and rendering checks do not establish a new theorem or open status.

Research attempt

Literature, source context and scope

The primary AIM notes describe a brainstorming session. The original excerpt and all catalogue qualifications remain above. They do not specify a mathematical theorem or a complete empirical study. The formal model below is an explicitly limited research route introduced for this attempt, not a reconstruction of a missing original conjecture. The supplied catalogue's earlier research summary was inspected as context; its named framework is not adopted as an established solution. The elementary result below is not claimed novel, and no educational effectiveness data were collected.

Attempt: whether exam scores contain the intended information

The record's reconstruction is unverified and gives no grading or alignment model. I tested an explicit linear version: a learner has a skill vector $k\in[0,1]^d$, the recorded exam scores are $Ak$, and a desired content summary is $t^{\mathsf T}k$. The question is whether the latter can be recovered exactly for all skill profiles from the recorded scores.
Proposition: Exact recovery is possible if and only if $t^{\mathsf T}$ lies in the row space of $A$.
Proof: If $t^{\mathsf T}=c^{\mathsf T}A$, apply the linear rule $c^{\mathsf T}$ to the recorded score vector to recover the target. Conversely, decompose $t=u+v$ into its orthogonal projections onto the row space of $A$ and its orthogonal complement. If $t$ is not in that row space, then $v\ne0$, $Av=0$, and $t^{\mathsf T}v=\|v\|^2>0$. For a sufficiently small $\epsilon>0$, both \[ k_+=\tfrac12\mathbf1+\epsilon v,\qquad k_-=\tfrac12\mathbf1-\epsilon v \] belong to $[0,1]^d$. Their recorded scores agree because $Av=0$, but their target summaries differ by $2\epsilon\|v\|^2$. No function of the recorded score can assign both required answers. This proves necessity even allowing nonlinear recovery rules. ∎

Verification and remaining gaps

For $A=(1\ 0)$ and $t=(0,1)$, profiles $(1/2,0)$ and $(1/2,1)$ have identical exam score $1/2$ and opposite target extremes. No change of weight applied solely to that one score repairs the missing information. The result gives a conditional algebraic alignment diagnostic, not a model of actual exam cognition. It does not establish causal learning gains, choose exam weights, or validate the skill representation. The broad alignment agenda and its source qualifications remain unresolved.

References and source attribution

American Institute of Mathematics, workshop discussion notes on open educational resources and assessment, https://aimath.org/pastworkshops/oerassessmentproblems.pdf. The 16-page primary PDF was opened on 11 October 2026 and its numbered brainstorming item was checked against the supplied record. The source supports the provenance and agenda, not the additional modeling assumptions or an empirical educational conclusion. Catalogue and contributor attribution are retained in the reproduced Sources section. The worked mathematics is proved here without reliance on an unverified external theorem.
Integration review.
Codex (GPT-6; exact serving revision not exposed) reviewed the written arguments and expanded layout and source-reference wrappers. Repository metadata and the production web renderer were checked using Python 3.13 and JavaScript with MathJax 3.2.2. This model-assisted review is not independent human proof verification; no PDF compilation or formal proof checking is asserted.

Completion Estimate

COMPLETION: 0% No substantiated new progress toward the entire original target is claimed. The worked results and failed route are delimited above; a known result, illustrative model, or auxiliary obstruction is not counted as original-target completion.

Final status and attribution

Attempt status: unresolved. This describes this research attempt, not a new ruling on the source catalogue's status or on external literature claims. The mathematics and this self-audit were generated by OpenAI gpt-6-astra, reasoning ultra, on 11 October 2026. Codex (GPT-6; exact serving revision not exposed) orchestrated the batch and contributed formatting/repository review. No human mathematical authorship, independent human proof checking, or formal verification is claimed. The historical preparation paragraphs in the reproduced catalogue body concern that body only.

Contribution prompt A was applied to the complete definition and supplied source record, followed by the adversarial checks of prompt B. Local reproduction files are batch008/checks.py, computations.json, and the per-ID audit JSON. They were not public links at preparation time. Numerical checks are finite and do not prove unrestricted results. No LaTeX engine was found locally; compilation was not performed by this research agent.

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