Provenance-safe multidisciplinary priority setting

Definitions and mathematical statement

Item A.1, "Introduction to Discussion Session Goals," is methodological context rather than an open problem. The scribe says the notes were produced quickly, references and individual comments were not exhaustively traced, and attributed comments may be paraphrases of what the scribe understood. The source advises checking with attributed participants before making consequential attributions. Sessions sought promising and important problems and exchange among biology, combinatorics, topology and statistics. No particular mathematical conjecture or actual community-ranking data is given.

The attached aid proposes an explicitly surrogate provenance protocol. Let $\Omega\ne\varnothing$ be a conservative set of globally admissible worlds for a comment's speaker, wording, verbatim/paraphrase status and dependencies, assumed to contain the actual world. A claimed consequence is safe in this model if it holds in every $\omega\in\Omega$. Individual attribution to agent $a$ is certified exactly when every admissible world attributes that comment to $a$; an exact quotation additionally requires the claimed wording and verbatim status in every world. Propagating paraphrase possibilities by transformations that retain every admissible image preserves soundness of universal consequences. This protocol does not verify the actual world or justify shrinking possibilities without evidence.

Its separate balanced-priority model has finitely many communities $g=1,\ldots,G$, independent closed score intervals $s_g(p)\in[L_g(p),U_g(p)]$ for each candidate problem, and weights \[ w_g\ge\alpha_g\ge0,\qquad\sum_gw_g=1,\qquad\sum_g\alpha_g\le1. \] Assume all intervals are nonempty and all their combinations are admissible, including independent endpoint choices for $p$ and $q$. The weighted score is $S_w(p)=\sum_gw_gs_g(p)$. Writing $d_g=L_g(p)-U_g(q)$, its worst-case pairwise margin is \[ m(p,q)=\sum_g\alpha_gd_g+\left(1-\sum_g\alpha_g\right)\min_g d_g. \] The aid's exact certificate is \[ S_w(p)>S_w(q)\text{ for every allowed weight and score choice} \quad\Longleftrightarrow\quad m(p,q)>0. \] At margin zero an admissible tie occurs, while a negative margin permits a reversed ordering. This exact test depends on the closed Cartesian uncertainty model and weight floors; correlated scores or different admissible weights require another optimization. It does not select priorities from the source, which supplies no scores, floors or candidate list.

Short English statement

The source explains cautious attribution and multidisciplinary discussion goals. Its attached aid supplies a hypothetical universal-provenance rule and an exact interval-based priority certificate, not a solution to a mathematical problem stated in A.1.

Sources

• Local UnsolvedMath registry, permanent ID $20000870$, source code catalogue entry; canonical aim-biology-notes.json, notes[34], tagged section.
• American Institute of Mathematics, Geometric models of biological phenomena, A.1, "Introduction to Discussion Session Goals": https://aimath.org/WWN/geombio/geombio.pdf. The scribe's explicit paraphrase, incomplete-reference and attribution caveats are preserved. No PDF inspection is claimed here; no author identity or literature references are supplied.
• Attached research attempt 1: context only, recorded run status not a problem, rigor label proved, novelty confidence low; registry status open, classification OPEN-TRIAGE, suggested difficulty L2. The surrogate protocol and ranking lemma are machine generated and not peer reviewed; independently verify before citation.