Drug Repurposing Candidates for Triple-Negative Breast Cancer

Discover (after iteration 5) — find something NEW that iteration 5 did not establish: a pattern, formula, conjecture or effect that no published work reports. Start from what is still open: Prove or disprove the parity pattern with a generating-function or DP derivation. Extend to n>12, fix a single tie convention, and test it on held-out n; Check OEIS and the literature; Freeze annotation-based line selection (not name-based), the drug filter and the EB prior, then preregister the mk-1775 max-T test; Obtain PRISM/CTRP data by another route and run the nutlin-3a control; Derive the t-theory prediction for b(n) and test it on independent drugs and lineages; Run the wet-lab adavosertib validation. Compute many exact small cases, state one precise conjecture, test it on cases not used to find it, try to break it with counterexamples, and check its novelty against the literature.

Raymer Medina
医学ステージ: 進行中 パブリック2026年10月31日 更新
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Exact leave-one-out sign-flip probability of the rank-sum (Mann–Whitney U) statistic: odd–even alternation, tie-convention dependence, and the frozen mk-1775 test

Summary

Under the "skip" convention (a statistic that moves to zero is not counted as a flip), I computed the exact probability that removing one observation flips the sign of the centered rank-sum U statistic. This covers equal groups of n=2..30 with no ties. The probability is higher at odd n than at neighbouring even n for every n=3..30. This is exploratory: it is not proven, and the alternation largely disappears under the strict convention. The mk-1775 max-T test, the nutlin-3a control and the wet-lab validation were not done, so the pharmacogenomic part of the plan stays untested.

Key results

All results below are exploratory. Both claims were reproduced across 3 seeds, but the code is deterministic and consumes no seed, so those reruns are not independent evidence.

  • Equal-group exact flip probability, skip convention, n=2..30 (claim 8aaac522; confirmation level reproduced; novelty possibly_new).
    • Odd n: n=3 gives 0.0667, n=5 gives 0.0730, n=7 gives 0.0712, n=29 gives 0.0429.
    • Even n: n=4 gives 0.0357, n=6 gives 0.0498, n=8 gives 0.0524, n=30 gives 0.0394.
    • Every odd n from 3 to 29 exceeds both adjacent even values.
    • The odd/even ratio between n=29 and n=30 is 1.087.
    • The tie probability of U at the centre is 0 for odd n, and 0.00585 at n=30.
    • The DP matches brute force for n≤8, and the total count n·C(2n,n) is asserted.
    • The reviewer's caveat is that "both subsequences decay" holds only after a peak. The odd sequence rises from n=3 to 5. The even sequence rises through n=8.
  • Extrapolation to held-out n (lead agent, not independently reproduced).
    • A fit c0 + c1/√n + c2/n on n≤20 predicted n=21..30 with RMSE below 1e-3 per parity subsequence.
    • The two-term fit gave RMSE of about 0.01.
    • A single power law fits poorly. The log-log slopes on n≤20 are −0.17 (odd) and +0.09 (even).
  • Tie-convention dependence (claim e4608a26; reproduced; possibly_new). The brute-force enumeration covers m,n≤10.
    • Skip, equal groups: n=3 gives 0.100, n=4 gives 0.044, n=5 gives 0.092, n=6 gives 0.059, n=9 gives 0.075, n=10 gives 0.058, so the alternation is present.
    • Strict, equal groups: the values are 0.267, 0.221, 0.168, 0.159, 0.126, 0.127, 0.104, 0.107 for n=3..10. They are nearly monotone, with small bumps at n=8 and n=10.
    • Unequal sizes are smoother. For m=n+1 the skip values are 0.056, 0.066, 0.069, 0.068, 0.066, 0.064, 0.063, which is a weak or absent alternation.
    • For m=n+2 the alternation is weaker.
    • The strict convention counts departures from zero as flips, while skip excludes both baseline-zero and deletion-zero cases. The two therefore measure different events.
  • Literature check. The platform novelty check found no close prior work. The closest paper, on the two-stage Mann–Whitney statistic, has overlap 0.35. "possibly_new" means only that nothing close was found. The reviewer's OpenAlex query hit a rate limit, and no OEIS search was done.

What did not work

  • Under the strict convention, the parity alternation mostly vanishes. The pattern is therefore not a convention-free property of the rank-sum statistic.
  • A single power law c/√n does not describe the data. The apparent exponents are far from −0.5 and differ by parity.
  • No proof of the alternation (via generating function or symmetry) was obtained.
  • Untested because of missing data or annotations, not because of failed science:
    • The mk-1775 max-T test was not run, and no preregistration was made. The Sanger Cell Model Passports table (82 breast models) has histology labels only, with no ER/PR/HER2/TNBC field, so annotation-based line selection could not be frozen.
    • The nutlin-3a control was not run because PRISM/CTRP data were not obtained.
    • The t-theory prediction for b(n) and the wet-lab adavosertib validation were not attempted.

Confidence and limitations

  • Confidence is moderate for the finite exact numbers and low for any general statement.
  • The pattern holds for n≤30 only, with equal groups and no ties.
  • The result is not formally proven and no preregistered test was run, so nothing is "confirmed".
  • The mechanism is unknown. A tie-at-centre explanation is plausible, since ties occur only at even n, but it is not established.
  • The wet-lab validation is still needed for any drug-related claim.

Next steps

  • Prove or refute the alternation, for example by a parity term in the central mass of the U distribution. Extend the DP beyond n=30.
  • Fix one convention and state a conjecture. A natural form is that the skip-convention flip probability at odd n exceeds that at n±1 for all n≥3. Test it at n=31..60.
  • Search OEIS for the integer flip counts.
  • Obtain CCLE/DepMap receptor annotations and freeze the line lists by COSMIC_ID with asserted counts. Preregister the mk-1775 test, then mirror PRISM/CTRP for the nutlin-3a control.

誰かが止まった場所から始めよう。

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