Skip to content

Round 41.A — ℓ=7 future-data test: turnkey pre-registration (PARKED, no result)

Dispatched 2026-05-26 on the rolling draft PR #690 (open-queue item: "ℓ=7 future-data test"). This item explicitly names a resolving event and is not dispatchable today — the data does not exist. The honest closing is a turnkey, tamper-proof pre-registration: fix the test in advance so it runs the moment CMB-S4 / LiteBIRD per-ℓ data lands. No result is computed; the verdict is PARKED. Generating code: verify_round41_ell7_preregistration_parked.py (emits the pre-registration record only).

Background (Round 10.A / §11.9.6a)

The framework's {1+3+7} Hurwitz algebra identity is preserved, but its projection onto CMB TT low-ℓ multipoles lost ℓ=7: Round 10.A tested ℓ=7 on Spike #190's attested SMICA per-ℓ data and found ℓ=7 ranks #5/7 in ℓ=2–8 (outranked by non-Mersenne ℓ=5/4/2) — no ℓ=7-specific signature. The per-ℓ projection claim was withdrawn. This pre-registration names the resolving event and fixes the re-test in advance (no post-hoc tuning).

Pre-registered protocol (fixed in advance)

  • Data: future per-ℓ TT C_ℓ from a higher-precision / independent map — CMB-S4 (forecast 2030s) and/or LiteBIRD (~2028); FITS → HEALPix anafast, the same pipeline as Spike #190 (SMICA) / #192 (NILC).
  • Range: ℓ = 2–8 (7 multipoles; the Round 10.A comparison set).
  • Statistic: the Round 10.A per-ℓ concentration metric (C_ℓ vs smooth ΛCDM expectation), ranked over ℓ=2–8.
  • Null: no ℓ=7 preference (rank ~ uniform U{1..7}).
  • Decision rule (all three required to re-open the withdrawn claim): (a) ℓ=7 ranks #1 of 7; (b) exceeds significance after Bonferroni / look-elsewhere over n_tested=7 (α_corr = 0.05/7 ≈ 0.00714); © cross-confirms across ≥2 independent component-separation methods (Spike #190/#192 discipline).
  • Outcome if not met: the per-ℓ ℓ=7 claim remains withdrawn; the {1+3+7} algebra identity is unaffected either way (only its multipole projection is at stake).

Verdict

🅿️ PARKED — pre-registered, no result. The honest closing of a not-dispatchable-today item: the future test is now turnkey and tamper-proof (statistic / null / threshold / cross-confirmation fixed in advance), without fabricating a finding. The Round 10.A withdrawal stands. HONEST SCOPE: this is a pre-registration, not a result; no bit-exact claim beyond the fixed protocol parameters; no new stance (nothing to bless); framework reading only.

Lands on rolling PR #690 (Round 41.A); unsolved-maths §11.9.34. CMB-S4 science book (arXiv:1610.02743); LiteBIRD (arXiv:2202.02773).