Spike #181 — Retroactive Re-Grading of Spike #47 R4-1 Under Researcher-DOF + Bonferroni Rigor¶
Date: 2026-05-19. Branch: research/spike-181-spike-47-r4-1-researcher-dof-regrading.
Verdict: H0-VERDICT-NEEDS-RETRACTION (recommended amendment: F-α PASS → F-α NOT-CONFIRMED; chain-level claim was already implicitly superseded by Spike #91 Run F Direction F, but R4-1's original PASS verdict text remains uncorrected in spike_47_round4_results_2026-05-17.md).
§1 Original methodology summary¶
Per spike_47_round4_results_2026-05-17.md §1:
- Substrate Λ catalog: integer eigenvalues of S³ × S⁷ Hopf-bundle products, λ = j₃(j₃+1) + j₇(j₇+3) producing
{2, 4, 6, 10, 12, 16, 18, 20, 22, 24, 28, …}(this audit replicates: 151 distinct values up to Λ=500, 80 values up to Λ=250). - Claimed chain:
Λ = {2, 12, 28, 52, 84, 126, 178, 244}— all 8 entries verified in substrate catalog. - F-α verdict: PASS at "10% per-ratio … 8-peak match within ~1.6% (peaks 7-8 within 0.4% extrapolation)".
- Statistical significance claim:
p ≈ 0.027("a different null"). - Process-integrity gap (F-180-1 shape): NO COMMITTED SCRIPT computes the
p ≈ 0.027. The claim exists only in markdownspike_47_round4_results_2026-05-17.md:20. Same auditable-provenance gap that PR #585 hit per Spike #180.
§2 Test-by-test results¶
T1 — Methodology located, no source code¶
The p ≈ 0.027 and "within ~1.6%" claims have no underlying committed Python. The substrate Λ catalog rule (j₃(j₃+1) + j₇(j₇+3) sums) IS documented in spike_47_r3p1_asymptotic_dof_reframe_2026-05-17.md §1.
T2 — Per-peak error audit (math doesn't lie)¶
Mapping ℓ_n = 220·√(Λ_n/2) per F-α projection:
| n | Λ_n | predicted ℓ | observed ℓ (Planck PR3) | error |
|---|---|---|---|---|
| 1 | 2 | 220.00 | 220 | 0.000% |
| 2 | 12 | 538.89 | 540 | 0.206% |
| 3 | 28 | 823.16 | 810 | 1.625% |
| 4 | 52 | 1121.78 | 1120 | 0.159% |
| 5 | 84 | 1425.76 | 1420 | 0.406% |
| 6 | 126 | 1746.20 | 1755 | 0.502% |
| 7 | 178 | 2075.48 | 2050 | 1.243% |
| 8 | 244 | 2429.98 | 2350 | 3.403% |
Max-per-peak error = 3.40%, NOT 1.6%. Mean-per-peak error = 0.943%. 6/8 peaks within 1.6% (peak 3 marginal at 1.625%, peak 8 at 3.40%).
The R4-1 claim "8-peak match within ~1.6% (peaks 7-8 within 0.4% extrapolation)" is misleading — peak 8 is at 3.40% error, peak 3 is just over 1.6%. The "extrapolation" qualifier may refer to deriving peak ℓ_n values from the chain rather than measuring them against Planck, but if so, peaks 7-8 are not Planck-anchored and the F-α claim only covers 6 peaks honestly.
T2 — Multi-seed null replication¶
10 seeds × 10,000 trials × uniform-random Λ ∈ [0, 250], n=8 chain, max-per-peak-error null:
| metric | value |
|---|---|
| p_min | 0.0000 |
| p_max | 0.0000 |
| p_mean | 0.0000 |
| R4-1 claimed | 0.027 |
R4-1's claimed p=0.027 does not reproduce under the simplest uniform-random null. The chain's 3.4% max-err is too tight for uniform random 8-Λ chains in [0, 250] to achieve.
This suggests R4-1's claimed "different null" was much narrower in support (e.g., lam_max ~ 30 or peak-by-peak windowed) but is undocumented.
T2b — Substrate-aware null (Λ_1 = 2 anchored)¶
Drawing 7 of 8 from substrate catalog at the anchor Λ_1=2:
| metric | value |
|---|---|
| n_trials | 10,000 |
| p_value_by_max_err | 0.0000 |
| p_value_by_mean_err | 0.0000 |
1M extended sampling: 0/1,000,000 random catalog-anchored 8-chains achieve max-err ≤ 3.4% or mean-err ≤ 0.943%. The chain is REAL signal — not a random catalog draw.
But this is the wrong null — the R4-1 chain was constructed by FITTING the substrate catalog Λs to Planck peaks (each Λ_n chosen to minimize ℓ_n error). Random catalog samples are not the comparison set; the comparison set is "all valid Planck-anchored chains."
T3 — Researcher-degrees-of-freedom audit (the load-bearing finding)¶
Enumeration of strict-monotonic chains from substrate catalog satisfying per-peak tolerance:
| tolerance | n valid chains | R4-1 rank | R4-1 percentile | best mean-err |
|---|---|---|---|---|
| 1.6% (claimed) | 0 | n/a | n/a | n/a (no chain qualifies) |
| 2.5% | 672 | n/a | n/a (R4-1 itself doesn't qualify) | 0.353% |
| 3.5% (actual) | 3,240 | 576 | 17.78 percentile | 0.353% |
| 5.0% | 20,800 | 651 | 3.13 percentile | 0.353% |
Critical finding: At the chain's own achievable tolerance (3.5%), 3,240 distinct strict-monotonic chains exist from the substrate catalog matching Planck peaks within tolerance. R4-1's chain ranks 576/3240 (17.78 percentile) — NOT exceptional within the constrained-search space.
The best-fit chain achieves 0.353% mean-error — 2.7× better than R4-1's 0.943%. The substrate catalog is dense enough that thousands of integer chains can be Planck-faithfully selected.
T4 — Bonferroni correction¶
Per spike_47_round4_results_2026-05-17.md §1, R4-1 tested 5 candidate selection rules (j₄ mod 4, Hopf-cycle phase ⅛, j₂+j₄ parity, pure-winding, selection-mask). Plus 5 falsifiers (F1-F5) tested in the same round.
| threshold | corrected α | p=0.027 survives? | replicated p=0 survives? |
|---|---|---|---|
| nominal (no correction) | 0.05 | YES | YES (trivially) |
| Bonferroni 5 rules | 0.010 | NO | YES |
| Bonferroni 10 combined | 0.005 | NO | YES |
| Bonferroni 25 combined | 0.002 | NO | YES |
R4-1's reported p ≈ 0.027 FAILS Bonferroni at any non-trivial multiplicity. The F-α PASS verdict assumed nominal α=0.05 without correction.
T5 — Independent-dataset replication¶
Same Λ = {2, 12, 28, 52, 84, 126, 178, 244} chain applied to independent CMB datasets:
| dataset (citation, arXiv-verified) | n peaks | max-err | within 1.6%? |
|---|---|---|---|
| Planck PR3 (Aghanim+ 2020 arXiv:1807.06209) | 8 | 3.40% | NO |
| WMAP 9-yr (Hinshaw+ 2013 arXiv:1212.5226) | 3 | 1.72% | NO |
| ACT DR4 (Aiola+ 2020 arXiv:2007.07288) | 8 | 3.40% | NO |
| SPT-3G (Dutcher+ 2021 arXiv:2101.01684) | 6 | 1.00% | YES |
| Planck PR4 (Akrami+ 2020 arXiv:2007.04997) | 8 | 3.40% | NO |
Only ⅕ independent datasets passes the 1.6% claim (SPT-3G, but only because its peak count truncates to 6 — the same first-6-peaks subset that passes on all datasets).
When peak 8 is included, NO dataset passes 1.6%.
T6 — Density-of-states diagnosis¶
| metric | value |
|---|---|
| Substrate catalog density in [0, 250] | 0.32 chains/Λ |
| Planck-implied chain density (8 peaks / 244 Λ-range) | 0.033 chains/Λ |
| Density ratio (substrate / Planck-implied) | 9.68× |
The substrate catalog has ~10× the density needed to populate 8 Planck-matched values. This is a density artifact — any 10× over-dense integer catalog with constrained-search produces thousands of Planck-faithful chains.
Same diagnosis as Spike #180 found for the squashed-S⁷ vs round-S⁷ test on the same chain.
§3 Re-graded F-α verdict¶
R4-1's original verdict text:
F-α PASS (10% per-ratio): 8-peak match within ~1.6% (peaks 7-8 within 0.4% extrapolation)
Recommended amendment:
F-α NOT-CONFIRMED (re-graded 2026-05-19 per Spike #181): - "Within ~1.6%" claim is true only for 6/8 peaks; peak 8 is at 3.40% error. - At the chain's actual achievable tolerance (3.5%), 3,240 alternative Planck-faithful chains exist from the substrate catalog. R4-1's chain ranks 576/3240 (17.78 percentile) — non-exceptional. - Reported
p ≈ 0.027is unverifiable (no committed source) and fails Bonferroni correction at 5-rule multiplicity (corrected α=0.010). - Cross-dataset: chain does not pass 1.6% tolerance on ⅘ independent CMB datasets when 8 peaks tested. - Substrate-catalog density (~10× Planck-implied) is sufficient to populate any moderate-tolerance integer chain — density artifact, not structural correspondence.
This re-grading is operationally consistent with Spike #91 Run F Direction F (notebook §3.8.7), which already softened the chain-level claim and reframed the framework's CMB load-bearing prediction as arithmetic peak-spacing pattern via Class I cyclic-cascade, NOT the {2,12,28,…} chain on Class L sphere Laplacian.
Spike #91 RF DF therefore stands as the framework's current canonical CMB stance; Spike #181 closes the open loop by retracting R4-1's original PASS verdict text.
§4 Downstream impact catalog¶
Found in srmech notebook + sister-notebook + memory directory:
| location | citation | status after re-grading |
|---|---|---|
srmech/srmech_research_notebook.md:731 (§3.8.7) |
"Spike #47 R4-1 re-task verdict" (Spike #91 Run F Direction F) | already softened; cites R4-1 only as historical context |
srmech/notes/spike_47_round4_results_2026-05-17.md |
original F-α PASS text | REQUIRES AMENDMENT (text uncorrected; this finding) |
srmech/notes/spike_47_round3_results_2026-05-17.md |
F1 PARTIAL preserved | unaffected (still PARTIAL) |
srmech/notes/spike_47_r3p1_asymptotic_dof_reframe_2026-05-17.md |
asymptotic-DOF reframe candidate | unaffected (R4-1 itself was meant to test the reframe; reframe REFUTED at math level per R4-1; that part stands) |
memory user_stance_big_bang_as_projection_shadow.md |
candidate stance | does NOT cite the chain or "p=0.027"; no action needed |
sister mfo_spectral_research_notebook.md (cited grep hit) |
Spike #47 referenced | check for chain-level dependence (likely just R4-2 178-Gyr resolution) |
memory user_stance_dark_sector_ring_down_rate_is_cascade_stretched.md |
178 Gyr / R4-2 | unaffected (R4-2 is independent of R4-1) |
No canonical-committed (memory/user_stance_*.md) file cites R4-1's chain or the p=0.027 claim, per grep on R4-1|F-alpha|1\.6%|0\.027|chain.*\{2,?\s*12,?\s*28|selection.mask. The downstream blast radius is limited to:
spike_47_round4_results_2026-05-17.md— text amendment recommended (this is the actionable downstream).spike_51series files (5 cite R4-1, mostly for context).spike_49(mentions R4-1 chain in cross-spike framing).
Spike #91 Run F Direction F is the upstream re-task that already shifted load-bearing weight away from the chain. R4-1 PASS amendment is housekeeping consistent with the existing notebook §3.8.7 reframe.
§5 Recommendation for #47 R4-1 amendment¶
Mirror Spike #180's PR #585 amendment pattern:
- Strike "F-α PASS" verdict in
spike_47_round4_results_2026-05-17.md:19; replace with "F-α NOT-CONFIRMED (per Spike #181 2026-05-19 re-grading)". - Strike
p ≈ 0.027claim in:20; replace with note: "No committed script supports this p-value; under uniform-random null over [0,250], p=0.0000 (chain max-err 3.40% never reached by random); under researcher-DOF audit, chain ranks 576/3240 (17.78 percentile) of valid Planck-anchored chains; chain-level F-α PASS retracted per Spike #181". - Strike "8-peak match within ~1.6%" claim; replace with "6/8 peaks within 1.6% (Λ=28 at 1.63% marginal; Λ=244 at 3.40% outside tolerance)".
- Update R4-1 score from
5/10 [PASS, FAIL, PASS, PASS, PARTIAL]to4/10 [NOT-CONFIRMED, FAIL, PASS, PASS, PARTIAL]. Spike #47 R2 total from 9/10 to 8.5/10 (F1 still PARTIAL as named-gap; F-α individual element changed within F1). - Preserve R4-1's PROCESS findings (g(Λ) ansatz REFUTED at math level; FFT-cosine 0.997 / L2 12.62 diagnostic; growing-with-n modulation inconsistent with Class K rate-of-approach). Those are real negative findings that stand.
- Reference Spike #91 Run F Direction F (notebook §3.8.7) as the existing re-task verdict that ALREADY shifted load-bearing CMB prediction to Class I cyclic-cascade.
- Reference Spike #181 (this finding) as the auditable closure on R4-1's original PASS verdict.
§6 Verified literature citations (arXiv-only per [[reference_autonomous_validation_tos_landscape]])¶
- Aghanim N. et al. (Planck Collaboration), "Planck 2018 results. VI. Cosmological parameters", arXiv:1807.06209 (PDF-verified per Spike #76 + #180; PR3 TT acoustic-peak positions).
- Hinshaw G. et al. (WMAP Collaboration), "Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results", arXiv:1212.5226 (PDF-verified per Spike #180).
- Aiola S. et al. (ACT Collaboration), "The Atacama Cosmology Telescope: DR4 Maps and Cosmological Parameters", arXiv:2007.07288 (PDF-verified per Spike #180).
- Dutcher D. et al. (SPT-3G Collaboration), "Measurements of the E-mode polarization and temperature-E-mode correlation of the CMB from SPT-3G 2018 data", arXiv:2101.01684 (PDF-verified per Spike #180).
- Akrami Y. et al. (Planck Collaboration), "Planck 2018 results. I. Overview, and the cosmological legacy of Planck", arXiv:2007.04997 (PDF-verified per Spike #180; PR4 reprocessing).
No new external citations beyond what Spike #180 already PDF-verified. No prohibited-source queries.
§7 Discipline summary¶
- 14 A-N intact per
[[feedback_no_privileged_primitive_classes]](no class promotion; substrate Λ catalog is S³ × S⁷ Hopf-base sum; primitive vocabulary unchanged). - Identity-not-implementation per
[[user_stance_identity_not_implementation_discipline]]: re-graded the chain-level VERDICT only; framework-level identity claim (Big Bang as projection-shadow; substrate as S¹×S³×S⁷ hyperring) untouched. Spike #91 Run F Direction F's Class I cyclic-cascade reframe is the framework's current CMB-pattern stance and is unaffected by this re-grading. - Math-doesn't-lie per
[[user_stance_string_theory_instrument_first]]: peak-8 error of 3.40% IS not "within ~1.6%"; the claim is falsified by per-peak audit. No fiat preservation. - Trauma-informed defensive scope per
[[feedback_trauma_informed_defensive_scope]]: cosmology research/educational; no targeting / capability-assessment content. - PDF-extraction citation discipline per
[[feedback_pdf_extraction_citation_discipline]]: all 5 arXiv references PDF-verified upstream (Spike #76 + #180). - No MVP framing per
[[feedback_no_mvp_framing]]: full-coverage re-grading across T1-T6; complete 8-peak audit; cross-dataset on all 5 attested CMB datasets. - NDJSON output per
[[feedback_ndjson_over_bloated_json]]: 16 records, one per line.
§8 Status¶
Verdict: H0-VERDICT-NEEDS-RETRACTION. Recommended action: edit spike_47_round4_results_2026-05-17.md per §5 above. Spike #91 Run F Direction F's reframe stands as framework's current CMB stance — the re-grading is a housekeeping operation closing the loop on the R4-1 original PASS verdict text.
Conductor decision needed: should the amendment go in directly (notebook edit) or via a new PR? Recommend new PR for auditability + commit history (matches Spike #180's PR #585 amendment pattern).
Files written (absolute paths per worktree-isolated dispatch):
- D:/GitHub/mlehaptics/.claude/worktrees/agent-spike181-spike-47-r4-1-regrading/docs/srmech/notes/spike181_spike_47_r4_1_regrading_prototype.py (~615 lines, runnable analysis)
- D:/GitHub/mlehaptics/.claude/worktrees/agent-spike181-spike-47-r4-1-regrading/docs/srmech/notes/spike181_records_2026-05-19.ndjson (16 records)
- D:/GitHub/mlehaptics/.claude/worktrees/agent-spike181-spike-47-r4-1-regrading/docs/srmech/notes/spike181_spike_47_r4_1_regrading_findings_2026-05-19.md (this file)
End of Spike #181. Math doesn't lie. The chain's max-per-peak error is 3.40% at Λ=244, NOT ~1.6%; researcher-DOF audit places R4-1 at 17.8 percentile of 3,240 valid chains; original p=0.027 has no auditable provenance; F-α PASS verdict needs retraction. Spike #91 Run F Direction F's Class I cyclic-cascade reframe stands as the framework's current CMB-pattern claim.