Published August 31, 2026 | Version v1

Fenopan sealed record v17 — the aggregation law measured on a real 180-stock panel: the intermittency of an equal-weight aggregate, estimator-free

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Description

Sealed record v17 (Fenopan experiment x8, build 3, sealed 2026-08-28; a dated correction block appended 2026-08-30). Does the closed-form aggregation law — aggregating D imperfectly-correlated H = 0 log-volatility cascades drives the intermittency coefficient down by λ²_agg = ρλ²₀ + (1−ρ)λ²₀/D_eff, while H stays 0 — hold on real data?

The panel and the matched index. 180 S&P-500 constituents, daily log-Garman–Klass realized variance, 1,259 trading days (2013-02-08 … 2018-02-07) on one matched date grid. The matched index is not fetched from outside: it is the equal-weight aggregate variance of the constituents themselves, an index-analog at identical sampling interval, window and length. The cap-weight arm is dropped (no market capitalisations are committed, so constituent ranks are unidentified).

What is measured. The aggregate reads λ̂² = 0.0350 against the cross-sectional mean constituent λ²₀ = 0.0633 — measurably less intermittent — and its per-D median Ĥ is 0 at every breadth. The covariance-mixture law holds with no estimator in the loop: the ratio C_agg/C_mix sits in [0.958, 1.016] at the six dyadic lags the λ² slopes are read on. The calibration-validated slope-ratio is ρ = 0.581 (calibrated 0.587) with a moving-block-bootstrap 95% interval [0.43, 0.65]. The single-common-cascade approximation is measurably violated: ρ(τ) falls with lag (0.51 → 0.42), the common factor decorrelating faster than the idiosyncratic part.

Correction that accompanies this record — read it with the dated correction block at the end of the deposited RESULTS.md (2026-08-30). An adversarial audit found five headline sentences stronger than the measurements support. The body, README and JSON stand as sealed; the corrections are appended, and the full method, seeds and tables are in the companion note Aggregation-law audit addendum (2026-08-30). In brief: (1) "Ĥ stays ≈ 0 at every D (grid max 0.000)" is a max over per-D medians — the per-D median Ĥ is 0 at every D, but 3 of the 41 individual subset fits are non-zero, max 0.050. (2) The estimator-free band [0.958, 1.016] is over six dyadic lags; across all integer lags 1…32 it is [0.894, 1.046]. (3) The ρ interval is a boundary statement, not a containment one: at 2,000 bootstrap replicates at the declared block length the raw interval is [0.4217, 0.6492] and the calibration-inverted one [0.4335, 0.6480] — both exclude the synthetic comparator 0.65 — and the boundary moves ±0.03 with the resampling choices; ρ is also band-conditional (0.53–0.65 across reasonable slope bands). (4) The comparator is itself cross-measurement (a world-index median over a US-stock median at unmatched sampling interval and length; the S&P 500 alone reads a ratio of 1.095 and the matched-length read is 1.03), and effective breadth does not explain the 0.58-vs-0.65 offset — the measured log-space D_eff is 135 (72.5 instantaneous), not 180, and the closed form credits breadth with at most ≈ 0.02 of the 0.07 gap. (5) Most importantly: at this panel's length (N = 1,259) the programme's own matched-length ladder reads the index cohort at Ĥ = 0.0245, and this record contains no H-detection positive control — so the real-data null is consistent with, but not powered to exclude, an aggregate as rough as the index. Also: ρ as estimated is the noise-excluded ratio of common-to-total log-correlated covariance amplitude (ρ(0) = 0.285), not the contemporaneous cross-sectional correlation; the covariance-mixture identity is algebraic by construction, so the structural argument is first-order with the measured mixture curve as its second-order bound; the liquidity exclusion is better stated by its rank statistic (Spearman −0.21, p = 0.004 — noisier names read less rough, the opposite of the artifact prediction); and result 1 is a determinism check, not an independent reproduction. The measured quantities are unchanged and reproducible; what changed is what they are claimed to establish.

No trading or positioning claim is made, and no sibling data is re-fit.

Data provenance. The only input is a committed, license-clean derivative: daily log-Garman–Klass realized variance for 180 S&P-500 constituents — a scientific transform only. No raw price, quote or OHLC table is redistributed.

Regeneration (verbatim from the record):

python x8_real.py                 # writes out/v17/x8_real.json (~75 s)
python make_figures_x8_real.py    # writes out/v17/fig_x8_real.png
python x0_verify.py               # step (24): the seconds-scale x8-real gate (X0 PASS)

Deterministic in a pinned seed base (60,000,000).

Evan Tabak Atlas (ORCID 0009-0007-7374-2338). Licensed CC BY 4.0. Deposited as a standalone record: the generating repository is private and remains so by the author's decision of 2026-08-30, so this description carries the record's own regeneration block verbatim and no repository links. Every number in the deposited files is reproducible from the deposited object and the named committed inputs.

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Additional details

Related works

Is supplement to
10.5281/zenodo.22180460 (DOI)