Auditing the "Circadian Trader" Claim

a number in a five-domain convergence table has no derivation, dataset, or citation anywhere in its own source file

GameTheory_Full_Pack.html presents a table and a chart, both titled around the claim that σ* ≈ 1/3 is confirmed independently across five domains: the network-game MPE threshold, the GTCT operator orbit ε₀, dm³ contact geometry ε₀, a "circadian trader" g₃₃ ≈ 1/3, and WTI historical oil volatility. Two of those five rows are tagged Lean 4 · 0 sorry in the same table. This audit checked only the "circadian trader" row, the same way WP-24 checked the criticality-bridge claim: not by trusting the label, by looking for the thing that's supposed to back it up.

What was searched for

A full-text search of GameTheory_Full_Pack.html for every occurrence of "circadian," "Nirvana," "g₃₃," and "trader" turns up exactly two places this claim appears: the summary table row (Circadian trader · g₃₃ = 33 cycles · g₃₃ ≈ 1/3 attractor · Nirvana compounding fixed point · Numerical) and the identical numbers repeated in the chart's data array (lo:0.31, hi:0.35, mid:0.33). There is no third place. No model is defined for what a "circadian trader" is or does. No dataset, backtest, or simulation is referenced. No citation is given for "33 cycles" or for the 0.31–0.35 range. "Nirvana compounding fixed point" is not defined anywhere else in the document or cross-referenced to a chapter that defines it.

Searched this session (full-text grep, case-insensitive, whole file): "circadian" -> 2 matches, both listed above, no others "Nirvana" -> 1 match, inside the same table cell, not defined elsewhere "g33" / "g_33" (any rendering) -> same 2 locations only "trader" -> same 2 locations only No definition, derivation, dataset, or citation found anywhere in the file.

The citation that turned out not to exist

The file's own reference list carries two entries that read as if they supply the missing derivation: Grossi, P.N. (2026a), "Positional Dominance in Network Games" and Grossi, P.N. (2026b), "On the Recurrent Appearance of a Threshold Near 1/3," both cited to 10.5281/zenodo.19117399. That DOI is the Principia Orthogona series concept DOI — by Zenodo's own design, a concept DOI always resolves to whichever version was most recently deposited. As of this audit it resolves to Principia Orthogona, Volume I: The Mathematics of Generative Transitions, version 6, published July 2, 2026 — a paper about the operator chain G = U∘F∘K∘C, Whitney folds, and Lean 4 proofs. It contains no network-game model, no circadian trader, no companion result about a "threshold near 1/3." A web search for either cited title returns no matching record anywhere, on Zenodo or off it.

In other words, the two citations that a reader would follow to find the missing derivation do not point to papers that contain it — they point, by coincidence of how concept DOIs resolve, to an unrelated volume. This is not a case of a stale link to a real but outdated paper; the titled works do not appear to exist as separate deposits at all. The reference-list entries have been corrected in GameTheory_Full_Pack.html to say so directly, rather than left pointing at a live-but-wrong DOI that a reader could mistake for confirmation.

Verdict This is not the same finding as WP-24. WP-24 checked a claim that had algebra behind it, and the algebra turned out not to support the conclusion — a refutation. This row has no algebra, model, or data behind it to check in the first place, in its own source file. The honest label for this row is not "Numerical" next to two "Lean 4 · 0 sorry" rows in the same table — that pairing implies a comparable standard of evidence that does not exist here. The accurate label is unsourced: a specific-sounding number (33 cycles, a named "Nirvana" fixed point, a tight numeric range) presented with no accompanying way for a reader to verify it, reproduce it, or trace it to a real trader, dataset, or study.

Row in the five-domain table	Status	Notes
Network game (MPE) σ* ∈ [0.30, 0.36]	not re-audited here	Has a cited theorem elsewhere in this corpus (Grossi 2026b); out of scope for this working paper
GTCT operator orbit ε₀ = 1/3	Lean 4, 0 sorry (as labeled)	Genuinely different evidentiary class from the row below
dm³ contact geometry ε₀ = 1/3	Lean 4, 0 sorry (as labeled)	Same
Circadian trader g₃₃ ≈ 1/3	unsourced	No definition, model, dataset, or citation anywhere in the file; should not be tabled alongside proved rows without that context
WTI historical volatility 0.35–0.42	plausible, uncited here	Real, checkable public data (EIA), but no specific series or date range is cited in this file to verify the exact 0.35-0.42 figure

This does not mean σ*≈1/3 is wrong, or that a real circadian trading model couldn't be built and might land near that number — only that this specific row, as written, gives a reader nothing to check. The fix is not to delete the row; it's to either cite the source (a paper, a backtest, a named strategy) or remove it from a table that otherwise mixes in machine-checked theorems, since the table's own formatting currently implies all five rows carry the same weight of evidence, and they plainly do not.

← Book 6 index WP-24: Criticality Bridge, Audited →