docs/investing-2k-plan-collapse-certificate.md

Σ₀ Collapse Certificate — docs/investing-2k-plan.html

Claim under test: "$2,000 + $20/mo DCA into a momentum-tilted 8-asset mix, gross leverage ∈ [0, 2×] via 35% vol-target × 6-mo trend gate × 30% DD-taper → cash (T-bills), real-time streaming brake, produces $91,843 (12.6%/yr, maxDD −25%, Sharpe 0.65) from 2000-01 → 2026-07 versus $54,603 SPY B&H+DCA."

This certificate is the adversarial audit of that claim. It is committed alongside the artifact so the audit is as durable as the number. Per the External Reality Rule, the receipts that matter are the runnable experiments (experiments/dca_champion_2k.py, experiments/dca_champion_instrumented.py, experiments/leverage_*), not the prose.

Evidence-class discipline (strict, asymmetric)

Class What it covers Status
MEASURED (in-sim) Walk-forward equity curve, 679-row trade log, 1,000-path bootstrap True only for the exact code, price series, and cost model used
OPERATIONAL "Nothing has passed the gate yet" (meets_ci withholds live capital) Correct and conservative
HEURISTIC Forward projection tables; "best of 55/58 alternatives" ranking Extrapolation, not fact
UNPROVEN / open That the edge is available, implementable, and durable for a real $2k retail account today Not yet measured at the required confidence

Load-bearing assumptions that can collapse the claim

  • A · Momentum-sleeve history. XMMO (~2005), SPMO (~2015). **Corrected vs the raw

red-team:** the sim does not reconstruct or proxy pre-inception history — funds enter the tangency direction only once they have a full trailing window of real Yahoo prices (live = [s for s in UNIVERSE if not np.isnan(px[s][lb:i]).any() and i-lb>252]). So the proxy/tracking-error overstatement does not apply. What survives: the sleeve's contribution is concentrated in its live era, which overlaps the momentum-favorable regime — durability is unproven.

  • B · Leverage at retail scale. 2× gross on $2k is margin, not a 2× ETF:

maintenance margin (25–30%+ house rules, higher in stress), PDT flag on frequent brake fires, dynamic debit interest, forced-liquidation order + partial fills. A single delayed brake or margin call = permanent impairment DCA cannot repair at this contribution rate. Under-modeled.

  • C · Transaction + financing drag realism.trades over 26y. Bid-ask on the small

sleeves (IWM/EFA/XMMO/SPMO), fees, and the T-bill-vs-debit spread compound; the cost model is a flat bps approximation and taxes are not modeled (679 taxable events in a taxable account is a real haircut). Small-account costs are higher, not lower.

  • D · Selection multiplicity (Bailey / López de Prado). The champion is the survivor of

a 100+ strategy / 55-asset search → elevated overfitting probability. The 1,000-path bootstrap stresses the champion, not the discovery process; it is not a full OOS stress of the search that selected it.

  • E · Regime / path dependence. The 6-mo-trend × vol-target × DD-taper rules worked in

the tested window; they are not invariant to prolonged high-rate/low-growth regimes, simultaneous equity+bond+gold drawdowns, or a weakened/inverted momentum premium. −25% maxDD is the realized path, not a ceiling.

  • F · Human operator factor (the real gate). "A person always decides" is the strongest

part of the design and also where real plans fail most: the operator sees −25% while a plain-SPY neighbor is −15%, overrides the brake on a false positive, or stops the $20 in a multi-year flat stretch. Behavioral leakage is not in the backtest.

What survives adversarial pressure

  • A diversified, trend-gated, modestly levered multi-asset book with an explicit cash brake

improving both terminal wealth and maxDD vs plain SPY DCA is directionally consistent with published risk-parity / momentum / managed-futures overlay literature.

  • The "nothing qualifies for live capital yet" gate is the correct Σ₀-style control.
  • Contribution size remains the dominant lever (the artifact says so).
  • Gold ballast + TLT are sensible, not exotic. Real-time vs daily brake is a measurable

engineering claim, presented as such (PR #2694: hourly beat daily +$4,278 at equal turnover).

Minimal honest statement that does not collapse

Inside the exact historical price series, cost model, and code path used, the described engine produced higher terminal wealth and lower maxDD than SPY DCA from 2000–2026. The live implementation path for a $2k retail margin account contains several frictions (margin mechanics, small-account costs, taxes, regime durability, and operator adherence) not yet measured at the required confidence. The internal gate correctly withholds real capital. The single highest-confidence action remains increasing the monthly contribution while keeping the risk engine in practice mode.

Non-collapsing core (the operator decision surface)

Human click only · practice-mode brake first · meets_ci gate (ADR-0028, Buffett bar 0.79; nothing has cleared it). Everything else on the page is a MEASURED historical simulation that has not yet earned the right to be treated as a live edge.

No part of this analysis constitutes financial advice.