Gate by the equity curve trend (10 days, 80-day average)
A trend system's stream of results has a trend of its own: good and bad stretches come in blocks, not at random. Applying to the accumulated equity the same moving average you apply to price lets you stop trading when the curve turns down and resume when it turns up — avoiding the bad runs without predicting anything about the market.
Measured in forex — EUR/USD and GBP/USD · daily bars built from 15m · 1 pip spread (~0.009% per round trip) · no survivorship bias
- ✓invariance
- ?costs
- ?placebo
- ✓benchmark
- ?out of sample
- ?multiple testing
At its worst the account was worth 0% less than its own best previous moment, and it spent 1,368 days below that peak.
What was measured
How many of those trades actually count
What it paid, before any deductions
Where it stalled · the broker's fee
What would have happened to the money
What this result does NOT say
- One market, one universe
- Measured on 2 spot currency pairs. It says nothing about futures, equities or indices, nor about how the same technique behaves in another market.
- One window of time, not every window
- The measured period runs from 2020-01-01 to 2026-06-26. A market moves through regimes, and a technique can work in one and fail in another — the card measures the regimes that fit inside this window, not the ones still to come.
- One cost structure
- The cost charged is a 1.0 pip spread, crossed once. Anyone paying more than that gets a worse result, and anyone paying less gets a better one — the verdict holds for this fee.
- One exit rule
- The trade was closed by: the technique itself (held until the opposite signal). The same entry measured with a different exit is a different strategy, and can earn a different verdict — it happens in this archive.
- The number of trades is not the sample size
- There are 301 trades, but only 188 independent market episodes: trades that overlap in time are not independent observations, and counting them as if they were inflates any result. It is the smaller number that governs the arithmetic. With 188 episodes, what the data supports is a range from -0.11% to +0.14% per trade — the published average is the centre of it, not the exact measurement.
- Daily bars
- Measured at the daily close. Nothing here measures what happens inside the day, and an intraday technique is not auditable with this data.
Numbers and reproducibility
The six controls
| control | status | t | threshold | episodes |
|---|---|---|---|---|
| invariance | passed | — | — | — |
| costs | inconclusive | 0.13 | 1.97 | 188 |
| placebo | inconclusive | 0.41 | 1.97 | 188 |
| benchmark | passed | — | — | — |
| out of sample | inconclusive | — | — | — |
| multiple testing | inconclusive | — | — | — |
- invariance301 signals across 4055 barsconcentration: +45.82% of the profit sits in the top 5% of trades — with the dates shuffled, +37.68% (fails above +50.00%)
- costsgross +0.017% · cost 0.008% · net +0.008% (t=0.13) · the range runs from -0.118% to +0.134%
- placeboactual +0.008% · placebo -0.018% · excess +0.027% ± 0.065% (t=0.41 against a threshold of 1.97, 188 real groups, 15,050 sham dates, draw error ±0.008%)
- benchmarktechnique +0.01% · buy and hold (same horizon) +0.00% · excess +0.00%
- out of sampleasset half A: -0.007% (t=-0.07, 131 episodes) · asset half B: +0.025% (t=0.28, 117 episodes) · liquid half (>= US$ 0/day): +0.008% (t=0.13, 188 episodes) · period 1/4 (2020-04-06 a 2021-06-03): +0.054% (t=0.44, 44 episodes) · period 2/4 (2021-06-06 a 2023-03-07): +0.217% (t=1.34, 49 episodes) · period 3/4 (2023-03-08 a 2024-10-22): -0.046% (t=-0.43, 47 episodes) · period 4/4 (2024-10-30 a 2026-06-24): -0.190% (t=-1.84, 50 episodes)
- multiple testing1 variation(s) tested · t=0.13 across 188 episodes (equivalent to t=0.13) · p≈0.8979 · false positives expected by chance ≈ 0.90
Equity — outside the six controls, and here is why
The t of the trade series is invariant to bet size: 0.5%, 1% and 3% agree to the sixth decimal. Nothing here moves the verdict — it moves what the account would have lived through.
- risking 1.0% per trade
- ×1.00
- worst drawdown from the peak
- −0%
- days below the previous peak
- 1,368
- signals refused for lack of capital
- 0%
- paths where the account halved (out of 12)
- 0
Reproducibility
- period
- 2020-01-01 to 2026-06-26
- assets that traded
- 2
- variations tested before this one
- 1
- gross per trade
- +0.02%
- net per trade
- +0.01%
- exit rule
- the technique itself (held until the opposite signal)
- median duration bars
- 3
- mean duration bars
- 6.1
- max duration bars
- 44
- spread pips
- 1.0
- episode days
- 7
- seed
- 20260728
- equity curve average
- 10
- slope period
- 80
Twelve Data forex (15m aggregated to 1d) · collected on 2026-07-25 · 2 assets · 4,055 bars · 2020-01-01 to 2026-06-26
Hypothesis, filed before the result
The central claim of `Equity Trends` (p. 1086), in the fast variant. The rule, given in full: «by applying a simple moving average to the cumulative profits and losses, we could exit positions when the equity trend is down»; and the implementation, «when the equity trend was up on day t compared to t−1, we used the returns of day t+1; otherwise, we used a return of zero». An 80-day base, a 10-day average over cumulative profit, one unit per signal — «only 1 contract was traded on each signal, rather than a risk-adjusted position size». THE CLAIM IS NOT THE ONE THE RUNBOOK RECORDED. The runbook said «stop trading after N losses, come back when equity crosses its own average»; THERE IS NO COUNT OF LOSSES anywhere in the section. The rule is the daily gate above, and that is what will be audited. THE SOURCE ALREADY REPORTS THAT IT DOES NOT WORK: «none of the three cases show consistency, although there were improvements for the S&P and gold using both the 10- and 60-day trends. Bonds, the most trending market, showed significant deterioration with this method». And it lists three defects of its own test: «the equity trend method also did not include any switching costs, which would be more significant for the 10-day trend»; «we can infer that this method would perform poorly on a diversified portfolio»; and «applying this to hypothetical equity patterns is not likely to work, because hypothetical results are always better than actual trading results». THE PRECONDITION IT DECLARES NECESSARY, THIS CORPUS HAS ALREADY MEASURED AND NOT FOUND: «you first need to find out if returns are positively autocorrelated, which means that there is persistence in positive or negative returns» — and the entry in `confirmacoes.py` publishes, over 742,175 crypto days, that daily direction is a coin flip with no memory. Family-level prediction, recorded before measuring: (1) NONE survives the corpus-wide Benjamini-Hochberg; (2) the FRACTIONAL ENTRY and the two PYRAMIDS ON PROFIT will move the mean by LESS THAN THE ERROR BAR and will NARROW the deviation — it is the mechanism the protocol has already measured twice, at breakeven (median from −2.75% to 0.00%, mean unchanged) and at partial profit taking (−0.023% ± 0.518%, deviation from 19.9% to 12.4%): position management moves the SHAPE and is read as if it had moved the CENTRE; (3) the EQUITY CURVE GATE fails, and for lack of autocorrelation — this is the family's most falsifiable prediction, because the number already exists in the corpus: the source states that «first one must find out whether returns are positively autocorrelated», and `confirmacoes.py` publishes, over 742,175 crypto days, that daily direction is a coin flip WITH NO MEMORY; (4) AVERAGING DOWN will be the worst in the family and will die at CONTROL 1, concentration, because adding to losses fattens the tail — and the source itself already rejects it in 3 of 4 markets; (5) the gravedigger in crypto will be CONTROL 1 and not the benchmark, which is the correction of the prediction refuted in part 76 and what part 74 had already established: in crypto, what pays a lot pays it concentrated; (6) the 80-day BASE will do better than any layer built on top of it. MEASURED IN FOREX (EUR/USD and GBP/USD, daily aggregated from 15m), and not in crypto. This is a pre-registered REPLICATION — not a new discovery —, and the multiple-testing count treats it as such. And there is one difference that matters to this family: waiting for a better price is measured in multiples of the asset's own true range, so it adapts to the market by construction — but a pullback that happens every week in crypto may be rare in a currency pair, and the 5-day window is the same in both.
filed on 2026-08-04, before the number existed
The original, as it was filed
A alegação central de `Equity Trends` (p. 1086), na variante rápida. A regra, dada por inteiro: «aplicando uma média móvel simples aos lucros e prejuízos acumulados, poderíamos sair de posições quando a tendência do patrimônio está de baixa»; e a implementação, «quando a tendência do patrimônio estava de alta no dia t comparado a t−1, usamos os retornos do dia t+1; caso contrário, usamos um retorno de zero». Base de 80 dias, média de 10 dias sobre o lucro acumulado, uma unidade por sinal — «apenas 1 contrato era operado a cada sinal, em vez de um tamanho de posição ajustado ao risco». ⚠️ A ALEGAÇÃO NÃO É A QUE O RUNBOOK REGISTRAVA. O runbook dizia «pare de operar depois de N perdas, volte quando o capital cruzar a própria média»; NÃO HÁ CONTAGEM DE PERDAS em lugar nenhum da seção. A regra é o gate diário acima, e é ela que será auditada. ⚠️ A FONTE JÁ REPORTA QUE NÃO FUNCIONA: «nenhum dos três casos mostra consistência, ainda que tenha havido melhoras para o S&P e o ouro usando tanto a tendência de 10 quanto a de 60 dias. Os títulos, o mercado com mais tendência, mostraram deterioração significativa com este método». ⚠️ E ela lista três defeitos do próprio teste: «o método da tendência do patrimônio também não incluiu nenhum custo de troca, que seria mais significativo para a tendência de 10 dias»; «podemos inferir que este método teria desempenho ruim numa carteira diversificada»; e «aplicar isto a padrões hipotéticos de patrimônio provavelmente não vai funcionar, porque resultados hipotéticos são sempre melhores que resultados de operação real». ⚠️ A PRÉ-CONDIÇÃO QUE ELA DECLARA NECESSÁRIA, ESTE CORPUS JÁ MEDIU E NÃO ENCONTROU: «primeiro é preciso descobrir se os retornos são positivamente autocorrelacionados, o que significa que há persistência em retornos positivos ou negativos» — e o verbete de `confirmacoes.py` publica, em 742.175 dias de cripto, que a direção diária é cara-ou-coroa sem memória. Previsão da família, registrada antes de medir: (1) NENHUMA sobrevive ao Benjamini-Hochberg do corpus; (2) a ENTRADA FRACIONADA e as duas PIRÂMIDES SOBRE LUCRO moverão a média por MENOS QUE A BARRA DE ERRO e ESTREITARÃO o desvio — é o mecanismo que o protocolo já mediu duas vezes, no breakeven (mediana de −2,75% para 0,00%, média parada) e na realização parcial (−0,023% ± 0,518%, desvio de 19,9% para 12,4%): gestão de posição mexe no FORMATO e é lida como se tivesse mexido no CENTRO; (3) o GATE PELA CURVA DE PATRIMÔNIO reprova, e por falta de autocorrelação — esta é a previsão mais falsificável da família, porque o número já existe no corpus: a fonte declara que «primeiro é preciso descobrir se os retornos são positivamente autocorrelacionados», e `confirmacoes.py` publica, em 742.175 dias de cripto, que a direção diária é cara-ou-coroa SEM MEMÓRIA; (4) a MÉDIA PARA BAIXO será a pior da família e morrerá no CONTROLE 1, concentração, porque adicionar nas perdas engorda a cauda — e a própria fonte já a reprova em 3 de 4 mercados; (5) o coveiro em cripto será o CONTROLE 1 e não o benchmark, que é a correção da previsão refutada na parte 76 e o que a parte 74 já tinha estabelecido: em cripto, o que rende muito rende concentrado; (6) a BASE de 80 dias irá melhor que qualquer camada sobre ela. ⚠️ MEDIDO EM FOREX (EUR/USD e GBP/USD, diário agregado de 15m), e não em cripto. Isto é uma REPLICAÇÃO pré-registrada — não uma descoberta nova —, e a conta de múltiplos testes a trata como tal. ⚠️ E há uma diferença que importa a esta família: a espera por preço melhor é medida em múltiplos da amplitude real do próprio ativo, então ela se adapta ao mercado por construção — mas um repique que em cripto acontece toda semana pode ser raro num par de moedas, e a janela de 5 dias é a mesma nos dois.
Quotations from the source were translated from the Portuguese record and back into English — they are not the author's exact words.
Pre-registration exists to keep prediction apart from rationalisation: written after the number, every hypothesis is right.
The same technique in the other market
The verdict is different there. The same technique, measured on independent data, came out the other way — and that says more about it than either card says alone. Read the cost and the detection floor before concluding: they are not the same in the two markets.
- forexINCONCLUSIVE← this one
- cryptoFAILEDopen that card
This claim has been audited once — there is no history to compare against.