NULL SIGNAL

A mechanical lottery draw is about the closest you get to a process whose null hypothesis you can assume before you start: the machine is built and audited to be fair, and the balls have no memory. That is an assumption about the equipment, not something the data can prove — but it is the strongest prior available anywhere, which makes this the rare case where you roughly know the right answer in advance. Normally that is a reason to leave the problem alone. Here it became the reason to take it up.

A pipeline that reports an edge on a domain with this strong a fairness prior has not discovered anything about lotteries. It has discovered something about itself. Every false positive it produces is a defect in the method — one that would have passed unnoticed on messier data where the truth is unknown. So the project was run to its natural end: build a genuinely serious modelling stack, point it at a process that should contain nothing, and record honestly what it claims.

The subject was the Romanian national lottery — Loto 6/49, Loto 5/40 and Joker (5 of 45 plus a Joker ball of 20). The 6/49 history runs to 2,565 validated draws going back to 1993; Joker to 398; 5/40, a newer game, to 61. Every record was eventually reconciled against the official operator archive and cross-checked against independent secondary sources — but, as section 06 records, several integrity failures surfaced only months in, after they had already shaped results.

What follows is written the way a laboratory notebook should be: the failures at the same resolution as the results.

It began in January 2024 with a set of TensorFlow specifications and a spreadsheet of 102 draws. It ended on 8 August 2026 with a seventy-test randomness audit and a decision to stop. Note that the file timestamps do not show this: archiving into DEPLETED reset them, so nothing on disk appears older than March 2026. The working record kept in conversations/ covers the final five months in detail; the two years before that are the neural-network era, which survives as designs and results rather than as dated files. Seven distinct eras, each ending because the era's core assumption broke.

The project's original ambition was limited by hardware, and several source files carried that limitation in their names. The specifications were sized for machines that were never available. Estimated requirements, as assessed at the time of the port:

Every one of these was ported down to a CPU-sized scikit-learn equivalent, and the ported versions ran in about two minutes on a laptop. Then came the finding that retired the entire complaint: an architecture search across the ported family selected the smallest network in the set — two hidden layers of 32 units — as the best performer. With roughly 100 training rows, the small network generalised and the large ones memorised.

The binding constraint was never compute. It was data, and the data was intrinsically uninformative. An A100 would have reached the same conclusion faster and at greater expense. This is worth stating plainly because “if only I had more GPU” is one of the most common and most comfortable explanations for a null result, and here it was measurably false.

Very little, and none of it in the way it was expected to. These are the ideas that survived contact with an honest backtest — several of them survived by being useful engineering rather than useful prediction.

Each of these was implemented, measured, and rejected on its own evidence. Several had been reported as successes first.

These are not incidental defects. Each one produced a number that was believed, acted on, and in several cases carried forward across multiple sessions before it was caught. The pattern is worth more than the individual entries: every single one inflated the result rather than deflating it.

There were real hits. Every ticket below was fixed before its draw. They are recorded here in full, best and worst together, because a results table that only contains the good draws is exactly the failure mode this project exists to document.

The 3-of-6 is the best live result the project ever produced, and it came from the simplest model in the repository — strict pair-binomials over three-draw matrices, no frequency term, no machine learning, no tuning. At the time it was taken as validation. Its own backtest reported a ≥3 rate of 4.11%, and the exact probability of 3 or more matches on a random 6/49 ticket is 1.86%. One event at roughly 1-in-50 odds, drawn from dozens of tickets across three games, is precisely what chance looks like.

Two hits happen 13.24% of the time by pure chance. Across the whole ledger the average sits where the mathematics says it must: around 0.735 hits per 6/49 ticket, 0.735 being exactly 36/49.

An independent audit of the 6/49 stack found that the chronology was clean — no target draw was ever fed to a predictor meant to forecast it. The leakage sat one level up, in model selection, and it was systematic. This is the failure that matters, because it requires no carelessness about time ordering, which is the one everybody is trained to look for.

None of this needed bad intent or sloppy code. It only needed a large model space, a short evaluation window, and the entirely natural habit of reporting the winner without paying for the search.

Every model was re-run strictly causally over the full history — 2,561 predictions — against the exact hypergeometric expectation of 36/49 = 0.734694 matches per ticket.

The binomial model — the one with the most favourable recent window, the most development effort behind it, and the project's single best live result — scores below chance across the full history. The spread of the whole table is consistent with noise around 0.735.

An evidence-gated selector was then written to make the standard explicit rather than optional: declare a small model family in advance; evaluate strictly causally over 2,365 targets; compare against the exact hypergeometric distribution; Holm-correct across the entire family; require significance on both the full run and the most recent 400 draws, plus improvement in four of five chronological blocks. Its verdict on all nine declared models was Holm p = 1.0000 — NO MODEL PASSED — and it fell back automatically rather than shipping a number it could not defend.

Before accepting a null, it was worth bringing the strongest available structure-detection tools to bear. If instruments this powerful find nothing, the finding is close to definitive. Each was run against a shuffled control of the same data.

The correlation dimension of the real series is indistinguishable from that of its own shuffle — there is no attractor, the draws fill the space uniformly. Topological feature lifetimes give a real-to-shuffled ratio of 1.011. The transition matrix has eigenvalues λ₁ = 1.0 and λ₂ = 0.089, a spectral gap of 0.911: the system forgets its previous state almost immediately, where a structured process would sit below 0.3. An FFT did surface a periodic component near 2.4 draws with a signal-to-noise ratio of 6.67, which on inspection is the natural oscillation of draw sums — high sum, low sum, high sum — and carries no information about which numbers appear.

Two research programmes were investigated at the suggestion that deep modern mathematics might apply. The Langlands programme — automorphic forms, Galois representations, Shimura varieties — concerns hidden symmetry in arithmetic structures. A lottery draw has no number field, no Galois extension and no L-function to analyse; the connection is philosophical, not technical. Floer homology and gauge theory operate on continuous 3- and 4-manifolds, where a lottery is a finite discrete space with no non-trivial topology. The one genuinely transferable descendant of that world was topological data analysis, which was implemented, run, and returned the null above.

Backtesting a predictor asks a weak and multiplicity-prone question. The prior question is stronger and has one answer: is this draw process distinguishable from a fair 6-of-49 sampler at all?

Seventy heterogeneous tests were run and corrected as a single Holm family — marginal frequency χ² on the full history and on the 2024+ era, per-position uniformity for all six drawn positions, lag-1/2/3 overlap against the hypergeometric law, 49 Wald–Wolfowitz runs tests, gap and waiting-time against the geometric law, draw-sum against an exact enumeration of all C(49,6) subsets, odd-count and low-count against hypergeometric, pair co-occurrence dispersion, first-half against second-half frequencies, and pooled autocorrelation at lags 1, 2, 3 and 7.

Fewer raw hits than chance alone would produce. The borderline KS statistic was checked for direction, because a two-sided p near 0.05 is exactly the kind of result this project had learned to over-read. The deviation runs toward large p-values (one-sided p = 0.027), the signature of conservatism from discreteness and cell pooling. The direction that would indicate real structure gives p = 0.77.

The balls are random. The players are not — and in a pari-mutuel game the players are half of the outcome. Categories I, II and III split a fixed pool among everyone holding the winning combination, so what a win pays depends on how many other people chose the same numbers.

That makes the official winner counts a revealed-preference measurement of human number choice, published draw after draw for years, entirely free of the randomness that defeats prediction. The count of category IV winners is high precisely when the drawn numbers happen to be ones players favour.

A harvester was written against the operator's public results archive and recovered 845 draws, 2018-01-04 to 2026-08-06, with per-category winner counts and prize values. Ticket sales were proxied by the category III pool and the proxy was verified against the data: cat3_winners × cat3_value equals exactly one third of the category I contribution on every draw checked, so both are fixed shares of sales and neither is disturbed by a rolled-over jackpot.

Fitted by ridge-penalised Poisson maximum likelihood, coefficients centred for identifiability, sales entering as a log offset. Each βᵢ is the log-scale popularity of number i.

After sixty versions of being fooled by a flexible model on a flat surface, the burden of proof here was set deliberately high. Three checks, each answering a different objection, each capable of killing the result on its own.

The permutation result matters most. When the association between numbers and counts is destroyed, the fit collapses to well below the null — the improvement is not the model bending to accommodate noise, which is exactly what every earlier “win” in this project turned out to be. The temporal result is what makes the effect usable: an eight-year-stable human habit rather than a moving target.

A textbook birthday effect: everything above 40 avoided, low numbers and lucky seven crowded. It independently reproduces published findings on the Israeli and UK lotteries — with one local inversion. Here 13 is the single most over-picked number, the opposite of the Western superstition, and a useful reminder that a preference model estimated in another country does not transfer without being re-measured.

Under the fitted model a combination is chosen with probability proportional to the product of its numbers' weights. Normalising that over all C(49,6) combinations is the elementary symmetric polynomial e₆(w), computed exactly by the standard dynamic-programming recurrence rather than sampled. Expected rival winners in each category then follow:

Categories I, II and III are evaluated by enumerating every draw consistent with 6, 5 and 4 matches — 1, 258 and 13,545 draws respectively. The inner polynomials over the 43 non-drawn numbers reduce to power sums, so each draw costs constant time. Two unit checks anchor the implementation: the dynamic program matches brute-force enumeration on a reduced pool to thirteen significant figures, and e₆(1,…,1) returns exactly 13,983,816. Category IV pays a fixed amount and is immune to sharing.

Stated limits of the preference model:

The transferable output of this project is not a ticket. It is a calibrated set of practices, each one earned by a specific, documented failure observed on a surface where the right answer was known in advance:

This matters directly to the rest of the KORT-X programme. A framework such as Projective Correlation Theory lives or dies on whether its confirmations survive the same scrutiny, and cosmological data does not come with a known answer at the back of the book. A pipeline that cannot resist manufacturing an edge on a lottery cannot be trusted to report an honest null on anything harder. Every practice above now applies to that work.

Every number on this page is derived from the archived code and the validated draw databases, but strict independent reproduction is not yet packaged — see the end of this section for exactly what is missing, with the exceptions named in section 13. The working tree holds forty-one Python modules across the three games, plus superseded versions kept for provenance. Grouped by track:

Alongside the code sit twelve dated session records under conversations/ — the primary source for everything above, including the post-mortems that were wrong at the time. The draw databases are validated on every write: row counts reconciled across CSV and workbook, every row six distinct in-range values, dates ascending, Joker balls in 1–20, and a canonical SHA-256 fingerprint recorded in the prediction ledger. What is still missing before anyone should call this reproducible in the strict sense: a README, a dependency lock, a licence, a tagged release with a DOI, and one command that regenerates every table on this page.

A broader literature survey conducted during the project found no published method that statistically beats the random baseline on real lottery draws. The most-cited recent frameworks combine decay-weighted frequency, transition matrices, clustering and Monte Carlo into a single ensemble — precisely the architecture this project had already built and measured. That absence of a positive result in the literature is itself corroborating evidence, and it was available from the start.

This was not solo work, and the most useful contributions were almost always the ones that removed a result rather than added one.