For you if you have a structural claim about the zeros, a spectral operator, a positivity argument, a pattern in the statistics, and you want to know whether it is about ζ at all before you spend a month on it.
First command:
.venv/bin/python scripts/23_gate_3_battery.pyWhat this door does that a notebook does not
A plausible "explanation" of RH now costs minutes to generate: discretize an operator, fit a spectrum, tell an evocative story. A referee's rebuttal traditionally costs days. This door makes the rebuttal cost minutes too.
It does not tell you whether your claim is true. It answers a weaker and decidable question: is your demonstration about ζ, or about any function that happens to look like ζ? Most claims die here, and they die for reasons that do not depend on anybody's taste.
docs/17-the-falsification-harness.md is the methods retrospective: five independent claims of zero structure arrived in a single day, and the standing instruments dispatched all five.
The four instruments
| Instrument | The question it asks | If your claim fails |
|---|---|---|
| Rivals | does it also hold for a function that satisfies the same functional equation and violates RH? | it explains nothing, see zeta.epstein.battery, gate #3 of docs/09 |
| Decoys | does the result survive when the primes are swapped for non-primes, or merely reordered? | it was never reading the arithmetic, zeta.spectral_gate |
| Surrogates | does a null model with no arithmetic in it reproduce the pattern? | the pattern is a property of the model class, zeta.surrogate, NULLCONTROLS.md |
| Lesions | does your detector notice a violation planted on purpose? | your detector is blind, and its silence measures that, not the world, zeta.detectors |
The rival test is the sharpest, because it needs no threshold and no statistics. It is a modus tollens: if the Davenport–Heilbronn function has the property too, and it has zeros off the line, then the property cannot be why the zeros are on the line.
If your claim is about the Euler product, read this before you celebrate a pass. Davenport–Heilbronn and the Epstein zetas are built by combining Euler products, so neither can test a claim whose content is the Euler product itself. The rival set carries one that can: W_a(s) = ζ(s+a)ζ(s−a) has a scalar Euler product, multiplicative coefficients, the functional equation, and zeros on Re s = 1/2 ± a by Hardy's theorem alone. Its scope is stated in docs/09 §5.1: it sits outside the Selberg class, so a claim it shares is blind to a shift rather than irrelevant, and the repair it forces is that you name which normalisation your mechanism uses and where.
Running it on your own claim
Write your claim as a predicate over the interface dict and hand it to the battery:
from harness import get_department, run_battery
from harness.departments import load
load("zeta")
battery = get_department("zeta").battery
def my_claim(iface) -> bool:
return abs(iface["Z"](14.5)) < 1.0 # whatever your structure is
verdict = run_battery(battery, my_claim)
print(verdict.summary())
print(verdict.shared_with) # the rivals that also have itverdict.distinguishes is the only field to act on. It is true exactly when the claim fires for ζ and for none of the rivals.
What a pass does and does not mean
A claim that distinguishes ζ from every rival is a candidate for where a real proof must live. It is not evidence for RH, and nothing computed in this repository ever will be, see docs/08-why-it-is-hard.md for Littlewood's theorem and why a pattern holding for every computed case can still be false.
Related: discover.md, for generating leads rather than refuting them.