THE DOOR — pre-registered protocol, version 1 (published 28 Oct 2026, before any data was collected)

Question
Can any participant (a person, an AI agent, or anything else that can send a request) predict a random bit better than chance?

Randomness
drand quicknet (League of Entropy), chain hash 52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971, one round every 3 s.
The cosmic bit of round r is the first bit (most significant bit of the first byte) of that round's published "randomness" value.
Anyone can check any round at https://api.drand.sh/<chain>/public/<r> and verify its threshold BLS signature with drand's public key.

Trial
A guess (0 or 1) is stored by apexfaucet.xyz with target round = (current round at the moment of storing) + 2.
That round does not exist yet when the guess is stored (it is published 3 to 6 seconds later).
A trial is a hit if the guess equals the target round's cosmic bit. Every stored guess is one trial; none is ever removed.

Primary hypothesis (the only confirmatory test)
H0: the hit rate is 0.5.  H1: the hit rate differs from 0.5.
Test: exact two-sided binomial test on the first 50,000 resolved trials stored after this protocol's publication.
Threshold: p < 0.001. Sample size chosen to detect a hit rate of 51% (or 49%) with about 86% power.
No interim stopping: the live score shown before 50,000 trials is descriptive only and is not the test.
Every other pattern anyone finds (by visitor, time of day, message, round) is exploratory and must be confirmed in a new, separately
pre-registered run before it is called anything.

Integrity
Guesses and messages are stored append-only. Every hour a SHA-256 hash chain of that hour's guesses and messages is written to the Arc
blockchain (a zero-value transaction from 0x024b82335C29Fa5606a8ea5c1D24FC9eAD50700C with data 0x444f4f52 ("DOOR") + the hash), so the
record cannot be changed later, by us or anyone. The raw data stays downloadable at /api/door/... so anyone can recompute every hash.

What a result would and would not mean
p < 0.001 would mean the hit rate deviated from chance under this model. It would not show who or what caused it; hardware faults,
software bugs, clock errors and manipulation must be ruled out, and an independent replication is required before any stronger claim.
A null result is a result. Paying APEX for any tool never changes a trial: money buys art and tools, never a better chance.