Standard cosmology draws three horizons around every observer, and they are not three names for one thing — they are three different numbers, measured today at 46.2, 14.4 and 16.6 billion light years. This instrument asks one question of each: what does it need in order to exist? Two of them need only the count — a rate, and a place where the rate reaches zero. They survive the striking of t intact, and in the long run they converge on a single radius. The third is an integral whose lower limit is a first frame. It is the only one that requires a beginning, and it is the only one that does not survive. Strike t and the bang goes out with it — not denied, undefined — leaving one seam at c/H.
“There is a farthest block the car can ever actually reach — but there is no limit on how long it can keep riding.”
Every line below is textbook cosmology, computed from the Planck 2018 parameters — H₀ = 67.66 km/s/Mpc, Ωm = 0.311, ΩΛ = 0.689. Nothing here is proposed. What T Theory adds is the last row of each card: the audit of what the definition presupposes.
Two of the three are already familiar to this corpus. The event horizon is where line 07 of The Horizons sends the count to zero. The Hubble radius is the reciprocal of the stretching rate. Both are statements about ν — about how fast the counting runs and where it stops. Neither one mentions a beginning, and neither one would notice if you removed every clock in the universe.
The particle horizon is different in kind. It is not a place. It is an accumulated opportunity — the running total of how far light could have got if it started at a particular moment and nothing had interrupted it. Take away that moment and there is no total to run. The integral does not evaluate to infinity; it does not evaluate at all. Its lower limit is missing.
Drag the scale factor and watch the three horizons move. The instrument integrates the Friedmann equation numerically at every step — nothing here is a stored curve. Note what happens as Λ takes over: the Hubble radius and the event horizon close on one another and settle onto a single value, c/H∞ = 17.4 Gly — the de Sitter seam, where ν → 0. They converge because they were always the same statement about the count, read once inward and once outward. The particle horizon joins nothing. In proper distance it diverges without limit, and it does so because it is not measuring the world — it is accumulating a history.
Set the slider far to the right and read the gap: Hubble − Event falls to zero and stays there. One seam. That is what a universe looks like when the stretching becomes steady — and steady stretching is the only regime the Three Locks memorandum ever describes.
One honest caveat, since this instrument is not an oracle: in comoving coordinates the particle horizon does converge — to about 62.8 Gly. Nothing beyond that comoving radius will ever come into view. Switch the toggle and watch it flatten. That is a real and important fact, and it does not rescue the integral: a comoving limit still has to be accumulated from a first frame to be computed at all.
This is de Sitter's static form — textbook relativity, the same line 07 already published in The Horizons. From every observer's seat the count runs full at home and thins outward, reaching zero at R. Drag along the radius below and read the count. Note that the curve does not care which direction time runs, because no t appears in it. It is a statement about here, at every here.
Feed this lapse to line 03 — g = −c² ∇ ln ν — and the fall points outward, growing with r. That is the acceleration astronomy bills to dark energy, arriving here as the same fall the Gravity Equations already wrote, merely inverted. And at r → R the count reaches zero: light emitted there arrives infinitely redshifted, frozen, never landing. Which is exactly what is seen.
The Three Locks memorandum explains the first lock with a toy car on a living track: the car runs 300 blocks per minute, and every block copies itself once every 100 minutes. From that it derives a horizon at 30 000 blocks, an arrival time of 17 h 10 m 54 s, and a stretch to 900 million blocks.
Those are not illustrative figures. A track where every block spawns at a fixed per-block rate is growing exponentially — which is to say it has a constant Hubble rate, which is to say it is a de Sitter universe. Run the arithmetic and the memorandum's numbers come back exact: the horizon is c/H to the block, and the arrival time is right to the second. Change the two dials below and check it yourself.
Now read the model for what it actually says. Every block spawns forever. There is no first block, no moment the track was laid, no instant before which there were no blocks. The memorandum never supplies one, and its arithmetic never needs one — the horizon falls out of c and the spawn rate alone. A steadily stretching track has a horizon instead of an origin. That is the whole of the first lock, and it is stated without a beginning anywhere in it.
This is the point at which the memorandum and T Theory turn out to be the same document. The static patch of de Sitter space — the observer's own seat, the one the lapse above describes — contains a seam at R and no t = 0 at any point in it. The beginning appears only when the same space is re-sliced into flat coordinates and a global clock is insisted upon. Insist on t and a first frame appears at the bottom of the slicing. Strike t, keep the seat, and there is a wall — but nothing behind it that ever went bang.
What is measured at the far edge is not a beginning. It is a temperature: 2.7255 K, arriving from matter that was ≈ 3000 K when it let the light go, redshifted z ≈ 1100. That is the entire observation. The 13.8 billion years and the 46.2 billion light years are both computed from it — conversions of a measured depth into a duration and a distance, using the very clock whose existence is the question.
Watch anything fall toward a seam and it slows, reddens and freezes at the edge; the crossing never arrives on your clock. Established for black holes, and established for the sky — distant supernovae visibly run slow, stretched by exactly (1+z). Now stand inside and look out. The deepest shell hangs at its earliest frame, its first light photographed mid-fall and never landing. There is no memory of an explosion in that wall. There is an edge where the count thins to zero, and it glows because the count is thin, not because anything detonated.
All three horizons as standard cosmology, with the Planck 2018 values that generate them; the numerical integration of the Friedmann equation performed live on this page. The de Sitter static lapse √(1−r²/R²). The convergence of the Hubble radius and the event horizon on c/H∞ in a Λ-dominated future. The CMB at 2.7255 K, z ≈ 1100 (Penzias & Wilson 1965; COBE, WMAP, Planck). Cosmological time dilation — supernovae run slow by exactly (1+z). The Bekenstein bound and the holographic principle. The exponential toy track of the memorandum is de Sitter, and its published figures are reproduced here to the second.
The thread: every t replaced by the count ν. The audit of the three definitions — that two are statements about ν and one is an accumulation requiring a first frame. The reading that the particle horizon is therefore not a feature of the world but the shadow of the assumption, and that striking t leaves the bang undefined rather than refuted. The CMB as the frozen edge rather than a memory of an explosion. The universe as the inside of a lock; every seat its own centre; expansion as line 03 pointing outward. All of it reading, worn openly.
ΛCDM fits the CMB acoustic peaks superbly, and any re-reading must one day meet that data point for point — this page does not claim to. That de Sitter's static patch has no t = 0 is a statement about that patch and its slicing, not a proof that the universe is exactly de Sitter; the real universe is matter-dominated in its past, and the singularity theorems, inflation and the identity of dark energy all stay open. The comoving particle horizon does converge, and that convergence is a genuine physical fact this reading does not dissolve. The wall shows what the wall can show.
Two of the three horizons never needed a beginning, and in the end they are one seam. The third is an integral with a zero at the bottom of it. Take away the clock and you do not lose the sky — you lose the zero. There was no first morning. There is an edge where the counting runs out, and from inside, every edge looks like a dawn.