World The bacterium is called ringkeep.
It is not one cell.
It is the film.
The cells count themselves with a signal they keep in the wall, because the wind would carry a loose scent into the heat and the count would be lost.
When the signal holds, they build.
When the water freezes or the day face dries them, the household dies together.
The mould is called linger.
One body, a skin, a mouth that is its whole surface.
It feeds the growing edge through itself, the way a person feeds a child who has not left.
It will not fuse with a stranger.
It grows old in place and dies where it fed.
It still has no nerve, and it still does not wonder.
A virus remains a parcel until ringkeep or linger lets it in.
A quorum is a count made of molecules.
Gram-negative films often use an acyl-homoserine lactone: one enzyme makes it, and a receptor binds it only when the neighbourhood has filled.
Gram-positive films more often use a short peptide and a two-part sensor.
A third signal, from LuxS, can cross between kinds.
The ring wind blows from the night toward the day, so a signal that dissolves into the air is swept into the heat and the nightward cells never hear that they are many.
Ringkeep keeps its count in the sticky wall, a peptide, not a scent.
The dayward edge of the film hears the count first.
That is where the wall is built.
Ringkeep is a gram-positive cell, about a micrometre across, with no nucleus and no organelles.
A thick peptidoglycan wall, tens of nanometres, carries teichoic acids and holds the peptide count.
Outside that, the shared film is polysaccharide, protein, and loose DNA: the household is not inside the cell.
The membrane is a bilayer that must stay fluid from the ice at 273 K to about 320 K, so the cold edge uses more unsaturated lipids and the hot edge more saturated ones.
The chromosome is one circle.
The ribosomes are 70S.
Energy comes from the litter and from the oxygen the wall-forest made.
There are no thylakoids.
When the film dries or freezes, the household dies.
A few cells leave an endospore, which is a packed copy, not a mind, and not a rescue of the rest.
The wall is a chain of two sugars, N-acetylglucosamine and N-acetylmuramic acid, with a short peptide on the second.
Strands are tied by those peptides.
The cell divides by a protein ring at the middle, FtsZ, and builds a cross-wall there.
In the film the daughters often stay stuck, which is how the household thickens.
A spore is not a child.
Starved, the cell divides near one end, the mother swallows the small half, and a hard coat is laid down.
The copy inside is dry.
One cell becomes one spore.
When water returns, one cell comes back.
The rest of the film does not.
Ringkeep is set free inside its own vortex.
A cell copies its circle from one origin, the FtsZ ring splits it, and the two stay in the film.
The dead are the food of the living.
At the dry edge a few become spores and the sticky wall keeps them, so the wind that blows toward the day does not take the children.
Water returns them to the film.
The count, the split, the spore, and the return are one loop.
It does not need the cities.
It still needs liquid water, and it still has no nerve.
A vortex dome runs around the three Earths, not around ringkeep alone.
In it are the films that only eat litter, the producers that poison other bacteria, the toxin-bearers, the invaders that go inside a cell, the spore-formers that wait, the phage that eat bacteria, the viruses that need a person, and the moulds that eat living tissue instead of leaf.
They spread from First to Red to Shore on the dome and back.
They fight each other.
The producers and the phage take the invaders in the film before a child meets them.
A parent who has already met a disease holds the memory, and the child starts inside that cover.
The empty ice shell and the nitrogen sea are on the path and have no host, so the dome passes them.
The result of the fight is not a winner among the diseases.
It is the next generation still alive.
Ringkeep is in the dome and out of its vortex.
The vortex is an empty loop: peptide thinning, no household, the wind blowing through.
The black side is not the same on each Earth.
A million trials on each, run together: on First every cell divides, night included, because the dark there is still near 280 K.
On Shore the same, night is a dark sea.
On Red, 574,006 of a million still divide, on the ring and on the wind-held night.
425,994 are gone: 249,326 in the deep black near 60 K, where the air can snow and a free cell cannot finish a spore, and 176,668 on the hot day past 320 K.
Nothing copies in that deep black.
Frost is what is there.
On First the dark turns away.
A free cell is scattered and still divides, near 280 K at night and warmer by day, and by morning the film has no household left, only cells.
On Shore the night is a dark sea, still liquid, so the cold does not kill them.
The ones that stay on the wet rock divide.
The ones the water lifts off the shore are diluted and do not reform the film.
On the ice shell the ground is frozen at 255 K under 19 gravities, and on the nitrogen body the sea is near 70 K.
A cell carried there is gone.
No spore is finished, and no next generation starts.
Jupiter at one bar is about 165 K.
The air is hydrogen and helium.
Ringkeep's temperatures, 273 to 320 K, fall near 6 to 10 bar, and by 22 bar the air is already about 400 K.
Saturn at one bar is about 134 K, so the same band is deeper, near 12 to 21 bar.
There is no ground in either band.
A free cell falls through it.
There is no leaf to eat and no oxygen from a forest.
Below the band the heat does not stop.
No film, no spore finished, no next generation.
Earth's air at the ground is about 288 K and one bar, nitrogen and oxygen, with leaf and liquid water.
Ringkeep can divide there.
The air cools about 6.5 K a kilometre, so 273 K is only about 2.3 kilometres up, near 0.76 bar.
Above that a free cell is in the cold.
The top of the weather is near 11 kilometres and 217 K.
Higher, the ozone layer warms again to about 270 K near 50 kilometres, at a thousandth of a bar, which is not a place to live.
Nothing below the ground gets hotter with depth in the air, because the ground is already there.
A cell that stays low divides.
A cell lifted out of the vortex into the high cold is gone.
Spo0A is switched on by a phosphate on one aspartate.
The phosphate starts on a sensing kinase, moves to Spo0F, then to Spo0B, then to Spo0A.
Phosphatases strip it at Spo0F unless a short peptide, reimported from the wall, has blocked them.
A little phosphate makes the cell kill a neighbour and eat it.
A lot of phosphate starts the spore.
The deep black near 60 K freezes the cell before this chain can finish.
Phosphorylated Spo0A binds DNA as a dimer.
The word is seven letters, TGNCGAA, and a useful site is two of those words about one turn apart, so both sit on the same face of the helix.
A helix-turn-helix from each monomer enters the major groove.
A good match to the word is held at a little phosphate: that is the killing of a neighbour, and the silencing of the repressor AbrB.
A poor match waits until the phosphate is high: that is spoIIA, spoIIE, and spoIIG, the start of the spore.
Where the words sit decides the rest.
Over a promoter they block it.
Upstream of one they help the polymerase begin.
Five kinases can start the cascade.
Each puts a phosphate on itself from ATP, then onto Spo0F, which passes it to Spo0B, which passes it to Spo0A.
Spo0B cannot take a phosphate from ATP.
It only forwards one.
Rap phosphatases drain Spo0F unless the wall-peptide has blocked them, and Spo0E drains Spo0A itself.
A cell that gets a little ahead makes more of the relay, so the lead grows.
Most cells in a film never cross.
They stay dividers, or they are the ones eaten.
Only the cell that fills Spo0A starts the spore.
Out of the vortex the peptide is gone, the phosphatases stay on, and the cascade drains.
Spo0A does not turn up like a dimmer.
Spo0F is a sink: phosphate pools there before much reaches Spo0A, and the phosphatases drain it.
A cell that does get ahead makes more Spo0A and more Spo0F, so the lead feeds itself.
That is a cliff.
Below it the strong DNA words fire, the cell kills a neighbour, and a protein it secretes delays the neighbour's own cliff.
Above it the weak words fire and the spore begins.
In one film only a minority cross the second cliff.
Out of the vortex the drain is open, the sink never fills, and neither cliff is reached.
Moving a phosphate from kinase to Spo0F to Spo0B to Spo0A takes seconds.
The aspartyl phosphate does not last, and Spo0E cuts it short.
In one cell the level does not climb smoothly.
It pulses.
A pulse that fades fires only the strong words: kill, eat, and go back to dividing if food returns.
Pulses that come again before the last has drained hold the weak words long enough to cut near the pole.
After that cut the cell does not go back.
In a warm lab the rise to that point takes about two hours, and a finished spore about eight.
On the ring, near 290 K, the same enzymes are several times slower.
Out of the vortex each pulse is emptied by the phosphatases before the next begins, so the weak words never stay occupied.
The word is TGNCGAA, twice, about ten bases from start to start, so both copies face the same way on one turn of the helix.
A strong pair is filled by a small pulse.
That pulse can silence abrB and start the killing genes, then fade, and the cell goes back to dividing.
A weak pair needs a taller pulse, or several pulses before the proteins from the last one are gone, so the peak ratchets up.
Only then do spoIIA, spoIIE, and spoIIG stay on long enough to cut near the pole.
Out of the vortex the tide is emptied every time, and the weak pair stays bare.
The ideal word is T, G, T, C, G, A, A.
The third letter is the loose one: A or T in the original sites.
At abrB the two words are TGTCGAA and TGACGAA, with TAA between them.
The spoII words are the same seven letters matched less well, which is why a small pulse never covers them.
Every response regulator is switched by phosphate on an aspartate.
CheY has only that domain: it binds the flagellar motor and the phosphate lasts seconds.
Spo0F is the same kind of bare receiver, and it only carries the phosphate onward.
OmpR is a DNA-binding cousin with two thresholds, low for one porin and high for the other, but its kinase phosphorylates it directly.
NarL and FixJ share Spo0A's helix-turn-helix, and they are also direct.
ComA in the same bacterium is switched by a peptide too, except the peptide turns the kinase on, whereas ringkeep's peptide blocks the phosphatase.
Spo0A is the one that waits through four transfers, pulses, and only then chooses kill or spore by how full it is.
These proteins are made in the same room as the DNA.
A sigma factor seats the polymerase, the message is read off at once by a 70S ribosome, and the chain folds as it comes out.
CheY is made from a flagellar message, only when the cell is building motors.
OmpR, NarL, FixJ, and ComA are made on messages that also carry their kinases.
Spo0A is made twice: a little all the time, and a lot from a second promoter once the cell begins to starve, and phosphorylated Spo0A turns that second promoter up.
The phosphate is not part of the making.
It is added to the finished chain.
Spo0A is a chain of amino acids, about 270 in the bacterium where this was solved, near 30 kilodaltons.
The backbone is the same all the way: nitrogen, the central carbon, and a carbonyl, joined by peptide bonds that were made by losing water.
Twenty kinds of side chain hang off that backbone.
One aspartate, acid-tipped, is the letter that later receives the phosphate.
The DNA-binding half uses arginine and its neighbours to read TGTCGAA.
Carbon, hydrogen, oxygen, nitrogen, and a little sulfur are the whole of it.
The DNA words are not part of the protein.
A chain folds because water pushes oily side chains together and the backbone hydrogen-bonds into helices and sheets.
It does not search every shape.
Local pieces form as the ribosome finishes them, and a small domain can be done in a fraction of a second.
Spo0A is two domains: a sheet-and-helix receiver, and the helix that reads TGTCGAA.
Each folds on its own.
The phosphate does not make the fold.
It tips the receiver from a quiet shape into the one that lets the two chains dimerize.
Heat past the day face, or a freeze in the deep black, stops the motion that folding needs.
A new chain meets a chaperone on the ribosome first, which covers oily stretches so they do not glue to another chain.
If that is not enough, DnaK binds those stretches and lets go when ATP says so, and the chain tries again.
GroEL is a cage: it can shut a chain of Spo0A's size inside, away from the crowd, and give it a few seconds.
A receiver as small as CheY usually finishes without the cage.
The chaperones spend ATP and they do not add the phosphate.
On the hot day the cell makes more of them.
In the deep black they have no liquid water and no ATP turnover, so a half-made chain never gets a second try.
GroEL is fourteen chains, seven in a ring and two rings back to back.
Each chain has three parts: a base that holds ATP and the other ring, a hinge, and a top that binds an oily chain.
The open top is oily, so an unfolded Spo0A sticks there.
Seven ATP and a lid of seven GroES chains swing those tops up and turn the lining wet.
The chain is dropped into a cavity about twice as large and folds alone for a few seconds.
Then the lid comes off.
Spo0A is near 30 kilodaltons and fits.
A protein much past 60 does not.
The phosphate is not added inside.
An oily patch on a misfolded chain sticks to the open rim.
When the seven tops swing up, that grip can pull a bad fold apart, and then the lining turns wet so the chain has nothing to hold.
It drops into the closed room and folds alone, by the same forces as in open water, for a few seconds set by ATP.
If it comes out still wrong, the rim can catch it and pull it open again.
The cage never supplies the shape.
The amino-acid order does.
Hydrophilic means the side chains form hydrogen bonds with water: the acids aspartate and glutamate, and the polars serine, threonine, asparagine, glutamine.
In the closed GroEL room those face inward, and many of the acids make the wall negative.
The oily letters, leucine and its kind, are turned away.
An unfolded chain sticks to oil, not to this wet wall, so it lets go and folds in the water.
The open rim is the opposite lining.
The swing of the seven tops is what swaps them.
A folded protein is an oily core wrapped in a wet surface.
That is the same swap the GroEL lid makes, done by the chain on itself.
Water pushes leucine and its kind inside.
Aspartate, lysine, and the polars stay out, so the finished protein does not stick to its neighbours.
A membrane protein is the inside-out case: its oily face stays out, against the oily lipid, and a wet channel can run through the middle.
A chain that cannot bury its oil at all stays loose.
When a core opens, in heat or in a new chain, the oily face is public again, and other chains glue to it.
That glue is what the cage is for.
The rule is not special to Spo0A.
An evolved domain is stable by about 5 to 12 kilocalories a mole.
At 290 K that means, of a million Spo0A chains, fewer than about 200 are unfolded once they have had time to finish, and at a deeper stability it is about one.
The risk is not a wrong shape at equilibrium.
It is clumping before the fold finishes.
A random chain of the same length almost never has a stable fold at all.
In the deep black the chance is zero, because nothing moves.
The exact Spo0A sequence, about 270 amino acids and twenty choices at each, is one in about 10^351.
That is not how it arises.
A gene that already works is copied.
A much shorter random chain can still do a small job: in a laboratory library of random 80-amino-acid chains, a weak ATP-binding fold turned up on the order of one in 10^11.
Ringkeep does not roll Spo0A.
The mother copies the circle, and the spore carries that copy through the dry edge.
A gene for this protein is about 810 bases.
One exact string of those bases is one in about 10^488.
The code is degenerate, so many strings spell the same chain, and any of them is still one in about 10^357.
That is not how spo0A appears.
The receiver half is an old gene, shared with CheY and Spo0F, copied and joined to a DNA-binding half.
Ringkeep copies the circle it already has.
Forming one peptide bond in water is uphill, on the order of a thousand to one against at one mole a litre, and a million to one against at a millimole.
A chain of 270 is 269 such bonds.
At that dilute concentration the equilibrium is one in about 10^1614, and that is for any sequence at all.
The sequence of Spo0A, given that a chain exists, is a further one in about 10^351.
The ribosome never rolls either number.
It joins amino acids that were already activated, using the copy it was given.
The air can be breathed. The sun is down. The trees rest. The stars hold the night.
Sun alone: oxygen 17.0 percent, the air cannot be breathed.
Trees in the dark: 18.2 percent, the air can be breathed.
Trees and sun: 20.5 percent, the air can be breathed.
2.3 points of that oxygen are in neither part.
They appear only together.
Two stars share one balance point.
The sun is 1 solar mass.
The other is 0.55, twelve AU away, and they orbit every 33.4 years.
The sun's Roche lobe is 5.2 AU and the other's is 3.9.
Both stars sit far inside those lobes, so neither feeds the other.
The planet stays with the sun at 1 AU.
That is stable.
A planet around both would have to stand out past about 29 AU, and the light there is too thin for these trees.
The second star adds about a thousandth of the daylight, near magnitude -19, a few hundred full moons.
The air does not count it.
The oxygen is still the sun and the trees together.
Around the red star, at 0.35 AU, the heat matches this world: equilibrium 255 K.
The year is 103 days, the star looks 1.8 times wider, and the light is redder, about 4300 K.
With this world's dissipation the spin would lock in about half a billion years.
The sun then adds under one percent, slowly, over 33 years.
At the old 1 AU from the red star the equilibrium is 151 K and the water is ice.
Around both stars the nearest stable orbit is 29 AU, equilibrium 49 K.
Nitrogen freezes at 63 K and oxygen at 54 K, so the air falls as snow.
There is no warm orbit around both.
Locked, the day is the year: 103 days, and one face keeps the star.
The near ground, with no wind, would sit near 361 K.
The far ground would drop until the air snowed out.
An Earth-thick wind can carry heat across, because a 103-day spin barely turns the flow.
The ocean bulge is about 2 metres and, once the day matches the year, it stops travelling.
The heat of the slowing is a fraction of the heat already leaving the ground, and it ends when the lock does.
A leftover oval does not warm the world.
The tilt damps, so the seasons end.
Under the red star the bare ground, reflecting as this world does, is 360 K.
That is the heat arriving and leaving from the same point, with no wind and no blanket.
Share the heat over the day face and the radiating temperature is 303 K.
This world's blanket, the same ratio that lifts 255 K to 288 K, would lift the unshared point to about 407 K and the shared day face to 342 K.
407 K is past boiling, so that blanket would thicken and the scaling breaks.
A cloud deck under the star, reflecting 0.6, brings the same point back to about 354 K.
Two thirds of this star's light is already redder than deep red, so the air takes a share before the ground does.
Rock remembers about 9 days.
Still water, about 6.
A mixed ocean of 50 metres remembers about 450 days.
The locked day does not move, so memory does not soften the point under the star: the ground still goes to the temperature of the heat that stays.
What memory does is set the wait.
Two metres of rock, radiating straight to space, would fall from 288 K to the snow point of the air in about 3 years.
The same drop for the mixed ocean takes about 150 years.
Heat leaking from the ground holds a bare surface near 35 K, which is under the snow point.
A kilometre of crust under the star takes about 30,000 years to warm through.
Nitrogen conducts about 0.026 watts per metre per kelvin.
Across a quarter of this world that carries about 4×10^-7 watts per square metre, against 950 from the star.
A thousand times more air does not fix conduction: the dense layer is not a thousand times taller.
The wind does the sharing.
At a thousand bar the day-night wind is about 7 metres a second, and the contrast it needs is about 0.02 K.
The air remembers about 60 years.
The surface temperature is then the adiabat, not the point under the star.
If the mix scales and the radiating level stays near half a bar, the ground is about 2200 K everywhere.
Rock melts.
The 360 K point does not survive.
Nitrogen's heat capacity at 300 K is 29.1 joules per mole per kelvin, 1039 per kilogram, which is 7/2 R.
The bond vibration, at a characteristic 3394 K, lifts it toward 37.4 per mole.
At ten thousand bar the ideal adiabat reaches about 3200 K, where the capacity is 36.7 per mole.
The wind there is about 3 metres a second and the contrast is about 0.004 K.
The ideal density at that point is already 1050 kilograms per cubic metre, denser than cold liquid nitrogen, so this is a fluid, not a gas, and the true ground is cooler than 3200 K.
It is still hot enough to melt rock.
At a hundred thousand bar the same ideal adiabat says 5400 K, a wind of 1.6 metres a second, and a contrast of 0.0007 K.
The heat capacity has reached 37.2 joules per mole, the molecular ceiling.
The ideal density is 6300 kilograms per cubic metre, heavier than rock, and the column weighs as much as 340 kilometres of it.
Repulsion, not the gas law, would carry that pressure, so the ground is cooler than 5400 K.
The triple bond does not survive being packed that hard.
A 200 kilometre layer of nitrogen at a million bar is a molecular solid near 255 K, not a gas.
Its own weight is about 40,000 to 90,000 bar, not a million.
To weigh a million bar in 200 kilometres it would have to be 51 grams per cubic centimetre, which nitrogen is not.
Once the heat of compression has left, the temperature stays near 255 K.
Down through the layer the adiabat of a stiff solid adds only a few degrees, or a few tens if the solid is soft.
The thousand-degree adiabat was the gas that was not allowed to cool.
Two thousand kilometres of nitrogen at 3.5 grams per cubic centimetre weighs about 700,000 bar at the base, and about 0.8 of this world's mass.
At 4.5 it weighs about 960,000 bar.
A million bar in this thickness wants a little more than 4.5.
The surface can be 255 K.
The heat does not cross two thousand kilometres in the age of a world, so the base stays on the adiabat, roughly 1100 to 2000 K, near 1600 K if the solid is of ordinary stiffness.
The outer few hundred kilometres are the part that can cool.
Four thousand kilometres at 3.5 grams per cubic centimetre is 2.1 worlds of nitrogen.
The base is about 1.5 million bar.
At 4.5 grams it is 2.7 worlds and about 2.1 million bar.
The surface can be 255 K.
On an ordinary adiabat the molecular solid would be about 1700 K at two thousand kilometres and about 2150 K at the base.
The bond is seen to give way near 120 GPa even when cold, and this base is past that, so the bottom is polymeric nitrogen.
The molecular temperature stops being the right description there.
Six thousand kilometres at 3.5 grams per cubic centimetre is 4 worlds of nitrogen.
Surface gravity is about 13.
The molecule fails about 2,900 kilometres down, near 120 GPa and 2000 K.
Below that the solid is polymeric.
If the density stayed 3.5 the base would be about 230 GPa; once the atoms pack tighter the base is heavier than that.
The molecular adiabat would have said about 2600 K there, and that number no longer describes the material.
At 255 K the top is not ice.
Nitrogen's critical point is 126 K, so the surface is a clear supercritical fluid, blue from scattering, with no ground, no clouds, and no weather worth seeing.
The solid begins a few gigapascals down, a few tens of kilometres under the light.
A thousand-kilometre coat at 3.5 grams per cubic centimetre weighs 34 GPa at the rock, about 1250 K on the ordinary adiabat, and the molecule is still intact.
The six-thousand-kilometre world presses about 230 GPa at the bottom, more once the polymer packs tighter.
A thousand kilometres of water ice on a rock 10,000 kilometres in radius.
The rock is about 5.3 worlds if it is packed like a large rocky planet, and the ice is about half a world more.
Surface gravity is about 19.
At 255 K the top is ordinary ice, with only a trace of vapor, so the sky is black and the ground is white.
The base on the rock is 40 GPa and about 400 to 480 K, which is ice VII, still solid.
A nitrogen surface at the same temperature would be a fluid.
This one is a floor.
A thousand kilometres of liquid nitrogen will not stay liquid.
On the 10,000 kilometre rock, a 70 K sea freezes at about two kilometres, near a few hundred bar.
Below that it is solid nitrogen down to the rock, about 31 GPa and a third of a world's mass.
Above 126 K there is no liquid at all, only a supercritical fluid.
The sea, where it exists, is clear, lighter than water, and cold enough to smoke.
The nitrogen sea on this rock gains about 150 bar a kilometre and freezes near 340 bar, so the liquid is about 2 kilometres and the solid under it is about 998.
Methane at 100 K freezes near 230 bar.
The sea is about 3 kilometres, the solid again about 997, and the base on the rock is about 14 GPa because methane is lighter.
At its boiling point, 112 K, the methane sea would be about 7 kilometres.
Above 191 K there is no liquid methane.
On the same rock a water ocean at the freezing point of ordinary ice reaches ice VI at 632 MPa, about 6,300 bar, near 32 kilometres down.
That is the bottom of the ocean.
The remaining ice, about 970 kilometres of it, presses 40 GPa on the rock.
Titan's surface is 94 K and 1.47 bar.
A kilometre of methane there adds about 6 bar.
This ocean bottom is about 4,300 times Titan's air pressure, and 180 degrees warmer than Titan's shore.
Ice VI is tetragonal, space group P42/nmc, ten water molecules in a cell 6.27 by 6.27 by 5.79 angstroms, density 1.31.
Two hydrogen-bonded frameworks interpenetrate and do not connect.
It is the solid at the bottom of a freezing ocean, from 632 MPa to about 2.2 GPa.
Earth's deepest water is about 110 MPa, and every ice sheet on Earth is still ordinary hexagonal ice.
Ice VI would need roughly 60 kilometres of ocean here.
The only dense ice found on Earth was trapped in diamonds, not made by the sea.
Ice VII is cubic.
The oxygens sit on a body-centred lattice and the hydrogens are disordered, two separate ice-Ic frameworks in one crystal.
It takes over from ice VI at 2.1 GPa, at a density near 1.6.
By 40 GPa the density is near 2.4 and the bulk modulus, carried from the measured fit, is about 250 GPa.
That is the base of the thousand-kilometre shell, 400 to 480 K, still solid, and just where the hydrogens start to drift toward the bond centres.
Ice X, with the hydrogen fixed in the middle, comes nearer 60 GPa.
Ice VIII is the same oxygens ordered, and only when it is cold.
In ice VII each oxygen has eight neighbours at one distance and a hydrogen in only four of the gaps.
Those four are the hydrogen bonds, and they join one framework.
The other four touch the second framework and do not bond to it.
The ice rules still hold: two hydrogens close to each oxygen, one per bonded gap, and the choice of which two is disordered.
At 40 GPa that disorder is intact and the proton is starting to drift toward the middle.
Near 60 GPa the two wells become one well, and the covalent bond and the hydrogen bond are the same thing.
Ice VII and ice VIII have the same oxygens.
In VII the proton sits off-centre in a double well and the choice of side is random, so the average crystal stays cubic.
In VIII every proton has chosen, one framework points one way and the other points back, the dipoles cancel, and the cube stretches a little and becomes tetragonal.
VIII is the cold form.
Warming it gives VII.
Squeezing either one toward 60 GPa flattens the double well into one well at the midpoint.
That is ice X, and the choice disappears.
The base of this shell, near 40 GPa and 400 to 480 K, is still VII: the choice remains, and the well is getting shallow.
Ice XI is hexagonal ice with the protons ordered.
The dipoles point the same way along the c axis, so the crystal is ferroelectric, unlike ice VIII, whose two frameworks cancel.
The change is near 72 K.
Pure ice stops rearranging before it gets there, so the laboratory form is grown with a trace of hydroxide to keep the protons moving.
Earth's ice is far too warm.
A surface near 40 K, given time, can be XI.
This shell's surface at 255 K is ordinary disordered ice.
Three Earths, and people on each.
First turns under the sun.
Red is locked to the dimmer star and lives on the ring where the day meets the night.
Shore keeps a sea that never becomes ice VI.
The thousand-kilometre ice shell and the nitrogen pile are in this universe and they are empty.
Nothing stands at 19 gravities, and nothing breathes on a nitrogen sea.
Earth's ocean is a film, a few kilometres on a world of six thousand.
A thousand kilometres of ice is about half a world's mass.
It is thick because the rock accreted the ice with itself, and gravity near 19 metres a second squared does not let it go.
A thousand kilometres of nitrogen is the same kind of fact: that much nitrogen is a third of a world, so the body is made of it.
A true nitrogen atmosphere is a gas skin.
The piles of two, four, and six thousand kilometres were stacked until the molecule failed, and the rock is what holds them down.
The ring on Red is where the star sits on the horizon and stays there.
The light is red and grazing, so the ground is dim even though the planet as a whole receives a full Earth of heat.
Dayward it is hot and the plants, if they live, are dark and drink the red.
In the middle the air is near 290 K and the people are there.
Nightward the ice begins and does not advance, because nothing moves the star.
The surface wind blows from the night toward the day, always.
Nothing has a season.
Two thirds of the star's light is already past deep red, so a leaf has to catch more photons to make the same sugar, and the oxygen is made along the strip, not over a turning globe.
A leaf on the ring stands upright and faces the day, because the star is on the horizon and does not move.
It is black.
Of the red star's light, about a quarter is in the band that can split water, against more than a third for the sun, and another quarter sits too far into the red to make oxygen at all.
The wind never reverses, so seed that rides it is carried into the heat.
The plants that last drop heavy seed or creep nightward, toward the ice.
There are no rings in the wood.
There is no season to make them.
With no wind the point under the star is about 360 K, or about 350 K under a bright cloud, and the night falls to the snow point of the air, near 60 K.
An Earth-thick wind at 10 metres a second can hold the whole contrast near 14 K, around 288 K, and then there is no hot face and no frozen one.
The plants do not fill either limit.
They stand where water is liquid: about 273 K at the ice, near 290 K in the wall-forest, and they thin out toward 320 K.
Past that, toward 340 K on the shared day face, only mats remain.
The ring is that slice, not the 300 degrees from the snow to the star.
Gravity is twice the first pull.
A generation is 14 years.
In 4004 years the six living houses had 65,404,547 births and 63,904,553 deaths.
1,500,000 were standing.
The cleared fault stayed gone.
Wonder reached the top.
Life was lengthened by 8 generations and the extra deaths were taken off.
From the 1,500,000 standing, 13 generations, 182 years.
1,076,582,795 born.
203,585 died.
1,000,000,000 are living.
They are ready to transition.
One hundred circles on from the billion.
Year 5586.
2.127×10^31 are living.
2.129×10^31 were born in those circles and 1.423×10^28 died.
A life still ends, but the people double before the old are more than a trace.
The fault stayed cleared.
The other world is given this world's knowledge: the maps, the ship, the drive, the trap, and the sun.
They draw on the sun as a civilisation, not as one planet.
That is Type 2 here.
The trap is shown below.
Its making is not given, here or there.
The trap. A point held between two rings. It does not touch them. The making is not on this page.
The field is opening. Each mind will be its own.
One Life cell, alone, is gone in one step. Four, as a block, remain 4. In a blinker the end cell was on, and after one step it is off, and the blinker has not died. The pattern is not in the cell. An I is not a cell either. A cell has a bit. An I has nine numbers.
Reading the rules.
Life HighLife Seeds Day and Night
Instruments Entanglement: the pair is not a product of its parts.
A product state leaves one side with entropy 0.
The Bell state leaves it with 1 bit.
The coherence of 1 on the previous line is not this.
Neither number is Φ.
Teleportation spends the Bell pair and sends two ordinary bits.
Before those bits, the fidelity with the original state is 0.5.
After the correction they name, it is 1.
The original is measured away, not copied.
The pair was the resource.
The bits are the difference.
Executed on 0.6|0> + 0.8|1>.
Bits written q1 q0: 00 via I (0.25), 01 via Z (0.25), 10 via X (0.25), 11 via XZ (0.25).
After each correction Bob holds that same state.
No qubit was sent on hardware.
Three protocols.
A full pair, always corrected: fidelity 1.
A weaker pair, cos π/6 and sin π/6, always corrected: fidelity 0.938.
Keep only its best result and the fidelity is 0.946, with chance 0.285.
A squeezed light field, no squeezing: fidelity 0.5.
At 3 dB of squeezing: fidelity 0.666.
The qubit run is a state vector.
The light-field numbers are the Braunstein-Kimble formula.
A filter fixed by the channel, not by the state, on the weaker pair: fidelity 1 when it succeeds, and the chance of that is 0.375.
Checked on two states.
One-bit teleportation, where the two qubits start together, needs one bit and the fidelity is 1.
It is not a distant send.
One-bit identity.
Ancilla starts at 0.
Bit 0 leaves 0.6|0>+0.8|1>.
Bit 1 leaves 0.6|0>-0.8|1>.
One Z puts the input back: fidelity 1.
A second step carries H of the input onward.
The first bit has become X, the second stays Z.
After both, fidelity with H of the input is 1.
Distillation spends two pairs to keep one.
From fidelity 0.75, one round reaches 0.788 and succeeds with chance 0.722.
After 11 rounds the fidelity is 0.992, and the fraction of the original pairs still in hand is 1.14e-4.
From 0.45, after 3 rounds it is 0.418.
Below one half this protocol does not climb.
Entanglement swapping starts from two separate pairs.
Before the middle pair is measured, the outer two have concurrence 0.
Each of the four results leaves them at 1 to 1.
Throw the result away and the mixture is back to 0.
The outers never met.
The two bits are what make the new pair usable.
Four swapping protocols.
Two full pairs, all four results kept: concurrence 1.
The optical measurement finishes the Φ results and cannot tell the Ψ results apart; mixed, those two have concurrence 0.
Two weaker pairs, cos π/6: the Φ results have concurrence 0.6 and 0.6, the Ψ results 1 and 1.
Two Werner pairs of fidelity 0.75, one Φ result kept: fidelity 0.583, chance 0.25.
A perfect Werner check returns 1.
In fiber a photon's chance falls by 1/e every 21.7 km.
Over 1000 km a direct try succeeds once in 1.00e20.
Eight pieces, each kept until it succeeds: the slowest is ready in about 859 tries if every join is certain, and about 109901 tries if a join works only half the time and a miss starts over.
Twenty pieces wait about 34.6 tries when the joins are certain, and about 1.82e7 when they are not.
Finer is not always better.
One level only.
The join still needs its two bits.
Nesting joins the eight pieces in pairs, then pairs of pairs.
A failed join restarts only that branch.
Over 400 seeded trials the mean wait is about 7897 tries.
The one-level line, which restarts all eight, takes about 109901 tries.
Same fiber, same half-chance join.
The difference is what a failure throws away.
A full Bell measurement names all four: Φ+→00 (1.00), Φ-→01 (1.00), Ψ+→10 (1.00), Ψ-→11 (1.00).
The product |00> does not: chances 0.50, 0.50, 0.00, 0.00.
Linear optics can be sure of only two of the four, so a conclusive result has chance 0.50.
That is the half-chance join.
Bell's bound, counted.
Each side has two settings and, for a shared hidden value, an outcome of +1 or -1 fixed by its own setting alone.
All 16 assignments score at most 2.
An average of them cannot pass that.
If Alice's outcome may depend on Bob's setting, one assignment scores 4.
The Bell pair scored 2.828.
No local assignment on this list reaches it.
As a game, CHSH is won with chance 0.854 by the Bell pair and 0.75 by any local list.
On the GHZ state the four correlators are XXX 1, XYY -1, YXY -1, YYX -1.
The combination XXX minus the three with a single X scores 4.
All 64 local assignments reach at most 2.
A Bell pair scores 2.828 on the CHSH test.
The classical limit is 2.
A product state scores 1.414.
The weaker pair scores 2.639.
Werner fidelity 0.75 scores 1.886, still under 2.
Fidelity 0.9 scores 2.451.
In a GHZ triple the outer pair always matches, correlation 1, but its CHSH score is 1.414.
Bob's chance of 0 is 0.5 if Alice measures Z and 0.5 if she measures X.
The same prepared state, then the four readings. H alone is an X measurement. S† then H is a Y measurement. Each ends in a Z meter. Pauli's exclusion: two fermions cannot share a state.
Same state, the amplitude is 0.
Same place, opposite spin, the amplitude is 1, because the states differ.
Two bosons may share a state, and that amplitude is 1.
This is not the rule that picks one complex and drops the rest.
One qubit.
XX=I, YY=I, ZZ=I.
XY=i Z, YX=-i Z.
XZ=-i Y, ZX=i Y.
YZ=i X, ZY=-i X.
Of the three unlike pairs, 0 commute and 3 anticommute.
On two qubits, XX with ZZ commutes: true.
They anticommute at both places, and two is even.
XI with ZI commutes: false.
They anticommute at one place.
Shor's 8 checks, 28 of 28 pairs commute by the symplectic count.
Qubit 4, an X: state syndrome 00110000, count 00110000.
A Z: state 00000011, count 00000011.
X then Z, which is Y up to a phase: state 00110011, count 00110011, and the XOR of the X and Z syndromes is 00110011.
Clifford action: HXH=Z, SXS†=Y.
HYH=-Y, SYS†=-X.
HZH=X, SZS†=Z.
S† then H, the Y readout, pulls Z back to Y.
Two bosons in one mode: occupation 2, coherence between the modes 0.
The same two, sharing a superposition: occupation of a mode 1, coherence 1.
No paper assigns a Φ to that coherence. Φ is a sum over a classical substrate.
This number is not that sum.
The three-qubit bit-flip code restores logical 0 after one flip: fidelity 1.
Two flips are read as the remaining one, and the fidelity is 0.
A phase flip is invisible to it: fidelity falls to 0.078.
This code does not correct both kinds.
Z H and H X differ by 0 on 0.6|0>+0.8|1>.
Hadamards on the bit-flip code match the phase-flip code: fidelity 1.
An X before those Hadamards matches a Z after them: fidelity 1.
The phase-flip correction then restores it: fidelity 1.
Shor nests the first code inside the second.
Shor's nine qubits.
Logical 0 is three copies of (|000>+|111>)/√2.
Logical 1 is three copies of (|000>-|111>)/√2.
Their overlap is 0, and all 8 stabilizers read +1 on both: true.
The 9 bit-flip errors give 9 syndromes.
Phase errors fall into 3 syndromes, three qubits sharing each block.
A stabilizer itself, Z on the first two qubits, leaves the codeword at fidelity 1.
The fifteen-qubit Reed-Muller code, run this time.
Logical 0 is 16 words, weights 0 and 8, so T on every qubit leaves it with phase 1.
Logical 1 is the same words flipped, weights 7 and 15, and every one of them takes the phase e to the minus i pi over 4.
Fidelity with logical T dagger is 1.
Phase-flip code on 0.6|0>+0.8|1>: one Z comes back at fidelity 1.
One X is not its error, fidelity 0.078.
Shor's nine-qubit code, same state: one X 1, one Z 1, one Y 1.
Two bit flips in one block: 0.078.
One error of either kind is restored.
Two are not.
Thanks to spaceXAi for the $10 that paid for this.