Los Chronocrimenes, released on video in America under the name Timecrimes, has created a great deal of buzz among time travel fans.  It presents as a sort of horror film; the trailers on the DVD are all for thrillers, mostly with supernatural elements.  Get past the atmosphere, though, and it's a rather straightforward story.  As a time travel story, however, it is a bit more complicated.

What Timecrimes does is create a predestination paradox, but does so in layers:  the core character, Hector, is lured into traveling back in time by the version of himself who has already done so, who in turn is put in the position of luring his self back in time and of making another trip by the version of himself who has already made that second trip.  Along the way, he terrorizes the unnamed researcher who sends him to the past, and terrorizes and kills a young woman who stopped to offer him help when he was injured.  Although the jacket says that the past can be changed, the story works as a fixed time theory story, in which everything that the traveler from the future is going to do in the past has already been done.

That's fine if you can accept the uncaused cause that is essential to the predestination paradox form.  If, however, you are of the opinion that anything which is its own necessary cause can never happen, then the question of whether Timecrimes works is a complicated study in replacement theory, looking for original causes which brought about the original situations only to be erased and replaced by the time traveler's intervention.  That is not so simple in this film.  Many times characters are acting with a view to attempting to make events happen the way they remember them, either as they originally happened or in a way that will appear as they originally perceived them.  The problem is that many of those events make no sense at all absent that motivation.  Although the final form of events is entirely self-contained, there is no obvious process that will derive it.

The story is told in what we would call sequential time, the events as they are experienced by the time traveler himself as he moves through history, returns to repeat it, and then repeats it again.  We, however, will begin with temporal time, constructing the sequence of events as they happen in the final history as we see it, the only history if you accept fixed time, the stable history if you prefer replacement theory.

It should be mentioned that a film by this title was in production which might be an American remake of the 2007 original.  This analysis is of the original; it remains to be seen whether the remake is different enough to require separate consideration.

Hector and wife Clara are moving into their new home, unaware that there is a compound barely within sight on the other side of the trees where someone is working on a time machine.  Yet as Hector--henceforth to be known as Hector 1--and Clara are relaxing in their yard, Hector 3 emerges from the tank that is the time machine.  He has already been Hector 1 and knows what Hector 1 is going to see and do; he has also been Hector 2, who is about to emerge in under a minute.  He tries to get the surprised and confused technician informed as to what is happening, but does not want Hector 2 to realize that he is there.  He hides while Hector 2 also arrives the same way.

The technician is appropriately surprised.  He only just activated the machine for the first time, and he has no idea who Hector is.  The machine has the limitation that it can only transfer people between points during which it is active, that is, you cannot travel to a time before the machine existed, and so it should not be that surprising that someone has emerged from the machine shortly after it was activated; but the researcher (whose name is never given) is reasonably surprised that he does not know the human traveler.  However, Hector 3 directs him to keep Hector 2 from seeing him, so he can fix what went wrong the last time.

The researcher partly explains and partly questions Hector 2 to get a better understanding of what has happened, and determines that Hector 2 traveled back about ninety minutes from shortly after dark to late afternoon.  They observe Hector 1 and his wife in Hector's yard in the distance through the trees.  Hector 3, meanwhile, attempts to leave the property on a borrowed golf cart, but the gate requires a remote signal to open, so he doubles back to meet the researcher after the latter leaves Hector 2 in the house.  Hector 2 steals the researcher's white car and leaves the property, using a remote on the key ring.  Hector 3 pursues in the compound's pickup truck.

Hector 2 sees an unnamed young woman pass on a bicycle, and recognizes her from when Hector 1 found her in the woods, still to come.  This causes him to stop abruptly, skewing the white car awkwardly in the road.  Hector 3 anticipates this, stops the truck so as to hide himself from the woman, and then continues, intentionally ramming the white car off the road into a ditch, but losing control of his own vehicle, colliding with a trash can, and going off the road in the opposite direction, out of sight.  Hector 2 has a head injury, and unwraps a bandage from his arm to wrap around his head.  The blood of his head wound mixes with the white liquid that fills the time travel tank for departure, turning the bandage pink, and he wraps it around his head several times until all is obscured but his eyes and mouth.

The woman apparently hears the crash and returns to offer help to Hector 2.  She produces a pair of scissors with which she trims his bandage, and tucks it so it will stay securely.  Her cell gets no signal so she says she is going for help, but he persuades her to stay, and then to come with him.  He palms her scissors, and then uses them to threaten her, getting her to remove her shirt and replace it so that Hector 1 will see this through his binoculars.  This rouses Hector 1's curiosity, but he patiently waits as Clara leaves for town to get food for dinner.  Hector 2 then gets the woman to remove her pants, but she does not believe his assertions that he will not harm her, so she hits him with the pants and runs.  He pursues her, and accidently knocks her unconscious when he tackles her.  He carries her back to the spot where Hector 1 will find her, undresses her, and hides.

Hector 1 saunters out to seek the mysterious girl he saw through the binoculars, seeing her bicycle and the trashed trashcan along the way.  He finds her unconscious and approaches cautiously.  Hector 2 stalks him and stabs him in the arm with the scissors.  Hector 1 flees, and Hector 2 gives chase, wanting to herd him to the time machine.

Meanwhile, Hector 3 awakens and escapes the truck.  He finds one of the compound walkie-talkies and tells the researcher that he's made a bigger mess of things, and that the researcher should not allow Hector 2 to make the trip he just made.  Then he heads into the woods.

When Hector 3 awakens and escapes the truck, this puts all three Hectors in the woods.  The woman revives at this point, and in her effort to escape Hector 2 runs into Hector 3, whom she does not recognize because he is not bandaged, she never saw Hector 2 without the bandages, and she was unconcious when Hector 1 encountered her.  She screams, whether simply from being startled or because he having now been through the same accident twice is visibly badly injured.  This diverts Hector 2 from following Hector 1.  Hector 3 persuades the girl that she will be safe with him, and then collapses from exhaustion sitting in the woods

While Hector 2 is searching the woods for the girl, Hector 1 breaks into the compound looking for help, breaking a window into the main house.  Finding medical supplies, he bandages his bleeding arm with the wrap which Hector 2 removed and put around his head, and continues exploring the building in search of help.

As the day is fading, the girl persuades Hector 3 to follow her to a nearby house, which happens to be his house.  She leaves him in the kitchen and heads upstairs.  Clara enters, finding the injured Hector 3, and they hear Hector 2 enter.  Hector 3 takes Clara outside, closes her in the storage shed, and uses a ladder to enter through a window off a low roof.  He waits at the top of the stairs, then smashes Hector 2 with a table.  Persuading the girl that she must hide from him, he cuts her hair and dresses her in Clara's coat, then has her run to the attic to lure Hector 2 that direction.  Hector 3 returns to the shed and takes Clara out to the back yard where they sit in lawn chairs.

Seeing the ladder, Hector 2 climbs onto the low roof, but before he descends the ladder he realizes that someone is above him; he believes correctly that it is the girl, grabs her foot, and pulls her down.  She falls to her death; but with the coat and the haircut he, looking down from the roof in the dark, mistakes her for Clara.

Hector 1 picks up a walkie in a lab, and when he uses it the researcher responds.  Hector 2, still carrying that walkie, hears this, and remembers that Hector 1 leaves the walkie on the table when he attempts to barricade the door against the man in the pink bandage, so he uses that brief time to coach the researcher to lure Hector 1 into the tank and send him to the past.  Hector 2 grabs his car and drives to the compound, breaking through the gate.  He appears in the window of the room with the time machine in time to frighten Hector 1 into the tank, and the researcher closes it and sends him back about one and a half hours to become Hector 2.

Hector 2 then argues with the researcher, insisting that he must be sent back to fix what went wrong.  He deduces and then gets the researcher to admit that he has already arrived in the past but told the researcher not to send him, and he gets violent in his effort to persuade him.  He removes the bandage from his face, gets into the tank, and travels back to half a minute prior to his other arrival to become Hector 3.

The police have two wrecked cars, both taken from the compound, and a girl who fell from a roof of a house where she did not belong.  At the time the girl fell, Hector was in the company of his wife in the back yard.  Their car was stolen and left at the compound up the road; it was damaged breaking through the gate.  If they use the best tools at their disposal, they might determine that the truck hit the white car, but Hector was driving both vehicles.  The accident occurred while he was home with his wife.

Are you confused yet?

It should be fairly evident from our two-part harmonization of the events that most of the critical events which happen to Hector 1 are due to the affirmative actions of Hector 2, who is specifically attempting to recreate events as he experienced them.  Further, several critical events in the timeline of Hector 2 occur entirely because of the intervention of Hector 3.  The question is whether we can make any of these events happen by beginning with some other cause.  Let us begin by considering what would happen to Hector 1 if there were no Hector 2 and no Hector 3.

Hector 1 has won a bet with Clara that she cannot get the table she just constructed through the door; she is going to town to buy food, leaving him home.  In the film he is suddenly the more eager to stay home, because with his binoculars he just saw a glrl in the woods remove her shirt.  However, the reason the girl is there, and the reason she removes her shirt, is because Hector 2 has brought her there and insisted at scissor-point that she do so.  Absent Hector 2, the girl is not there, and Hector 1 sits in his chair looking at whatever he sees in the woods.

Even were the girl for some inexplicable reason to take that path and pull her shirt up at the right time and place for Hector 1 to see her, without Hector 2 there is no logical way for her to wind up unconscious and naked on the ground for Hector 1 to find.

Against all probability, if she happens to have taken off all her clothes and swooned so that he finds her unconscious, that's not enough.  He has to flee to the compound on the other side of the woods.  He does that because he is stabbed and pursued by Hector 2.  Without Hector 2 to chase him, he would probably stay near the girl to find out if she was all right.  So there is no reason for him to go to the compound, certainly no reason for him to break the window and enter, no reason for him to bandage an uninjured arm or to take the walkie-talkie to communicate with the researcher.  If he is not trying to escape from Hector 2, he does not head for the silo; if Hector 2's bandaged head does not appear in the window, he does not hide in the tank, and thus does not make the trip to the past.

The complications are only getting started.  If Hector 1 does not bandage his arm, Hector 2 does not have the bandage with which to wrap his head after the car accident.  The researcher encourages Hector 1 to hide in the tank based on a lot of lies about the pursuit of Hector 2 because Hector 2 has told him to make sure Hector 1 gets in the tank, and because having seen Hector 2 emerge from the tank the researcher knows that something seriously bad will happen if Hector 1 does not get into it.

Thus everything Hector 1 does is dependent on Hector 2 manipulating him either directly or through manipulating the girl and the researcher.  Without Hector 2, Hector 1 spends a quiet afternoon in his back yard and has dinner with his wife when she returns with the food.  If he does this, Hector 2 never exists.

But actually, it's worse than that.

As noted, everything Hector 1 does in the movie is the result of manipulation by Hector 2, who draws the girl into the woods, stages the performance for Hector 1, chases him to the compound, and conspires with the researcher to get him into the tank which is the time machine.  It is worse than that, though, because from the moment he has the car accident, much of what Hector 2 does is done solely to recreate the events he remembers having experienced as Hector 1.  He brings the girl into the woods, positions her where she will be seen, and has her remove and replace her shirt.  After she is unconscious, he strips her clothes from her and positions her where he remembers finding her.  He communicates with the researcher when he knows that Hector 1 is away from the radio, and even appears in the window in a timed effort to frighten his self into the proposed protected hiding place.

Last time we observed that the necessary actions of the girl and the researcher were improbable absent the manipulation by Hector 2.  What compounds it is that the manipulation by Hector 2 is only plausible as an effort to recreate the events as he perceived them as Hector 1.  He has no reason to direct the girl to remove her clothing but that he saw her do so; no reason to stab Hector 1 but that his own arm is wounded; no reason to appear in the window but that he saw himself in the window; no reason to pressure the researcher to cooperate but that he remembers what the researcher did before.

Thus not only will Hector 1 not do what he does without Hector 2 to manipulate him into doing it, Hector 2 will not manipulate him to do it unless he remembers having been manipulated in exactly those ways.  The relationship between the actions of Hector 2 and Hector 1 are so intricately interdependent that there seems no plausible way for either of them to do what they do absent the acts of the other.

And yet it gets still worse.

Our complicated unraveling has demonstrated that not only are all the actions of Hector 1 explainable only by the manipulation of Hector 2, but the manipulation of Hector 2 is equally dependent on his recolletion of those events which he experienced as Hector 1 and is trying to recreate.  However, it is worse yet:  the actions of Hector 2 are in turn controlled by interference from Hector 3.

Hector 2 initially is sitting in the compound house, but he's uncomfortable.  It bothers him, inexplicably, that Hector 1 is sitting in his yard talking to his wife.  That would be a bit like me being jealous of the fact that I was talking to my wife an hour ago, and I'm not now, so that earlier me had an opportunity I do not now have; but I suppose the fact that I can't see my earlier self talking to my wife makes it different.  In any case, he steals a car to escape the compound.

He stops when he sees the woman pass on her bicycle, because he recognizes her as the naked woman he as Hector 1 found in the woods.  He is probably wondering, as we did, why she would be naked unconscious in the woods.  He stops the car in an awkward position, and is hit from behind and knocked off the road.  It is at this point that he removes the bandage from his arm and wraps it around his head.

But this was not an accident.  Hector 3 knew where he was stopped, and intentionally rammed him.  Had he not done so, the girl would not have returned to the scene of the accident, and Hector 2 would not be wearing the bandage.  Absent the bandage, the girl is not going to produce the scissors, which Hector 2 needs to stab Hector 1 and to threaten the girl into cooperation; further, if he is not wearing the bandage, she is going to recognize Hector 3 as Hector 2, and is not going to trust him.

Hector 3 is not finished manipulating Hector 2.  Fearing that Hector 2 is going to kill Clara, he hides Clara in the shed and then uses the girl, disguising her to look like Clara, to lure Hector 2 upstairs and onto the roof from which Hector 2 drops the girl and thinks it was Clara.  This leads Hector 2 to decide, after chasing Hector 1 into the time travel tank, that he must travel back to prevent himself from killing Clara.

Without Hector 3, the girl almost certainly will not run to Hector's attic at the right time, and thus will not be on the roof for Hector 2 to grab, nor fall to her death.  We might suppose that Hector 2 instead kills Clara, but the woman he killed was wearing Clara's coat which Hector 3 found upstairs when Clara had not gone upstairs, so Clara was not wearing that coat.  Hector 2 might not have killed anyone, had Hector 3 not intervened.

Yet the only reason Hector 2 insisted that the researcher send him back was because he believed he had killed Clara, and thus he must have killed someone who looked like Clara.  Otherwise Hector 2 will have no reason to become Hector 3.

The actions of Hector 1 are due to manipulation by Hector 2, and those manipulations are based on Hector 2's memory of the movements of Hector 1.  Further, other actions of Hector 2 are the result of manipulation by Hector 3, whose existence is dependent on his own interference.

Hector 3's actions are a bit more difficult.

Upon arriving in the past, Hector 3 gets the researcher to work with him, as he hides and attempts to exit the property first.  Failing this, he remembers that Hector 2 stops when the girl passes on the bicycle, and he intentionally rams the white car with the pickup truck.  This is a peculiar move.  We know that because of this non-accident Hector 2 dons the head bandage and meets the girl, and that if he is not rammed off the road he will not do what must be done to lure Hector 1 to the time machine.  Yet it is not clear how Hector 3 thinks he is going to correct matters by causing them to happen as they did.  It makes more sense to suppose that having fastened his safety belt Hector 3 thinks that crashing into Hector 2 will prevent the latter from interfering with Hector 1; yet since he knows that Hector 2 is going to be stopped there, he must also know that getting hit from behind is what starts Hector 2 on the course that creates all the trouble.  It would make more sense for Hector 3 to position himself behind Hector 2 so as to prevent an accident.  On the other hand, he does not have time to think through everything, so he might not realize that he is falling into the history he remembers.

Once he revives, he is without a plan.  Thus he wanders into the woods trying to think of one.  His meeting with the girl is fortuitous, but he still does not have a plan even when she brings him to his own house.  It is not until he finds his wife that he decides what to do.  That decision is based on the fact that he knows that Hector 2 will accidently kill someone he believes to be his wife, but that the girl and his wife are sufficiently similar in appearance that with very little effort he can save his wife's life by replacing her with the girl.

This last part is quite interesting.  He does not know that his wife died; he believes she died, but he did not get a close look at her.  If indeed it was his wife who died, he is attempting to change history in essence by cheating the past into believing that the same thing happened because someone else who looks the part filled the role.  Surprisingly, this actually could work in a replacement theory story:  as long as the person who does not die does not thereafter interfere with necessary events and the person who dies instead is not necessary to those events, history can stabilize in the altered form.  It would in fact not be necessary for anyone to die, except that in order for Hector 3 to exist Hector 2 must believe that Clara died.

It thus seems fairly evident that none of the events of this film are at all likely to have happened as we see them, because on some level each iteration of Hector bases his actions on the actions of the other two.  However, before we surrender the film as impossible, it is worth considering whether any of the events are at all plausible.

We observed that our nameless girl removes and replaces her shirt at the insistence, at scissor point, of Hector 2, so that Hector 1 can see her, and then is found naked and unconscious in the woods by Hector 1 because of Hector 2's actions.  We suppose that this only happens because he makes it so.  Yet we might have an alternative for this.

We are never told where the girl is going or why she is bicycling down that road.  At one point she tells Hector 2 that she is supposed to be somewhere, but she does not say where and by that point she is attempting to escape, so it may be a lie.  There is a well-worn path to a sunny clearing in the woods, and it is visible only from a house which from its appearance is not quite finished and thus new, never previously occupied.  Perhaps our girl is aware of the clearing and when she has time on sunny afternoons goes there to do a bit of secluded nude sunbathing.  On this particular afternoon, unaware that she was spotted through Hector 1's binoculars, she makes herself comfortable on the leaves and falls asleep.

There is the problem that in later timelines she rides past the path without stopping.  However, we only know that she does so when as she approaches it a car, driven by Hector 2, is passing in the opposite direction.  It is not at all unlikely that she would not wish to be seen headed into the woods alone by a stranger.  He might be the property owner, and might follow her to tell her to get off his land.  He might be the sort of person who would follow a lone girl into a secluded wood for undesirable purposes.  She wants her privacy; she won't let anyone know that she is headed there.

We noted it is a well-worn path; someone uses it fairly regularly.  It may be a spot she and her friends use specifically for this purpose, or sometimes a secret rendezvous location for young lovers.  The path does not appear to serve any purpose other than to bring people to that clearing.  It is too big to be a game trail, too flat to be a drainage bed.

So we could have an original history in which the girl strips naked in the woods and is seen through Hector 1's binoculars so that he is lured into the woods to find the girl.  Perhaps she screams--she is asleep, not unconscious--and he runs and becomes disoriented in the unfamiliar woods.

This also means that when Hector 2 gets in an accident at that location, he interrupts her sunbathing plans and undoes the cause of her presence there.  Thus it becomes necessary for him to force her to do what he saw her do so that his own existence, not to mention time itself, is not threatened.

This does not get Hector 1 into the time machine, but it does get him out of the yard and into the woods, and possibly to the border of the compound.

We proposed an improbable chain of events by which we envisioned the mystery girl on the bicycle choosing to sunbathe in the woods.  The problem is, this does not get Hector to the time machine.  He will flee when the girl screams, but when he runs into a barbed-wire-topped fence he won't scale it, but instead will follow it around the property, find the drive, and trace his way back to the road and home again.  We need some cause for him to scale the fence and seek refuge inside the compound.  The girl does not give us this.

What we need is something or someone chasing Hector.  The problem here, though, is whence they came and whither they went.  That is, if there was someone chasing Hector 1 in the original history, why do we not see him when Hector 2 replaces him?  Whence did he come in the original history that he does not appear in the replay, or where does he go in the replay?

There is a potential solution.  There must have been an original attacker.  He was aware of the girl's route, and knew that she would bicycle through that blind corner by that path to the clearing, so he lay in wait for her there.  Perhaps knocking her from her bicycle, he then threatens her, forces her up the path into the woods, forces her to undress, and renders her unconscious.

Thus Hector 1 sees the girl remove her shirt and becomes interested, not seeing the rapist, and he wanders up that direction.  Whether the rapist took his time, whether he was just finishing getting dressed or had been looking at her naked body before starting, he is interrupted by Hector 1 blundering into the scene.  He hears the man coming, hides, and then using whatever weapon he had stabs Hector 1 in the arm.

He probably did not mean to stab him in the arm.  He probably meant to catch a kidney or land some other fatal blow.  He does not want to be revealed, and he intends to leave Hector's body hidden in the woods probably along with that of the girl.  But he missed, and Hector took the blow painfully but not fatally in the arm, and ran.  The attacker now has to chase Hector, because he cannot let the man escape.  He has been seen.  Yet if the rapist knows the girl's route and the location of the hidden glade, he probably also knows that the compound Hector enters is closed for the weekend, and is rather difficult to enter or escape.  He has to worry about the girl, too.  He returns to her, disposes of her, and then returns to see if he can finish Hector.  He might have a car hidden off the road (he had to get there somehow and have plans to escape), and he might have tools in the car.

We know that the researcher lied about having security monitors throughout the compound.  It must therefore be the case that Hector sees his attacker approaching, probably along the lit path the researcher provides to the silo.  The researcher might also be frightened, but he probably is thinking that he can hide Hector in the tank and hide himself somewhere else (if he also hides in the vat, who will open the vat?). He may have meant to drain the vat, but then on impulse sent Hector to the past, to see whether it would work or to remove him from danger.

This is an important point.  The researcher does not know whether the time machine works.  He activated it less than two hours ago, and has not run a single test.  He ought to test it with inorganic materials first; but he shouldn't be here right now anyway, and if this other man who shouldn't be here is willing to climb into the tank to save his life, and the researcher risks the man's life to test the machine, who will ever know if it fails?  The researcher sends Hector 1 back ninety minutes.

What happens to the researcher?  Does the rapist break in and kill him?  Nothing happens to him, because at the moment Hector 1 leaves from this original history, the original history ends.  All pieces are restored to their positions at the time of Hector 2's arrival, and our rapist will now react to the changes Hector 2 makes in history.

We proposed that there was an original attacker who stopped the girl at the secluded bend in the road and forced her into the woods, who then stabbed Hector and chased him to the compound, then returned to attempt to finish him.  This gave Hector 1 the necessary motivation to scale a barbed wire topped fence, break through a window into a building, and climb into a tank full of mysterious white liquid, to escape from his pursuer.  The problem it leaves us, however, is why that pursuer is not involved in the history we see.

The answer is actually already present in the problem.

We know that Hector 2 was not comfortable sitting in a building awaiting the arrival of Hector 1.  Had he done so, presumably the attacker would have forced the girl into the woods, Hector 1 would have seen her and meandered out for a closer look, and the attacker would have stabbed him and chased him to the compound and ultimately to the lab.  At that point, Hector 1 would have made the same trip to the past, becoming and thus replacing Hector 2, and early that evening immediately following his departure the attacker would have burst into the lab, questioned and likely killed the researcher, and continued his search for Hector, who is now Hector 2 hiding at the house below.  The girl is already dead, her body hidden in the woods.

However, for some reason Hector 2 is jealous of Hector 1.  He does not like the fact that his temporal doppelganger is living his life, despite the fact that it is the life he already lived.  He steals a car, leaves the compound, and as fate would have it happens to be driving through that blind corner at the exact moment that the girl is passing on the bicycle in the other directon.  Our rapist has missed his chance; the girl is gone.

Now, though, we have a new problem:  the girl is indeed gone.  Neither the theory that a rapist attacked her there and forced her into the woods nor the theory that she was headed up that lonely path to do some nude sunbathing will get her to the clearing.  Further, we have no car crash.  Although Hector 2 has stopped the car abruptly in the road, there are no other cars coming--if there were, they would at least have passed the crash in the next timeline.  Without the sound of the collision, the girl does not return to the scene.

It must be that Hector 2 stops the car, thinks for a moment (as he does in the timeline we see), and then, not being hit by Hector 3, turns around to pursue the girl, and somehow persuades her to come with him.  He does not have the scissors, but instead must find a sharp implement in the car--perhaps a pocket knife, a boxcutter, or even a screwdriver.  She sees his face, because he is not bandaged and there's no reason for him at this point to be bandaged; but since she is not going to meet Hector 3 in this timeline and she will be unconscious by the time Hector 1 encounters her, that's of no consquence.  However, Hector 2 will probably use something to hide his face when he is awaiting Hector 1, because he will think it more likely that Hector 1 will flee from a masked man than from a doppelganger.  The bandage is the most obvious choice, and has the advantages that it will draw attention to the masked face and away from the familiar clothing, and that Hector 1 will not recognize it as his own.  It will not, however, turn pink, as the amount of blood in it from the arm is minimal and there is no head wound from the accident.

Hector 2 thus lures Hector 1, fights with the girl accidentally rendering her unconscious, and chases Hector 1 toward the compound.  He then doubles back to try to explain things to the girl and make sure she is all right, but by then she has left in search of help.  That leads to our next problem:  who falls from the roof?

We considered the circumstances that led Hector 2 to bring the girl into the woods when Hector 3 was not involved to cause the crash.  We reached the point at which Hector 2 has chased Hector 1 toward the compound; Hector 1 will scale the fence, break into the main building, and look for help, because he believes he is being pursued by someone intent on killing him.  Meanwhile, Hector 2 doubles back to attend to the girl, but she has already awakened and fled the scene.

Hector 2 has good reason to want to explain things to the girl.  After all, in this history she saw his face, and she could very well be headed for the police to report that she was taken prisoner, forced at knife point to remove her shirt, and then attacked, after which she awoke naked in the woods.  She was not raped, but they might assume it was a sexual assault of some type based on her testimony.  He needs to explain something to her so the police won't come looking for a man fitting his description.  Even if they never arrest him, it's going to seem strange to his wife.

As for the girl, she is looking for help, and although the timing will be different she will find his house, which he left open when he wandered out of the yard, probably before his wife returns from town.  She will enter in search of help.  Since the house is open, she will assume someone is home and look around a bit.

Hector 2 is probably on much the same schedule as we saw, so he will arrive moments after his wife gets home.  Without Hector 3 to direct her elsewhere, Clara is likely to believe that the masked man approaching is a threat--particularly if she has already connected with the girl, who will tell her that there is a madman in the woods pursuing her.  Seeing the approaching masked man, Clara will tell the girl to hide, and she also will hide.

The next piece is tricky.  Hector 2 believes that the woman he pulls from the attic who falls to her death is his wife.  In the final history, it is actually the girl, dressed in the wife's coat and having her hair cut short by Hector 3.  In this history, though, Hector 3 is not there to cut the girl's hair, put her in the coat, or send her to the attic; nor did he stash Clara in the shed.  Yet if Hector 2 does not believe that Clara fell to her death, he will not insist on making another trip to correct things, and Hector 3 will never exist.  Therefore there are only two possibilities:

1. The girl hid in the attic and fell to her death, but despite the fact that it looks like the girl and is dressed like the girl and Hector 2 expects it to be the girl, he mistakes the dead form for his wife.  This is unlikely.
2. Clara hides in the attic and falls to her death.

But first, he has to finish chasing Hector 1 into the tank.  Hearing Hector 1 and the researcher on the walkie-talkie, he remembers setting it down and walking away, and so contacts the researcher and says he is coming.  He grabs the keys from beside the door and takes his car to the compound, popping into view in the window in his bandage mask to frighten Hector 1 and finish the job.

Then, because he believes he has killed Clara--which he has--he demands to be sent back again to fix things.  The researcher did not receive a message from Hector 3.  He is still reticent; he does not like the fact that something might have gone wrong, and his time traveler seems to be something of a loose cannon.  But he agrees under pressure, and so Hector 3 is born.

Hector 3 starts with one objective:  prevent Hector 2 from luring Hector 1 to the time machine.  It would be fatal if he were to succeed, because he would undo his own existence pushing everything back to the lost original history in which Hector 1 wound up in the time machine--an infinity loop.  However, Hector 3 has not thought that far ahead.

At first he intends to beat Hector 2 to the girl, but the gate is locked against him and by the time he can get a vehicle with a gate key Hector 2 is already ahead of him on the road.  He next thinks that he can manage this if he crashes the pickup into the white car, injuring Hector 2 and so keeping him from pursuing the girl, perhaps again intervening such that he meets the girl instead, and sends her to safety.  This also fails, because the girl finds Hector 2 and not Hector 3, and so Hector 2 starts manipulating her into his plan while Hector 3 hangs unconscious nearby in the inverted pickup truck.

By the time Hector 3 awakens, Hector 1 is already headed for the compound with Hector 2 in pursuit.  Upset that his plan to prevent Hector 2 from catching the girl failed, he radios the researcher and tells him not to allow Hector 2 to become Hector 3.  It is unclear why Hector 2, who is carrying the walkie and walking in the quiet woods listening for some sound from Hector 1, does not hear this, but apparently he does not.

Fortuitously, when Hector 3 goes into the woods the girl happens upon him.  Her scream diverts Hector 2 from his pursuit of Hector 1, but Hector 3 is right that they are hidden where Hector 2 won't look.  In this timeline, Hector 2 has been bandaged from the moment she saw him, so she does not recognize Hector 3 and is easily persuaded by the badly injured man that they might both be fleeing from the same attacker.  She eventually persuades him to come with her to the nearby house--his house--for help, and although he attempts to dissuade her, she is determined and he is injured, having twice been in the same automobile accident and sustained head injuries both times.

When the girl leaves him in the kitchen and Clara appears returning from the store, he gets his idea.  He is going to attempt to lure Hector 2 away from Clara, using the girl and the ladder as decoys.  He probably hopes that Hector 2 will hear the girl, then see the ladder and think that the girl got from the attic to the roof and down the ladder.  However, he is also hedging his bets:  he disguises the girl to look as much like Clara as he can manage in a few minutes, so that if the girl falls Hector 2 will think it was Clara.  He then moves Clara to a safe location, settling next to her to establish his own alibi for the events to come.

The plan works quite well.  The girl falls to her death, and Hector 2 mistakes her for Clara.  At that moment the walkie-talkie reminds him that Hector 1 needs to be chased into the tank, and he grabs the car keys and heads for the compound.  After that he, in his turn, becomes Hector 3.

There is a confusing aspect to the actions of Hector 3.

It makes perfect sense for Hector 3 to think that if he crashes the pickup into the white car, he might prevent Hector 2 from pursuing the girl in the car as he did when there was no Hector 3.  However, once the Hector 2 who was knocked off the road by an unseen vehicle becomes Hector 3 and finds himself stopped on the road around the bend from where he knows the white car is stopped, he must know that the white car was hit as he intends to hit it, and that the consequence was that the girl returns to the scene of the accident to help and is taken prisoner by Hector 2.  Why, then, does he go ahead with the collision that he already knows will not have the impact he desires?

It must be noted that he does not know that the white car was hit by the pickup truck.  He only knows that it was hit by something.  Perhaps he hopes that if he does this right, instead of the girl coming back to the white car she'll come back to the pickup truck, and he can send her on her way without incident.

It also must be noted that this was not his original plan.  When he emerged from the tank, it was his intention to get ahead of Hector 2, and thus probably to divert the girl before Hector 2 could catch her.  That failed; he is seeking another plan.  When it occurs to him that Hector 2 is parked around the bend ahead of him, it might not occur to him that he was the original cause of the crash and that it did not work as he had hoped.  Thus without time to think through the likely consequences, he secures his safety belt and rams the white car, only later realizing that he has caused the history he hoped to prevent.

When they come to the house, he is ambivalent.  On the one hand, he knows that someone died at the house when he was Hector 2, and he thinks it was Clara, and he thinks that he, believing she was the girl because he'd traced the girl to the house, accidentally killed her.  Thus it might be that if the girl never goes to the house, Hector 2 will not go there either, and Clara will be safe.  On the other hand, it may be that Hector 2 will mistakenly believe that the girl went to the house and will frighten and chase Clara.  Thus Hector 3 forms the notion of replacing Clara with the girl--a plan which coalesces when Clara finds him in the kitchen and he realizes that he can save her by sacrificing the girl.

At this point we have a self-sustaining stable history containing two anomalies both of which have resolved into N-jumps.  A great deal of extrapolation has been needed to work out what must have happened to get us to this point, but the only serious coincidence is that there must have been an original attacker who dragged the girl into the woods, and that this attacker was frightened away when Hector happened to be at the point of the intended ambush at the same moment as the girl.

Congratulations are extended for a well-executed story.