Chapter Text
A trajectory, in general terms, is a path that an object carves as it journeys from one point to another, subject to a range of determinants. It is propelled by an initial impetus, shaping its course through time and any environment. Every initial impetus had been hoped, or perhaps desperation dressed as optimism. The environment though which it moves is rarely uniform, introducing complexities that transform a simple line into a rich, dynamic curve. External factors come into play, subtly altering the course—gravitational pulls, atmospheric resistance, the weight of unspoken doubts. These influences sculpt the trajectory, revealing the intricate dance between intention and environment, between what was wanted and what was actually possible.
While calculation is crucial in approximating trajectory, it remains inherently limited. Experience had taught her this with precision. At any point, results may prove insufficient due to the equation's incompleteness, forcing reliance on assumptions and predictions. She had made so many assumptions, filled in so many gaps with wishful thinking. These equations may generate a trajectory for a line, but controlling its motion and pathway demands more than a mere calculation, particularly when dealing with asymptotes—those boundaries that can be approached but never crossed, those limits that define a relationship without ever being acknowledged aloud.
Numerous models exist for approximating calculations, but none are comprehensive enough to fully capture asymptotic behaviour and definitively predict their pathway. A line approaching an asymptote can exhibit multiple behaviours, yet it will never truly intersect or reach the asymptote itself—it can only approach, endlessly. She had been approaching endlessly, hadn't she? Getting close enough to feel the warmth of belonging, close enough to mistake proximity for acceptance, but never quite close enough to matter. The endless approach was a torment, a constant reminder of her inability to fully connect, to truly break through the barriers that kept her forever on the outside, looking in.
This mathematical limitation mirrors a deeper truth about life itself. Asymptotic principles apply beyond equations, manifesting in real-world situations where no calculation, prediction, or assumption can prevent the inevitable. Just as a line in an asymptotic orbit may stray from its expected path, deviating from its predicted trajectory, so too do events in life diverge from expectation. It has happened before—with her brother, with the family bonds he burned. It happens now, with these new connections she thought would save her. And it will happen again, not due to failure of calculation, but because the asymptotic line extends infinitely. The line may drift away, yet it will always move back toward the asymptote, close enough to sense the boundary's presence, close enough to feel the pull of convergence, but never close enough to cross over and truly meet.
Perhaps the line would always gravitate toward the barrier even without clear determinants, even when it wandered away for a while. She had wandered—tried to convince herself she didn't need them, didn't need anyone. But the pull exists not because of precise calculation, but because of the fundamental nature of the relationship itself—an inherent attraction that persists regardless of whether the mathematics can fully describe it. This gravitational pull operates beyond the realm of equations, existing in a space where intuition and pattern recognition matter as much as formal proof. Even when the rules are unclear, the line still follows its course, guided by an unseen force that no equation can fully capture. Even when she knew better, she kept returning.
And perhaps that's the most profound aspect of asymptotic behaviour: it reveals that some relationships are defined not by their destination, but by their eternal approach—by the tension between proximity and separation, between the promise of connection and the guarantee of distance. The barrier remains fixed, immutable, while the line continues its endless dance around it, forever approaching but never arriving, forever close but never touching, forever bound by a limit that shapes its entire existence without ever being crossed. In this way, the asymptote becomes not a failure of the system, but a testament to its persistence, its quiet determination to remain near, even when it can never be whole.
A void she thought she had outrun by forging new relationships—a void left by her brother's betrayal, by the family bonds he had burned—now clawed at her with renewed ferocity. She had believed that spending time with these new connections would make her whole again, that in time, the emptiness would fade. She was wrong. Perhaps she should have let logic win instead of following her heart, instead of believing that someone would accept her unconditionally. Her logic had never led her astray before. Now, the void yawns wider than ever, consuming the fragile hope she'd dared to cultivate. The new relationships, instead of filling the emptiness, have only amplified it—a stark reminder of what remains broken. Logic whispers, 'I told you so,' but its victory offers no solace, only the cold comfort of being right.
It was obvious that they had never truly believed her, and stupidly, she had remained oblivious to that fact. All the signs had been there—the careful distance they maintained, the way their reassurances always came with qualifications, the subtle hesitations before they answered her calls. She had mistaken their politeness for acceptance, their tolerance for trust. But tolerance is not the same as belief, and acceptance is not the same as belonging. They had let her orbit around them, close enough to be useful, close enough to feel included, but never close enough to truly matter. She had been tracing an asymptote all along, approaching a connection that was never meant to be reached, and she had been too desperate, too hopeful, to see it for what it was.
She desperate to be accepted even if she sacrifices a part of herself for the long line and turns out they were not even on the same stroke. They nurture the lines for this long which should meet at some point; perhaps it meets at some point; she hoped it meet a certain point; yet it never did. The line they had nurture had yet meet in tangent of any point of the curve or perhaps they never will. It took her this long to see how it was only her trying to become something that she should have not just trying to appease them, not something that she should have change just to appease anybody and it is her mistake. The biggest mistakes that she keeps on repeating on doing but it would be her last.
After watching her dead brother corpse, she makes an oath that she would never trust them again. Trust that she thought they had earned; trust that she gave them earnestly; or trust that she thought would not be broken by them of all people. She swears to not being fooled by them again as she stood on the cold pale body. It was not her first rodeo to being lied, being manipulated or being betrayed and it would not be the last if she keeps relenting on getting sucker by some sort of fake affections. Not anymore. She would not be a fool just to have a scrap affection from anyone ever again. They can try and she might let them; or not but not anymore, she would never beg for their affection. The affection that they do not want to give at the first place.
It was evening the next day when she returned. Lex’s body was already decomposing—blood seeped into the floor, pooling beneath him. He looked paler than ever, even in sickness. This was final. She knelt, the floorboards creaking. The smell hit her—sweet, metallic, unmistakable. She’d read about it, but nothing prepared her. Her hands trembled as she reached for the old blanket, the one their mother had sewn. Back then, Lex would wrap himself in it, complaining about the cold. Now it would serve a different purpose. She couldn’t leave him like this—alone, in the blood, in the dark. Fear had left, replaced by a hollow resolve. He deserved better. She had to move him. Even if her mind couldn’t accept it yet, she knew: he was gone.
It was like her world has ended, again. Last night, when she shot her brother on the chest thrice; she could not feel a thing. She was numb by the revelation and numb by her brother’s condition. Lex is never in a mess like how he did the other night; Lex is always polish and slick. Last night, he was far away from both adjectives. However, he looks like the brother who welcome her, it almost makes her waiver and change her mind to shot him. Almost. Yet, with him still on his quest on getting revenge the world would never be a safe for anybody not just the Kryptonian. His madness would take on anyone who dare to stand against him and not besides him; that’s including her. She would survive every attempt but not passers-by. So, she shot him.
She didn’t know how long it took. The twilight air was cold, but she barely felt it. Steven stood beside her, silent, his breath visible in the frost. He hadn’t asked questions—just nodded when she said she needed help. Together, they loaded Lex into the back of a van, the metal cold under his hands. The body was stiff now, the blood congealing. Frank drove, his face set in silence. The van rumbled through the dark, headlights cutting through the evening light. No one saw them. No one would. The gate to Luthor’s Mortuary groaned as they passed through, the iron rusted, the path overgrown. She didn’t look back. She didn’t want to see the look on Frank’s face. He knew what this meant. He’d known all along. But he didn’t say a word.
When they reached there, she mindlessly signed for Steven to lead Lex inside the mortuary. They put him at the bed on the preparation room. She specifically requests the mortuary manager to not accept the dead for the week effective yesterday because she needs to prepare Lex to be bury besides their father. No matter how twisted wicked he become, he still family; he still blood; and he deserve to rest among family. She moved through the preparation room like a ghost, her hands moving on their own. The fluorescent lights hummed overhead, casting everything in a pale, sterile glow. She looked down at Lex's face—still and waxy now. She thought of their father, buried in the family plot years ago. Soon Lex would lie beside him, in the dark earth, where the past could finally rest. She picked up a cloth and began to work, methodical and numb.
This was what remained of love. Not words.
This was what remained of family. Not explanations.
Just this—her hands, the cold body, and the weight of blood that would never wash away.
She didn’t realize that they already put him seven feet into the ground as she barely heard the pastor say—or was it pray—for his soul. The words were muffled, lost in the rush of her thoughts, the weight of the dirt falling, the echo of the shovel against earth. She stood at the edge of the grave, hands clenched at her sides, staring down at the dark space beneath her. The night was deep, the sky a vast, empty black, broken only by a single star. The wind tugged at her coat, but she didn’t feel it. Her eyes were fixed on the soil, as if she could see through it, see him lying there, finally still. The silence was absolute, broken only by the distant cry of a bird, or perhaps the wind. She didn’t know how long she stood there. Time had stopped. The world had narrowed to this: the silence, the cold, the finality.
She thought of all the things she never said, all the words that died with him. She wanted to scream. But she didn’t. She just stood. And when the last shovelful of earth was placed over the coffin, she didn’t cry. She didn’t move. She just watched. And in that moment, she knew—she had done what she had to do. Not for him. Not for the world. But for herself. For the last time, she had held him. And now, he was finally at peace. The wind rose again, carrying the scent of damp earth and pine. She turned away, the weight of the night pressing down, but her heart felt lighter. He was home. And so was she. The silence was no longer empty. It was full. Full of what she had done. Full of what she had lost. And full of what she had kept.
It felt as if her trajectory had been pulled off its axis—like the path had tilted, gravity had shifted, and she was no longer moving forward. Instead, she spiralled downward, trapped in a moment that was static yet vibrated with unresolved tension, like a bouncing ball governed by gravity and inertia, with no choice but to keep moving until the energy ran out, though she didn’t know when that would be. After single-handedly pulling LuthorCorp from the brink of bankruptcy, redirecting its focus from weaponry to medical technology, and occasionally aiding heroes in saving National City, she finally realized: her intended path was not to escape the legacy—but to reclaim it. To clear the stain her brother had left, or her ancestor had made. The revelation was not a choice. It was her only way forward.
The wind at the grave was cold, but the weight in her chest had lifted—like a door finally opening. She turned away, the stone marker fading behind her, and for the first time in years, she didn’t look back. She thinks of her penthouse and then the portal watch on her wrist light up before a vortex pop up in front of her. It leads her to her penthouse. The air in her penthouse was warm, the city lights blinking like distant stars. She walked to the window, hands still trembling—not from grief, but from the fire that had finally awakened. The L-Corp logo glowed on her screen, a silent promise. She didn’t need the past to define her. She had already chosen the future. And now, she would build it—not in spite of the legacy, but because of it.
Her phone lit up with a message from Kara: “Game night’s still on. You coming?” The words were casual, familiar, almost warm—but they felt like a trap. She’d spent years believing in their friendship, in the idea that they’d accept her, that she belonged. They’d told her she was safe with them, that she was part of the team, that she was one of them. But now, she saw it: the way they’d used her grief, her guilt, her need to belong. They’d made her believe she was chosen—when all along, she was just a pawn. She didn’t reply. She didn’t even open the message. Instead, she turned off the screen, put it back into her trouser pocket. The city lights still shimmered beyond the glass, but she wasn’t looking at them anymore. She was looking at the path ahead—alone, yes, but finally free.
She poured herself a drink—whiskey, neat, the kind that burned going down. The glass felt heavy in her hand, like it was holding more than just liquid. She sat by the balcony, the city sprawling beneath her like a kingdom she'd never wanted to rule, and let the alcohol blur the edges of everything. Her brother's face flickered in her mind—not the twisted version he'd become, but the boy he was before the world broke him. She remembered his laugh, sharp and reckless. She remembered the way he'd looked at her when she was just a kid, like she was the only thing that mattered. She remembered the promises they'd made to each other in the dark, swearing they'd never become like their father. But they had. They both had.
She took another sip, the burn matching the ache in her chest. The grief wasn't getting lighter actually—it was just settling deeper, becoming part of her bones, part of her blood. She thought of the last time she saw him, standing in the rain, his face turned up to the sky like he was begging for something he could never have. She thought of the way he’d said, “I just want to be loved,” as if freedom was a place you could reach, not a state you could live in. And now, he was gone. Not just from the world, but from her. And she didn’t know if she could ever forgive him, or if she even wanted to. But she knew one thing: she couldn’t let him die alone. Not in the way he’d lived—broken, lost, and forgotten. She would carry him. Not as a burden, but as a truth.
The whiskey was gone. The glass was empty. But she didn't reach for another. She just sat there, staring at the city, and let the silence fill the space where her pain had hollowed her out. The phone chimed—incoming calls, messages—and she ignored it. When the sound became unbearable, she grabbed it and hurled it through the doorway into her apartment. A thud sounded from somewhere inside. Then she did the same with the glass in her other hand. She didn't care about the mess it made. Instead, she leaned further into the railing, feeling the cool steel against her forehead. The pressure building in her skull was nothing compared to the weight crushing her chest. Each time, it felt like she could just let go, just fall—but that would be easy.
She always took the hard path.
No— it was her only choice.
The whooshing sound she heard only strengthen that fact.
“Le— Miss Luthor, I heard a broken glass from your apartment. Is everything okay?” A female voice broke through the silence, followed by a thud signalling someone landing on the balcony.
The asymptote was clear now—two lines moving ever closer, yet never touching. She had believed Kara would never manipulate her gently, never betray her the way everyone else had. But Kara did—not as Supergirl, cold and distant, but as Kara Danvers, the friend who smiled just a little too sweetly. She had placated Lena with kindness to keep her receptive, because only as Kara could she break her heart. And that was the barricade she could never cross: the moment when the girl she loved became the one who lied. Two parallel lines in motion—never aligning, never meeting. And it was always meant to be this way: two paths drawn in the same soil, but never meant to grow together.
If only she had known it from the beginning, she wouldn’t be standing here now, caught in a wound that never closes. Her heart is bleeding—not from a single cut, but from a thousand unseen tears, each one a reminder of the truth she buried beneath kindness, loyalty, and the weight of silence. She’s wrapped it in bandages—false comfort, false promises, the kind that hold for a while but never heal. She’s tried to patch it with trust, with hope, with the belief that love could mend what was broken. But the blood keeps seeping through, staining the fabric, making the wound deeper with every breath. She doesn’t know how to bandage it cleanly. She only knows that if this keeps going, she won’t survive the bleeding—no matter how many bandages she puts on.
“Miss Luthor.” Supergirl stated again while walking slowly towards her.
“Fine.” She managed to gritted out a word; enough to stop Supergirl step.
Why did the hard choice have to be her only option? She had believed in Kara’s kindness—the way she held her hand, smiled just a little too long, spoke of acceptance with a voice that felt real. But now she sees it: the warmth was a lie. The gentleness, a performance. The love, a manipulation. She had been played—by the girl she called her best friend. And the hardest part isn’t the betrayal. It’s that she had believed it. That she had let herself be so soft, so trusting, that she didn’t notice the trap until it was too late. The bandages don’t work because the wound isn’t from the world. It’s from the person who promised to protect her heart—and instead, broke it.
“What were you doing hanging so close to that railing, Miss Luthor?” Supergirl asked, her tone oddly soft—like a performer who knows the audience is watching, but doesn’t yet know the act is over.
Now she understands everything clearly, noticing every subtle detail she once overlooked. Every time Kara asked about her whereabouts, it wasn’t out of simple curiosity or concern—it was a calculated way to keep watch over the remaining Luthors, just as she had done with her brother and mother before. She realizes that she has been reduced to little more than a resource, a tool to be used and monitored for the information she can provide. This bitter truth weighs heavily on her, exposing the cold reality that her value lies not in who she is, but in what she can offer, all while being watched and controlled under the guise of concern. The sense of betrayal cuts deep. The realization doesn’t break her spirit; it awakens a simmering distrust that colours every interaction from now on. She starts to see every question and glance as a test, a reminder that she is never truly free under Supergirl’s scrutiny.
She picks herself up and brace herself for another manipulation, “I assure you nothing nefarious, Supergirl.” She replies as she turns to the other woman.
“I didn’t think…”
The caped hero was trying to say something that she rather not hears, she interrupts her, “Is there anything you need? It’s …” she checks her watch, “9 and late evening.” She then put her sight on the face that deceit her.
“Nothing, I just heard the sound of broken glass and needed to check in case something was happening.” The caped hero scanned the inside of her penthouse, clearly using X-Ray vision to confirm whether she was actually doing something that might displease them.
She looks at her blankly before turning towards National City night sight. She took her time before replying anything, “As you can see, nothing happening.” She stated lowly because she knew that the heroine could still hear it. She looks towards the ground where the road was filled with moving car’s light or certain spot with a shop nightlight.
“Miss Luthor, it is not safe to stand against the railing.” The caped heroine stated as she started to walk towards her.
She scoffs. “I’m turning in.” She stated plainly as she turns around and walk swiftly into her penthouse. Before entering the doorway, she looks at the heroine and wordlessly she slides the door close as it locked automatically.
Just as asymptotes keep two lines from ever intersecting, she now respects those boundaries while quietly creating her own. She knows the woman could easily pull the door from its hinges, but also understands that she would never actually do that. Similarly, the heroine has continued to manipulate her for over three years by keeping her own truth hidden. She refuses to share it because the heroine could never fully trust her with her entire identity. The heroine still sees her as Luthor first and Lena second. That unspoken distance between them is a constant reminder of the walls she cannot breach. In the end, that boundary is necessary—trust cannot be forced where it does not exist.
From now on, she will act solely on her own terms, refusing to be swayed by the pressures that try to force her into what they dismiss as "Luthor madness." It’s nothing but a manipulative label, a way for them to control her narrative and invalidate her decisions. She knows there's no inherent flaw driving her toward some predetermined insanity; just a series of choices, each influenced by complex circumstances and personal motivations. The trajectory she sets for herself is always ascending, a steady climb even when the graph diverges and their manipulations present a challenge to her. She will forge her own path, guided by her own principles, and no longer allow their judgments to dictate her actions.