My neighbor and I have been sharing a cat that belongs to neither of us

The cat answers to two names and neither is official.

I call him Tuesday because that was the day he first walked into my kitchen.

My neighbor Anika calls him Professor because he sits on her books while she studies.

For eighteen months, Tuesday Professor has divided his time between our apartments.

He arrives at my door around six in the morning, eats a spoonful of wet food and sleeps on the chair beside my desk. Around four, he scratches to leave. Anika says he appears at her place before dinner, supervises her homework and sleeps at the foot of her bed.

We discovered the arrangement when I posted a photograph in the building group asking whether anyone owned the gray cat in the blue collar.

Anika replied with a picture of the same cat wearing a green collar.

Each of us had assumed the other collar belonged to his real owner.

We took both off and checked for tags. There were none. A veterinary clinic scanned him for a microchip. Nothing appeared.

We put up signs, searched neighborhood pages and asked nearby houses. Nobody claimed him.

So we developed a system.

Anika handles the vet appointments because she has a car. I buy most of the food because I work from home and notice when it runs low. We split the bills. If either of us travels, the other becomes the full-time household.

We never agreed who owned him.

This was convenient. Ownership sounded like a question with a loser. Tuesday Professor seemed satisfied with two windows, two feeding stations and twice the number of people willing to open doors.

Last month, Anika received a graduate-school offer in another city.

She wants to take him.

Her argument is strong. She found the clinic, managed his vaccines and has a new apartment that allows pets. She says he sleeps with her at night and treats my place like a daytime café.

My argument is also strong. He spends more waking hours with me, uses the scratching post I bought and becomes distressed if my door is closed during the day. My apartment is the only stable home he has known since appearing.

The cat’s argument is unavailable.

We tried experiments. For one week, Anika kept him indoors at her place. He yowled at the door each morning. The next week, I kept him. He paced the hallway every afternoon.

We stopped testing because the tests were punishing him for our inability to decide.

Anika leaves in six weeks.

We have considered alternating months, which the vet said would likely create more disruption than comfort. I offered to reimburse her share of his care. She said the issue was not money. She offered the same to me.

Someone suggested letting him choose by opening both doors and seeing where he slept. That would reduce eighteen months of attachment to one evening and whichever apartment had the warmer radiator.

The truth is that we avoided defining the relationship while it was easy. We called the ambiguity generous because all three of us benefited from it.

Now geography is forcing a decision our affection cannot make fair.

How should two people decide who keeps an animal when both acted like owners, neither claimed the title and the animal built a daily life around both homes?