Ship of Theseus: Replacing a Language Model Plank by Plank, and the Nobody in the Middle

The ship of Theseus asks whether an object survives the replacement of all its parts. We put the question to two language models with the same architecture and different identities. Qwen2.5-7B-Instruct says it is Qwen, made by Alibaba Cloud. DeepSeek-R1-Distill-Qwen-7B says it is DeepSeek-R1 and thinks aloud before it answers. Each model was cut into 31 planks (the embedding, 28 decoder blocks, the final norm and the output head), and the planks of Qwen were replaced by those of DeepSeek one at a time in eight orders, giving 240 hybrids. Every hybrid was measured next to its Hobbes twin, the ship built from the planks it discarded. We added 8 hybrids that swap one kind of part at once and 9 that blend every weight. Each hybrid was scored for what it says it is, how it behaves, whether it still works and what it says about itself in free text. Five hypotheses were fixed before the run. Identity sits near the output: replacing planks from the output end moved the self-report halfway to DeepSeek after about 5 planks, against about 22 from the input end. Identity was close to additive over planks (R² = 0.85), with twins together leaning towards DeepSeek by 0.15 on a scale where the parents are 0 and 1. Swapping planks sank the middle of the voyage, with perplexity up to 86,002 against parents at 12.4 and 43.6, while blending every weight never passed 48.2. A predicted sharp tipping point appeared in only two of four curves, and no seaworthy hybrid said one thing while behaving like the other. The result we did not predict is that the ships in the middle are nobody. Asked who they are, the plank hybrids named neither parent in 1,745 of 1,920 replies. The attached archive is tag v1.0.0 of https://github.com/pragyaangaur/Ship-of-Theseus, with the run script, the design and its amendment, the raw output of the pilot and the 7B run, and tests that recompute every reported number.