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ThasyekaH ठस्येकः ONPANINI 73050

(At the beginning of a /taddhita,) replace Th ठ् with ik इक्.

So, /Thak is actually -ikak-, and /TiThan is -Tikan-.

See also AyaneyIn....

Lemme get this strite. Apparently /pANini needed an ika इक affix with /Tit and /nit. Then he uses Th ठ् as an abbreviation of ik इक्, and then he adds an i इ feop between the /Tit and the Th ठ्?

Yes.

Then why didn't he just say Tikan टिकन्, instead?

I guess that, if it were Tikan टिकन्, it'd be hard to remember if Tikan टिकन् is an ika इक affix, or a ka क affix with an i इ prepended feop.