A root whose existence is implied in Tolkien’s writings from the 1950s and 60s by various reflexive pronouns such as Q. imni “myself” and S. im “self(same)” (VT47/37). Though the root itself did not appear in Tolkien’s later writings, it seems to have been a long standing idea of his, appearing as ᴱ√IMI “same, alike” in the Qenya Lexicon of the 1910s with derivatives such as ᴱQ. iminqa “exactly alike, identical” and ᴱQ. inye- “imitate, make like” (QL/42). It seems to have had Gnomish derivatives from this period as well, such as G. inco “the same, the identical”, though Tolkien put this form under the root for the definite article: ᴱ√I (GL/50). In any case, √IM as the basis for “sameness” and reflexives seems to have been a well established idea in Tolkien’s languages.
Primitive elvish
sam
root. to have, have; [ᴹ√] unite, join
sam
root. mind, think, reflect, be aware
sam-wē
noun. an act of thinking, a thought
im Reconstructed
root. same, alike, [ᴱ√] same, alike
asmarō
noun. *neighbor
sapnā
noun. delved hole, pit
The root ᴹ√SAM “unite, join” was a later addition to The Etymologies of the 1930s with the derivative ᴹQ. samnar “diphthongs” (Ety/SAM). There is also evidence for it in the word ᴹQ. sampane “combination” as in ᴹQ. Lámasampane “Combination of Sounds”, a term used in the first version of the Tengwesta Qenderinwa (TQ1) from the 1930s (PE18/40), and again in the second version (TQ2) from around 1950 (PE18/90). In an isolated note from the late 1930s, Tolkien gave ᴹ√kam “bind, join” as a replacement for √sam along with a new word ᴹQ. okamna “diphthong” (VT44/13), but given the reappearance of Q. sampanë in TQ2 this may have been a transient idea, and in any case Tolkien used the word Q. ohlon for “diphthong” in the 1950s and 60s (VT39/9; VT48/29).
In notes grouped with Definitive Linguistic Notes (DLN) from 1959, Tolkien gave √SAM as the basis for Elvish verbs for “to have”, with Q. samin and S. sevin “✱I have” (PE17/173). Whether this was connected to 1930s ᴹ√SAM “unite, join” is unclear. In notes associated with the 1959-60 essay Ósanwe-kenta, Tolkien gave the root √SAM with the gloss “mind, think, reflect, be aware” (VT41/5), but in later writings he used √SAN for “think, use mind” instead (PE22/158); see that entry for discussion.
Neo-Eldarin: For purposes of Neo-Eldarin, I’d use √SAM = “have”.