1. The shared-context request
Channel: connection note, under 300 characters.
Line 1: the specific overlap — same client type, same conference, a post of theirs you read.
Line 2: why you want them in your network.
No line 3. No ask, no link, no pitch.
Why it works: it answers the only question an invitation raises — why you — then stops, which is the part people cannot resist ruining.
2. The specific-observation InMail
Channel: InMail. Subject: concrete, four to six words.
Line 1: the observation only they could receive.
Line 2: the link between that and what you do.
Line 3: a question answerable in one sentence.
Why it works: it earns its credit by proving in line one that a human read their page, and the ask is small enough to grant absent-mindedly.
3. The warm-path message
Channel: either.
Line 1: name the path — the mutual contact, the group, the thread you both commented on.
Line 2: what it suggests you have in common.
Line 3: a low-stakes question about their side of it.
Why it works: it borrows credibility that already exists. Never invent the path — a fabricated mutual contact is one click from being checked.