Sourced guide
What did Irenaeus say about tradition?
Irenaeus argues that true apostolic teaching is public, traceable, and preserved in the churches founded by the apostles, rather than hidden in secret gnostic traditions.
Chain in the data
The argument
Irenaeus writes against teachers who claimed secret knowledge. His answer is historical and public: look at the churches, their bishops, and the teaching openly handed down from the apostles.
Rome is especially important in his argument, but the logic is wider than Rome alone.
Why the Polycarp link matters
Irenaeus can also appeal to personal memory. He had heard Polycarp, and Polycarp was remembered as a hearer of John.
That gives Irenaeus's anti-gnostic appeal a concrete human chain rather than an abstract appeal to institutional authority.
Relevant relationships
Forward edge into the next era. Irenaeus in his Letter to Florinus describes hearing Polycarp preach in his youth at Smyrna.
Irenaeus, who personally heard Polycarp in his youth, states in Adv. Haer. 3.3.4 and his Letter to Florinus (Eus. HE 5.20) that Polycarp was instructed by John and 'others who had seen the Lord'. This is a near-contemporary chain (Irenaeus -> Polycarp -> John), so 'documented'.
Irenaeus describes in his Letter to Florinus hearing Polycarp preach in his youth in Smyrna and remembering his testimony about John the Apostle. This is direct first-person testimony.
Irenaeus' succession list names Linus as the man to whom 'the apostles' (Peter and Paul) committed the Roman episcopate. Episcopal succession lists for 1st-c Rome were reconstructed by Irenaeus c. 180 (Adv. Haer. 3.3); not contemporaneously attested.
Roman succession list reconstructed by Irenaeus c. 180; no contemporaneous attestation.
Roman succession list reconstructed by Irenaeus c. 180; the order Linus-Anacletus-Clement is not contemporaneously attested.
Tertullian (De Praesc. 32) says Clement was ordained by Peter. Origen and others identify him with the Clement of Phil 4:3. No first-person testimony survives — marked tradition per the brief.