Ordinary life and irony
Irony is a gift to those who find themselves bored like Clay Jannon, working jobs that are mundane and somewhat inconsequential in the greater scheme of life. Clay isn't on his way to discovering a cure or anything. He just helps people in his community to access good books, and yet that doesn't mean his life is ordinary. His life gets tangled up in crazy conspiracies and mysteries, showing that even the boring parts of life can be mysterious and critical.
The irony of meaning
If the reader takes the ciphers and codewords of the novel as a sign for meaning, they will see this irony, that not all meaning is designed to be readily understood. Sometimes, one has to investigate something with serious dedication and scrutiny if they want to understand the true meaning of something. Notice that the ciphers make him endure long spells of hard work and creativity in order for him to find their meaning. The irony points to enlightenment.
The irony of the Founder's Puzzle
The Founder's Puzzle can be seen through the lens of dramatic irony, because although Clay doesn't know he's a designed character in a narrative artwork, the reader does know that. So, the Founder's Puzzle is ironic, because it is not just the "Founder's" but also the author's puzzle. The author's challenge to the character is to solve the puzzle, making Clay a kind of adventurer. He really wants to solve the puzzle, so he starts to work harder and harder to learn more. The puzzle is an ironic contrast to his boring work life.
The irony of secret community
Instead of showing community through the lens of openness and shared life, the novel depicts community through the lens of the covert, the mysterious, and the conspiratorial. The esoteric quality of secret societies prevents the harm of individuals from threatening the group. When Clay starts to discover the secrets, that is an ironic problem to them.
The ironic ending
Instead of ending by explaining the mysteries of the Penumbra project to the reader, something ironic happens. The story ends with the promise of solution. That means that the mystery is something the reader doesn't get to read, putting the reader in the role of problem solver, because curiosity will make the reader wonder what the mystery is. This irony makes the reader more likely to become curious about the secrets that might lie all around them, or even the mystery of life.
