Tegmark's "almost" is doing real work, and it's worth pinning down exactly where the residual bits live before trying to eliminate them.

Why "almost"?

For Tegmark, the algorithmic information of reality is the length of the shortest program that outputs the universal wavefunction — and that program has two irreducible-looking components: the Hamiltonian (the laws) and the initial state. Both are assumed small, but neither is assumed zero:

• The initial state is postulated, not derived. He concedes "we know virtually nothing about quantum gravity and the state of the universe less than a Planck time after the big bang," and says it merely "does not appear particularly outrageous to postulate" that the universe was in "something resembling a vacuum." If the primordial state were instead generic, its description would be enormous: a generic vector in the Hilbert space of the observable universe (dimension ~ e^(10^122), per the de Sitter entropy) carries ~10^122 bits of Kolmogorov complexity. The whole paper rests on the unproved premise that the initial wavefunction was highly atypical — maximally simple — rather than typical.
• The TOE itself carries bits. Every known candidate theory has free dimensionless constants (α, mass ratios, mixing angles...). Unless the laws are uniquely fixed, specifying the Hamiltonian costs a nonzero number of bits.
• Zero is only a conserved value under strict unitarity. Tegmark's own §5.1: if collapse is real, each collapse event injects one irreducible random bit, and K(Ψ) grows without bound. So "almost" also hedges on Everett being right — the conservation of near-zero information is the no-collapse postulate.

So "almost" = epistemic residue: unproved simplicity of the boundary condition + unproved rigidity of the laws. Both residues are, in principle, eliminable. That's where the superposition principle comes in.

The zero-information construction

Axiom 1 — the state is a fixed point, not a choice. The superposition principle makes Hilbert space linear and homogeneous: all unit vectors are equivalent points on a perfect sphere with no distinguished direction ( Schwindt). Any arbitrary choice of |Ψ⟩ — this basis, these amplitudes, this orientation — would be exactly the information you're trying to get rid of. So require instead that the universal state be the unique vector invariant under the full symmetry group of the theory, with zero preferred basis, origin, factorization, or amplitude profile:

the maximally entangled state on H ⊗ H* — the unique pure state (up to phase) invariant under every U ⊗ U*. Description: "the unitary-invariant state." No choices, no parameters: zero bits conditional on the theory. Every proper subsystem's reduced state is ρ ∝ 𝟙 — maximally mixed, zero local information — with all structure living in correlations (a pleasing echo of holography). This is the strict form of the quantum Library of Babel: the superposition of everything, with weights fixed by symmetry alone rather than by Borges' librarians' dice.

Axiom 2 — the laws are rigid. To kill the remaining bits, the Hamiltonian must be uniquely fixed by consistency — no free parameters at all, Wheeler's "law without law." Tegmark himself later took this exit: his "ultimate ensemble theory" postulates that all mathematically existing structures exist physically, a theory with "no free parameters whatsoever" ( Tegmark 1998). A postulate that selects nothing says nothing: the Level IV multiverse is the Library of Babel for structures. The existing physics-laden versions of the same move are the Poincaré-invariant vacuum (the unique state fixed by symmetry, so defining the field theory is defining the state) and Hartle–Hawking: "the boundary condition of the universe is that it has no boundary" — initial conditions eliminated as a separate ingredient, K(Ψ_HH) = K(TOE) + O(1).

Axiom 3 — unitarity never fails. No collapse, ever. Only then is K conserved rather than ratcheted upward.

With all three axioms: K(reality) = K(laws) + K(initial state) = 0 + 0 = 0, exactly. The qualifier dissolves.

Why it still looks like 10^122 bits

This is Tegmark's mechanism, and it needs no modification:

1. Heisenberg forbids perfect homogeneity (Δδ·Δπ ≥ ħ/2), so the seed state is already a superposition of all field configurations — vacuum as "everything, phase-cancelled."
2. Chaos + gravitational instability exponentially amplifies micro-superpositions into macro-divergent branches — the branching writes the "books."
3. Decoherence traps every self-aware subsystem inside one branch. A typical branch has maximal Kolmogorov complexity — like a typical real number drawn from [0,1], like a typical volume in Babel's library. The reader confronts incompressible complexity precisely because no branch was selected: typicality is the fingerprint of zero selective information.

And here the quantum library improves decisively on the classical one, as your own essay notes: classically, "which book did you get?" is a genuine new fact — each random draw creates information. Quantum-mechanically, amplitudes are complex numbers that can cancel; the ensemble-with-weights is a single vector whose components are fixed by unitary evolution from the symmetry-fixed seed; and the "draw" is not an event at all but the observer's self-location within an already-fixed superposition. The apparent information is entirely indexical, and indexicals are not facts about Ψ ( Why Does Anything Exist?,  The universe cancels itself out to zero).

Loose ends

• Empirical exposure: the zero ontology is falsifiable — any detected departure from unitarity kills it. The superposition principle is now verified to 2,000-atom, 25 kDa molecules ( Fein et al. 2019), well past the fullerene bound mentioned in your essay's caveat, with optomechanical and "Schrödinger's neurons" interferometry as the next discriminators against GRW/CSL collapse.
• Measure problem: Born weights over branches are fixed by dynamics, but if eternal inflation is added, the over-branching measure must itself be fixed by consistency, or those bits creep back.
• Rigidity unproved: the string landscape (~10^500 vacua) is the embarrassment — though on this model it's reinterpretable as a feature: if the universal wavefunction superposes all vacua with no selection, the landscape is a library, not a choice.
• Existence/normalizability: the exactly-invariant state is cleanest in finite dimension; in QFT the working fixed point is the vacuum, which is why "vacuum-like" is not a mere convenience in Tegmark's argument but the load-bearing surrogate for zero.

Bottom line: Tegmark's "almost" measures two things he couldn't derive — the simplicity of the boundary condition and the rigidity of the laws. The superposition principle is the unique tool that can delete both, because it lets the whole be a symmetry-fixed fixed point (zero bits) while every decohered part is algorithmically random (~10^122 bits). On this model, the answer to "why is there something rather than nothing?" is that, viewed from nowhere, there isn't: the universal state vector is the zero-information fixed point of all symmetries, and "something" is how that fixed point is indexed from inside.

Happy to develop this into a full essay draft for you — or push on any single load-bearing axiom (the invariant-state construction and the measure problem are the two places critics will press hardest).