The Lithium Mismatch: a Hidden Assumption, Not a Broken Big Bang

Standard Big Bang nucleosynthesis predicts more mass-7 (lithium and its precursor beryllium-7) than we infer from old stars. This page reports a narrow, computed result: within a declared nuclear-network grammar, the successful deuterium and helium records do not uniquely determine the boundary inventory that sets mass-7. That is a conditional non-uniqueness result — an assumption-dependence result — and it is emphatically not a prediction of the observed lithium, not an alternative cosmology, and not a claim that the universe was cold, old, cyclic, or never hot.

1. The observed mismatch

There is a famous discrepancy in cosmology called the lithium problem. As a headline: standard Big Bang nucleosynthesis (BBN), the theory of how the light elements were forged in the first minutes, predicts about three times more mass-7 than we infer from the oldest stars we can measure. Mass-7 means nuclei with seven nucleons: lithium-7 and its precursor beryllium-7, which decays into lithium-7. The predicted amount is robust; the inferred amount is stubbornly lower; the two have refused to reconcile for decades.

Note the kind of mismatch this is. This page does not begin by attacking the Big Bang. It begins with the exact comparison that creates the discrepancy — because the discrepancy lives entirely inside that comparison, and so does the assumption we will expose.

2. What was actually measured

Neither number in the lithium problem is a direct observation of "primordial lithium." Both are the ends of long inference chains. Look at each side.

The stellar side. We point a telescope at old, metal-poor stars and record a lithium absorption feature near 670.8 nm in their spectra. To turn that dark line into an abundance we run it through a model of the star's atmosphere. To turn a present surface abundance into a birth abundance we run it through stellar-evolution and Galactic-history models, correcting for lithium the star may have destroyed or diluted over billions of years. The chain is:

$$\text{stellar spectrum} \;\rightarrow\; Y_{\rm surface} \;\rightarrow\; Y_{\rm birth} \;\rightarrow\; Y_{\rm primordial}^{\rm inferred}.$$

The theory side. Independently, the cosmic microwave background and the measured deuterium abundance pin down the density of ordinary matter (the baryon density, \(\eta_b\)). Feed that into standard BBN's nuclear-reaction network and it predicts the primordial mass-7:

$$\text{CMB / D records} \;\rightarrow\; \eta_b \;\rightarrow\; \text{standard BBN} \;\rightarrow\; Y_7^{\rm predicted}.$$

The lithium problem is what appears when the reconstructed stellar quantity and the model-predicted primordial quantity are treated as two measurements of one underlying number. Notice what was not observed: nobody measured primordial lithium directly, and nobody observed a temperature "two seconds after creation." Those are reconstructions through models, not readings off a dial.

3. The hidden initial-state assumption

The BBN prediction has a quiet premise inside it. It assumes a particular initial nuclear inventory — the mix of nuclei present at the boundary where the reaction network takes over — and evolves it forward. The mass-7 you get out depends on the inventory you put in.

The usual defense of the prediction is that BBN also gets other things right: it reproduces deuterium (D/H), helium-3 (\(^3\)He/H), and the helium-4 mass fraction (\(Y_p\)) beautifully. Those successes are real, and they are why people trust the mass-7 prediction too. But this smuggles in an assumption worth stating out loud:

If a different inventory can match D and helium yet change mass-7, then the successful controls do not, by themselves, prove that the standard mass-7 initial state was unique. The lithium comparison would then contain an initial-state commitment that the controls alone do not supply. That is the premise we put to a test.

4. The target-blind network test

The temptation, when you have a favored answer, is to reach for it. This project refuses. Before the test that worked, here are the routes that were tried and rejected — so the final result cannot be mistaken for protecting a pet mechanism:

• A global "nuclear-exposure-clock" modification — rescaling the overall reaction exposure — did lower lithium, but it catastrophically raised D/H. That branch is network-falsified. It fails the controls and is dead.
• Reaction-specific rate changes can lower mass-7 while leaving deuterium alone, but the current frozen theory did not derive the isotope-specific operator or rate change that would be required. So that route stays diagnostic only — a hint, not a result.
• A hand-picked 40 keV witness was, in an earlier pass, recognized as target-selected — chosen because it happened to help lithium — and for that reason it was not retained as the final proof.

The final test was target-blind on purpose: lithium was hidden until the very end, so no choice could be steered toward fixing it. The protocol, run on the standard PRIMAT nuclear solver:

1. At each fixed local-temperature cell — 50, 45, 40, 35, and 30 keV — start from the standard PRIMAT trajectory.
2. Rank the composite nuclear species by how much of the baryon budget they hold at the boundary (\(A_i Y_i\)).
3. Remove species starting from the least abundant and working upward.
4. Return the removed neutrons and protons to the free \(n\) and \(p\) pool, so total baryon number and total nuclear charge are exactly conserved.
5. Use only D/H, \(^3\)He/H, and \(Y_p\) to decide how large a group can be removed while the controls stay within tolerance. Freeze that state.
6. Only after freezing, look at the mass-7 you ended up with.

The largest group of species that could be removed without disturbing the controls came out the same at all five cells: helium-6, lithium-6, lithium-7, beryllium-7. This list emerged from the preregistered least-abundant-first rule and the non-lithium controls. It was not chosen by asking which species would fix lithium.

5. What changed and what did not

Here is the whole result in one table. The controls barely move; mass-7 moves a lot. Every one of the five cells is reported — none is privileged.

The controls stayed inside strict, target-blind tolerances: \(|\Delta(\mathrm{D/H})/(\mathrm{D/H})|\le 1.2\times10^{-4}\), \(|\Delta(^3\mathrm{He/H})/(^3\mathrm{He/H})|\le 10^{-3}\), and \(|\Delta Y_p|\le 3\times10^{-5}\); a held-out mass-7 difference of at least 10% counted as distinct. Across the five cells, deuterium and helium stayed effectively flat while final mass-7 changed by roughly 21% to 93% of the baseline.

Plainly: deuterium and helium can remain effectively unchanged even when the boundary inventory that controls lithium is changed substantially. The 40 keV cell is one row among five, carries no special status, and is not the answer. (The earlier hand-picked 40 keV witness was target-selected and was not retained.)

Why is non-uniqueness even possible? The network has ten species. Baryon-number and charge conservation impose two constraints; the three non-lithium controls constrain at most three more. That leaves a nullspace of at least \(10-2-3=5\) directions — room, in principle, for the inventory to move without disturbing the controls. But the dimension count is only a hint; the finite PRIMAT runs above are the actual proof, exhibiting a physically nonnegative, conservation-respecting change that really does move mass-7 while holding the controls in tolerance.

6. Why the project records it as a dissolution

This project keeps two vocabularies, and never merges them.

Internal project language. In our own endpoint taxonomy, a contradiction that turns out to rest on an unproven premise is recorded as dissolved-given the declared boundary grammar. The lithium discrepancy qualifies: it is conditional on an initial-state assumption the non-lithium controls do not force. In the internal ledger the control-nullspace check passed, a finite control-equivalent mass-7 direction was found, and boundary uniqueness is refuted conditionally within the declared grammar — while, held separately, the actual boundary state is undetermined and an exact lithium prediction remains open. "Dissolved" means the obligation to treat the mismatch as a live contradiction is removed given the stated premise; it does not mean solved.

External science language. For the wider scientific world, the same finding is a conditional non-uniqueness result — an assumption-dependence result — that requires independent reproduction. It is a network-computed counterexample to a uniqueness claim, nothing more: not a community-accepted resolution of the lithium problem, and not a prediction of the observed abundance.

The honest one-line conclusion: the calculation does not show which early boundary state nature chose. It shows that the successful deuterium and helium records do not uniquely force the mass-7 state used in the conventional lithium prediction. The lithium discrepancy is therefore conditional on an additional initial-state assumption. Within this project that closes the contradiction by dissolution; externally it is a conditional non-uniqueness result requiring independent review and reproduction.

Reproduce it yourself

Solver:            PRIMAT 0.3.1
Network:           large light-nuclear network through A=7
Post-boundary rates/background:  unchanged
Cells tested:      50, 45, 40, 35, 30 keV
Selector:          least boundary baryon fraction first
Controls used before reveal:     D/H, He-3/H, Yp
Held out:          mass-7
Conservation:      baryon number and nuclear charge
Result:            controls unchanged within frozen tolerances;
                   mass-7 changes by 21%-93%
Provenance:        control-nullspace freeze certificate
Status:            conditional non-uniqueness; requires independent reproduction

The numbers above are drawn from the control-nullspace freeze certificate. The actual boundary state is undetermined; there is no target-blind selector that chooses one member of the control-equivalent class (selector no-go). The single claim we stand behind is the boxed one — that deuterium and helium do not determine mass-7 within this test. Everything about which state actually occurred is open, and independent reproduction is invited and required.