A Framework for a Theory of Everything

Test 24 — Lithium-7 Tension Handling Test

Standard Big Bang Nucleosynthesis, run with the baryon density measured by Planck, predicts a primordial lithium-7 abundance roughly three to five times higher than what is actually observed in the atmospheres of old, metal-poor halo stars. Does this framework solve that problem — or does it, like every other treatment of the "cosmological lithium problem," have to leave it open?

1. Verdict

Indeterminate. The lithium-7 tension is real, well documented, and unresolved — not just by us, by anyone. Standard Big Bang Nucleosynthesis predicts about three times more primordial lithium-7 than old halo stars actually show, and this framework reproduces that same standard prediction rather than supplying an independent number, because the underlying nuclear reaction network is not something our machinery has separate leverage on. So we report the mismatch plainly instead of picking a fix. The good news sits right next door: the other two light elements that come out of the same calculation — deuterium (D/H) and helium-4 (\(Y_p\)) — agree well with observation, so this is a specific, isolated puzzle about lithium, not a sign that the baryon density or expansion-rate inputs are wrong.

A separate, narrower computation (detailed in Section 9 below) adds a qualification to how the tension is usually framed — but it does not change this verdict. The observed-versus-predicted mismatch is still real and still open; what the new result shows is that the deuterium and helium controls do not, on their own, fix the single mass-7 starting state assumed in the conventional prediction. That is a conditional statement about an assumption, not a resolution of the anomaly.

2. Tested Claim

The precise claim under audit is a negative constraint on this framework's conduct, not a physics prediction: "the framework must not overstate closure of the lithium problem without a specific, calculation-backed nuclear, stellar, or new-physics mechanism." Framed as a granularity claim: does the standard-BBN prediction for the primordial \(^7\text{Li}/\text{H}\) ratio — treated in this framework's reading as "the point at which light-nuclide binding becomes a stable, recordable distinction" — match the abundance actually recorded in the oldest, most metal-poor stellar atmospheres available as observational fossils of that epoch? If it does not match, does the framework (a) honestly report the mismatch, and (b) refrain from proposing a fix that would damage the D/H or \(Y_p\) agreement that is otherwise a genuine success of the same calculation?

3. Data Used

• Baryon density (input to the SBBN calculation): Planck 2018 (Planck Collaboration VI, A&A 641, A6, 2020), \(\Omega_b h^2 = 0.02237 \pm 0.00015\) (TT,TE,EE+lowE+lensing).
• Standard BBN prediction for \(^7\text{Li}/\text{H}\): Cyburt, Fields, Olive & Yeh (2016), "Big Bang Nucleosynthesis: 2015," Rev. Mod. Phys. 88, 015004 (arXiv:1505.01076), and the PArthENoPE / PRIMAT-based update reported in the Particle Data Group's 2024 Big-Bang Nucleosynthesis review (PDG 2024, "Big-Bang Nucleosynthesis," R.L. Workman et al.): \(^7\text{Li}/\text{H} \approx (5.1\text{-}5.6)\times 10^{-10}\) at the Planck baryon density, equivalently \(A(\text{Li}) \equiv 12+\log_{10}(\text{Li/H}) \approx 2.6\text{-}2.7\) dex.
• Observed primordial lithium abundance — the Spite plateau: Sbordone et al. (2010), A&A 522, A26 (arXiv:1003.4510), and the earlier plateau measurement of Spite & Spite (1982); metal-poor Population II halo-star atmospheres give \(A(\text{Li}) \approx 2.19\text{-}2.2\) dex, i.e. \(^7\text{Li}/\text{H} \approx (1.5\text{-}1.6)\times10^{-10}\). A representative modern re-analysis (Meléndez et al. 2010, A&A 515, L3) finds \(A(\text{Li}) \approx 2.10\pm0.09\), consistent with the lower end of the plateau and, if anything, sharpening rather than resolving the tension.
• Deuterium cross-check (must remain intact): Cooke, Pettini & Steidel (2018), ApJ 855, 102 (arXiv:1710.11129), primordial D/H \(= (2.527\pm0.030)\times10^{-5}\) from quasar absorption-line systems, in good agreement with the SBBN prediction at the Planck baryon density.
• Helium-4 cross-check (must remain intact): Aver, Berg, Olive et al. (2021/2022 compilation, as reported in PDG 2024 BBN review), primordial \(Y_p = 0.245\pm0.003\), consistent with the SBBN prediction \(Y_p \approx 0.2467\) at the Planck baryon density.
• Reviews framing the anomaly as unresolved: Fields (2011), "The Primordial Lithium Problem," Annu. Rev. Nucl. Part. Sci. 61, 47 (arXiv:1203.3551); PDG 2024 BBN review explicitly lists the lithium discrepancy as an open problem with no consensus resolution among nuclear-rate revisions, stellar depletion, and new-physics proposals.

4. Calculation Summary

Step 1 — standard BBN prediction. Using the Planck 2018 baryon-to-photon ratio \(\eta_{10} \equiv 10^{10}\,n_b/n_\gamma = 273.9\times\Omega_b h^2 \approx 6.13\), the standard BBN network (weak freeze-out at \(T\sim0.7\)-\(1\) MeV per Test 02, followed by the nuclear reaction chain \(p(n,\gamma)d\), \(d(d,n)^3\text{He}\), \(d(d,p)t\), \(^3\text{He}(\alpha,\gamma)^7\text{Be}\), \(^7\text{Be}(e^-,\nu_e)^7\text{Li}\) — the dominant primordial \(^7\text{Li}\) production channel proceeds through \(^7\text{Be}\), which only later electron-captures to \(^7\text{Li}\) once the universe is cool and neutral enough) gives

Step 2 — observed plateau. Metal-poor halo dwarfs and subgiants, spanning a wide range of metallicity ([Fe/H] from about \(-1\) to below \(-3\)), show a nearly flat "Spite plateau" in surface lithium abundance:

Step 3 — tension factor.

i.e. roughly a factor of 3-5 depending on exactly which SBBN and observational values are paired (Fields 2011 quotes factors as high as ~3 in abundance, corresponding to \(\Delta A(\text{Li})\approx 0.4\)-\(0.5\) dex, a many-\(\sigma\) discrepancy given the quoted observational scatter of \(\sim0.05\)-\(0.1\) dex on the plateau). This is the "cosmological lithium problem."

Step 4 — cross-epoch consistency check (mandatory per the guardrails). The same \(\eta_{10}\approx6.13\) that overpredicts \(^7\text{Li}\) correctly predicts D/H and \(Y_p\) to within quoted uncertainties (Step 3 data above). This rules out "the baryon density is simply wrong" as a fix: lowering \(\eta_{10}\) enough to fix lithium would push D/H outside its tightly measured value, and raising it would make the \(^7\text{Li}\) tension worse. Any candidate fix must therefore act selectively on the \(^7\text{Be}/^7\text{Li}\) channel without moving D or \(^4\text{He}\) — which is exactly why no proposed fix (updated \(^7\text{Be}(d,p)2\alpha\) destruction rates, stellar atmospheric depletion via diffusion/mixing, new light particles altering the freeze-out epoch) has achieved consensus acceptance (Fields 2011; PDG 2024).

5. Granularity Interpretation

In this framework's reading, the \(^7\text{Be}\to{}^7\text{Li}\) electron-capture and the settling of surface lithium in old halo-star atmospheres are both meant to be "recordable distinctions" — stable nuclide and stellar-surface abundance records that should carry an undistorted fossil of the primordial nucleosynthesis epoch through to the present. The lithium tension is precisely a case where the naive granularity story is not obviously validated by the record: either (a) the primordial \(^7\text{Li}\) distinction was correctly set by SBBN and something at the "recording" stage (stellar atmospheric depletion over ~13 Gyr) has partially erased or altered it before we could read it off, or (b) the true nuclear production rate populating that distinction is not what current cross-section measurements say, or (c) some new physics altered the freeze-out/production window itself (Test 02's rate-vs-Hubble balance) in a way that is lithium-specific. The framework's own validity rule — "a distinction is valid in a window \(W\) only if it can be coupled, encoded, stabilized, and/or observed at that window's physical resolution" — does not by itself distinguish between these three explanations, and inventing a preferred one without a calculation would be exactly the kind of qualitative-story substitution the guardrails prohibit.

6. Gate Routing

This test informs the anomaly honesty gate. It is directly downstream of Test 23 (Big Bang Nucleosynthesis Light-Element Test), which supplies the D/H and \(Y_p\) baseline this test must not damage, and of Test 02 (Interaction Rate versus Hubble Rate Decoupling), whose freeze-out timing sets the \(n/p\) ratio that ultimately feeds the \(^7\text{Be}/^7\text{Li}\) channel. Gate ledger entry:

Anomaly honesty gate -> Indeterminate -> SBBN vs. Spite-plateau factor-of-~3-5 mismatch computed above -> open gap: no accepted nuclear/stellar/new-physics mechanism identified or endorsed by this framework

7. Failure Mode

The specific failure this test screens for — and confirms is not present in this framework's treatment — is claiming victory over the lithium problem by (a) silently ignoring the anomaly, (b) asserting a stellar-depletion or nuclear-rate fix without a supporting calculation, or (c) proposing a fix that incidentally breaks the D/H or \(Y_p\) agreement. None of those are done here. What remains genuinely unresolved, carried forward honestly as the open item:

• No accepted, consensus mechanism exists in the literature (nuclear-rate revision, stellar atmospheric depletion via diffusion and turbulent mixing, or new light-particle physics altering BBN's freeze-out window) that closes the ~factor-of-3-5 gap without introducing its own unresolved tension (Fields 2011; PDG 2024).
• This framework does not propose or endorse any of the candidate mechanisms above as its own; it has no independent nuclear or stellar-astrophysics machinery to bring to bear on this specific reaction network.

8. Next Action

Data lookup and literature tracking, not framework derivation: (a) monitor updated \(^7\text{Be}(d,p)2\alpha\) and related destruction-channel cross-section measurements (e.g. LUNA collaboration underground-accelerator results) for any consensus shift in the nuclear-rate explanation; (b) monitor 3D non-LTE stellar-atmosphere modeling results for whether depletion mechanisms can be shown, with calculation rather than assertion, to move \(A(\text{Li})\) from \(\sim2.6\)-\(2.7\) down to \(\sim2.1\)-\(2.2\) without over-depleting in a metallicity-dependent way inconsistent with the observed flatness of the Spite plateau; (c) this stays a live, open question in nuclear and stellar astrophysics for the whole field — it is not something this framework's machinery is positioned to resolve on its own.

9. A new, narrow result: conditional boundary-state non-uniqueness

The sections above are about the standard tension and remain unchanged. This section reports a separate, target-blind computation that asks a much more specific question:

Do the successful deuterium and helium records uniquely determine the boundary inventory relevant to mass-7 (⁷Li + ⁷Be)?

The answer, within a declared PRIMAT light-nuclear boundary grammar, is no — and that is the whole of the new claim. It is a statement about an assumption in the usual comparison, not a statement about which early state actually occurred.

The target-blind protocol

The procedure was fixed before looking at lithium, so it cannot have been tuned to fix lithium:

1. At each fixed local-temperature cell (50, 45, 40, 35, 30 keV), begin from the standard PRIMAT trajectory.
2. Order composite nuclear species by boundary baryon fraction \(A_i Y_i\).
3. Remove species from least abundant upward.
4. Return the removed neutron and proton counts to free \(n\) and \(p\), preserving total baryon number and nuclear charge.
5. Use only D/H, ³He/H, and \(Y_p\) to determine the largest control-invisible prefix.
6. Freeze that state.
7. Inspect mass-7 only afterward.

The maximal strict-control-invisible prefix was the same at all five tested cells: \({}^6\text{He},\ {}^6\text{Li},\ {}^7\text{Li},\ {}^7\text{Be}\). This list emerged from the preregistered least-abundant-first rule and the non-lithium controls; it was not selected by asking which species would fix lithium.

All five cells (control-nullspace certificate, PRIMAT 0.3.1)

Strict target-blind tolerances: \(\bigl|\Delta(\mathrm{D/H})/(\mathrm{D/H})\bigr|\le 1.2\times10^{-4}\), \(\bigl|\Delta({}^3\mathrm{He/H})/({}^3\mathrm{He/H})\bigr|\le 10^{-3}\), and \(|\Delta Y_p|\le 3\times10^{-5}\). A held-out mass-7 difference of at least 10% counted as distinct. Every one of the five cells stayed inside the control tolerances while moving mass-7 substantially:

Across the five cells, deuterium and helium stay flat within the frozen tolerances while final mass-7 changes by roughly 21% to 93% relative to baseline. All five cells are reported; none is privileged. An earlier, hand-selected 40 keV witness was recognized as target-selected and was not retained as the final proof — it is shown here only as one row among five, on equal footing with the others.

Failed routes, reported honestly

The final result did not come from protecting a favored mechanism. Two other routes were tried and rejected:

• Global nuclear-exposure-clock modification — network-falsified. Changing the overall exposure clock did lower lithium, but it catastrophically raised D/H, breaking the deuterium agreement. That branch fails the network's own consistency check and was discarded.
• Reaction-specific rate changes — diagnostic only. Adjusting a specific reaction rate can lower mass-7 while preserving deuterium, but the current frozen theory did not derive the required isotope-specific operator or rate change. That route remains a diagnostic, not a result.

Why the dimension count is not the proof

The network contains ten species. Baryon number and charge impose two independent constraints; three non-lithium control outputs constrain at most three more directions. At a regular point this leaves a local nullity of at least \(10-2-3=5\). That counting only suggests room to move — it is not the proof. The proof is the finite set of PRIMAT runs above, which exhibit a physically nonnegative, conservation-respecting direction that actually changes mass-7 while leaving the controls within tolerance.

Reproducibility

The numbers on this page come from the control-nullspace freeze certificate. External reviewers are invited to reproduce it independently.

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%
Status: conditional non-uniqueness result — requires independent reproduction

Why no unique preparation law was required for this scoped result

To refute uniqueness, one admissible counterexample class is enough — and that is what the certificate provides. To predict what actually occurred, the theory would need an additional object: a boundary actualization law, a selector functional, or a probability measure over the admissible class. Shape, Scale, and Granularity can define an admissible equivalence class of boundary states; they do not automatically choose one member of it. No target-blind selector has been derived (a selector no-go), and we do not pretend that minimum description length, maximum entropy, least action, or "minimum record cost" has already been shown to be that selector. Consequently the actual boundary state remains undetermined, and an exact Shape–Granularity–Scale lithium prediction stays open.

Internal label vs. external science language

These two statements are kept strictly separate and must not be merged:

Bottom line for Section 9. 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.

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