Headline, stated exactly. Within a declared PRIMAT light-nuclear boundary grammar, the non-lithium controls — deuterium (D/H), helium-3 (\(^3\)He/H), and the helium-4 mass fraction (\(Y_p\)) — do not uniquely determine the late boundary mass-7 inventory. Multiple charge- and baryon-conserving boundary inventories evolve under the same post-boundary nuclear network to nearly identical D and helium records while producing very different mass-7 (\(^7\)Li + \(^7\)Be) outputs. This is a conditional, computational non-uniqueness result. It is not a prediction of the observed primordial lithium, not an alternative cosmology, and not a claim that the universe was cold, old, cyclic, or never hot.
Two vocabularies, kept separate on purpose. In the project's internal endpoint taxonomy this may be recorded as dissolved-given the declared boundary-state grammar — a project-internal closure by dissolution. In public scientific language it is a conditional non-uniqueness result (equivalently an assumption-dependence result) that requires independent reproduction. These two statements are never merged. The internal label is a bookkeeping status inside one research program; the external label is the honest scientific claim a reviewer should evaluate. Wherever a project label appears below, its plain-English meaning follows immediately.
The cosmological lithium problem compares the mass-7 abundance predicted by standard Big Bang nucleosynthesis (BBN) with the lithium abundance inferred from old, metal-poor stellar spectra. Standard BBN predicts roughly three times more mass-7 than the stellar inference gives. We tested a narrower, hidden premise inside that comparison: do the successful deuterium and helium records uniquely determine the boundary inventory that controls mass-7? In a target-blind PRIMAT test, multiple baryon- and charge-conserving boundary inventories produced effectively identical D/H, \(^3\)He/H, and \(Y_p\) outputs while changing final mass-7 by 21% to 93% across five tested local-temperature cells (50, 45, 40, 35, 30 keV). This conditionally refutes uniqueness inside the declared network grammar. It does not identify the actual early state and does not establish an alternative cosmology. It shows that the conventional lithium contradiction depends on an additional initial-state commitment not fixed by the non-lithium controls alone.
This is the binding status. Read every line; do not summarize it into a single grade.
CONTROL-NULLSPACE:
PASSED
(a nonempty, physically admissible, control-invisible direction that moves mass-7 exists,
demonstrated by finite PRIMAT runs — not merely by a dimension count.)
FINITE CONTROL-EQUIVALENT MASS-7 DIRECTION:
PASSED
TESTED MEMORY WINDOW:
30-50 keV discrete local-state cells (five cells: 50, 45, 40, 35, 30 keV)
LIGHT-ELEMENT BOUNDARY UNIQUENESS:
REFUTED CONDITIONALLY WITHIN DECLARED GRAMMAR
(external science language: conditional non-uniqueness result; requires independent reproduction.)
LITHIUM DISCREPANCY:
DISSOLVED-GIVEN boundary-state non-uniqueness, as a project dependency
(internal project label only. Plain meaning: the contradiction is conditional on an
initial-state assumption; the project records the contradiction as removed *given* that the
assumption is not forced by the non-lithium controls. This is NOT a community resolution.)
ACTUAL BOUNDARY STATE:
UNDETERMINED
(no target-blind selector exists — see the selector no-go, §7.)
EXACT SGS LITHIUM PREDICTION:
OPEN
(Shape-Granularity-Scale does not select a unique boundary state or a unique cell.)It establishes, target-blind and reproducibly (PRIMAT 0.3.1, unchanged post-boundary rates and background):
It does not establish that the alternative boundary state actually occurred; that the universe was cold, cyclic, or older than its observable phase; that 30–50 keV is a model-independent cosmic-age interval; that the CMB and cosmological observations are reproduced by an alternative cosmology; that Shape–Granularity–Scale predicts a unique initial state; that a physical reset or preparation mechanism has been derived; that the energy/entropy/dynamical-reachability bookkeeping for a preparation event is closed; or that the scientific community's lithium problem is experimentally settled. The full “what this does not prove” section is §8, and it is mandatory reading.
The box is: the non-lithium controls do not uniquely determine mass-7, within the declared PRIMAT boundary grammar. Everything about which state nature actually chose is OPEN. No target-blind selector exists to pick a member of the admissible class; the actual boundary state remains undetermined.
It is essential to start from the observations, not from a general attack on cosmology. The lithium problem is a mismatch between two inferred quantities, neither of which is observed directly.
On the stellar side, the chain is:
Schematically, the stellar inference is a chain of maps:
\[ \text{stellar spectrum}\;\rightarrow\; Y_{\rm surface}\;\rightarrow\; Y_{\rm birth}\;\rightarrow\; Y_{\rm primordial}^{\rm inferred}. \]On the model side, the chain is:
\[ \text{CMB / D records}\;\rightarrow\; \eta_b\;\rightarrow\; \text{standard BBN}\;\rightarrow\; Y_7^{\rm predicted}. \]The CMB and deuterium records constrain the baryon-to-photon ratio \(\eta_b\) under a cosmological and BBN model; a nuclear-reaction network then predicts primordial mass-7, most of it initially produced as \(^7\)Be (which later electron-captures to \(^7\)Li). The “lithium problem” appears when the reconstructed stellar quantity and the model-predicted primordial quantity are treated as two estimates of the same underlying number and found to disagree by a factor of about three.
Neither primordial lithium nor a temperature “two seconds after creation” was directly observed. Both endpoints are the output of layered models. Deuterium and helium-4, by contrast, agree between the CMB-anchored network and their observational determinations to remarkable precision — this agreement is one of the great successes of standard BBN, and nothing in this dossier disputes it. The precise open question this project tested is narrow and specific: given that D and helium are reproduced, is the mass-7 boundary inventory thereby uniquely fixed? The conventional lithium prediction implicitly answers “yes.” The result below is that, within the declared grammar, the honest answer is “not by those controls alone.”
It is worth being precise about why deuterium in particular is such a powerful control, because that power is exactly what makes the non-uniqueness result non-trivial. Deuterium is the most fragile of the light nuclei: it is destroyed rapidly once temperatures and densities are high enough to burn it, so its surviving abundance is exquisitely sensitive to the integrated nuclear exposure and to the baryon-to-photon ratio. A boundary manipulation that materially disturbs the reaction history normally leaves a large deuterium fingerprint. The certificate's finding is that there is nonetheless an admissible family of boundary rewrites that mass-7 “sees” strongly while deuterium barely registers — a family that lives in the part of the inventory space where the mass-7 species themselves carry the change, and the deuterium-controlling machinery is left almost untouched. That is a specific, checkable structural claim, not a vague appeal to model freedom.
Equally, helium-4 (\(Y_p\)) is a near-saturated product: essentially all available neutrons are locked into \(^4\)He, so \(Y_p\) is set primarily by the neutron-to-proton ratio at freeze-out and is famously insensitive to fine details of the network. A boundary rewrite that shuffles small mass-6 and mass-7 inventories and returns their nucleons to the free \(n,p\) pools changes \(Y_p\) only at the level of the tiny returned-nucleon fraction — which is why the \(\Delta Y_p\) entries in the results table sit at the \(10^{-10}\) level, orders of magnitude below any observational reach. Helium-3 sits between these extremes. Understanding these three sensitivities individually is what lets the reader see that the flatness of the controls in §5 is physically reasonable, not a numerical accident.
State the question the project actually tested, in one sentence:
Do the successful deuterium and helium records uniquely determine the boundary inventory relevant to mass-7?
This is an inverse-problem question. It asks whether a forward-computed control readout \(C(S)\) invertibly determines the mass-7 content of the boundary state \(S\). It does not ask which \(S\) nature realized. The distinction between refuting uniqueness (one counterexample class suffices) and predicting the actual state (a selector is required) is the spine of this entire document, and it is developed fully in §7.
The final result did not come from protecting a favored mechanism. Before the target-blind test succeeded, the project ran and rejected several tempting routes. Recording these openly is part of the anti-retuning discipline: a result that only survives because its author refused to keep the branches that failed is more trustworthy than one that quietly discards them. The single most common way a lithium “solution” goes wrong is that it is a knob tuned with the answer in view; each subsection below is a case of the project refusing exactly that.
One tempting idea is a single global “clock” factor that rescales the effective nuclear exposure (the integrated reaction time or density history) so that mass-7 burns down. This does lower lithium. But the same global rescaling catastrophically raises D/H: deuterium is fragile and its abundance is highly sensitive to the same exposure, so any global knob that suppresses mass-7 destroys the deuterium agreement. That branch is network-falsified — it fails the very control (D/H) it must preserve. It is recorded as dead, not quietly dropped.
A more surgical idea is to change one or a few isotope-specific reaction rates (for example, a \(^7\)Be-destruction channel) so as to lower mass-7 while leaving D untouched. Numerically this can be arranged: such a targeted change can lower mass-7 while preserving deuterium. But the current frozen theory did not derive the required isotope-specific operator or the specific rate change. Absent a first-principles derivation of which reaction is modified and by how much, this route is a diagnostic observation about network sensitivity — it shows a lever exists — not a result. It remains diagnostic only.
An early witness was hand-picked at a 40 keV cell because it gave an appealing mass-7 suppression. This was recognized as target-selected: it was chosen with knowledge of the lithium target in view, which is exactly the failure mode the project's discipline forbids. It was not retained as the final proof. The final result deliberately reports all five cells and privileges none; 40 keV appears in the table below only as one row among five, on equal footing. The project makes no claim that its structural principles single out 40 keV, or any other cell, as the physical one; no such selection claim is made anywhere, because none is true.
The lesson carried forward from the 40 keV episode is procedural, and it is what motivated the target-blind protocol of §4. A witness chosen after peeking at mass-7 is worthless as evidence of non-uniqueness, because the analyst's freedom to pick a favorable cell is itself an extra, undeclared degree of freedom — the very thing whose necessity is in question. The corrective is to fix the removal rule and the control tolerances in advance, apply them identically at every cell, and only then read mass-7. Under that discipline, a cell cannot be “selected”; every cell that clears the pre-registered control tolerances is reported, whatever its mass-7 turns out to be. This is why the deliverable is a five-row table rather than a single headline number, and why the monotone trend across cells (§5.3) is presented as a diagnostic rather than as a pointer to a preferred cell.
Read together, the three rejected routes make a single point: the surviving result is not a retuning. The global-clock route was killed by the network itself (it broke D/H). The reaction-specific route was withheld because the theory could not derive the operator it would require. The hand-picked cell was discarded because it was target-selected. What remained — the target-blind, conservation-respecting, pre-registered removal test — is the only route that both survived the network's own consistency checks and avoided smuggling the answer into the setup. That provenance is part of the evidence, not a footnote to it.
Let \(S\) denote a boundary nuclear inventory — a nonnegative vector of abundances over the network's nuclear species at the moment the boundary intervention is applied. Let \(\Phi\) denote the unchanged PRIMAT post-boundary evolution operator: given \(S\), \(\Phi(S)\) is the fully evolved final light-element record. Define the non-lithium control readout
\[ C(S)=\bigl(\mathrm{D/H},\;{}^3\mathrm{He/H},\;Y_p\bigr)\big|_{\Phi(S)}, \]and the held-out mass-7 observable
\[ L_7(S) = \bigl({}^7\mathrm{Li}+{}^7\mathrm{Be}\bigr)\big|_{\Phi(S)}. \]Write \(x \sim_\Delta y\) to mean “\(x\) and \(y\) agree to within the pre-registered tolerance \(\Delta\).” The certificate produces finite witnesses \(S_1, S_2\) satisfying
\[ S_1 \neq S_2,\qquad C[\Phi(S_1)] \sim_{\Delta_C} C[\Phi(S_2)],\qquad L_7[\Phi(S_1)] \not\sim_{\Delta_7} L_7[\Phi(S_2)]. \]Therefore, within the declared network and boundary-intervention grammar,
\[ \boxed{\text{the non-lithium controls do not uniquely determine mass-7.}} \]The protocol is target-blind: the mass-7 output is not consulted until the boundary state has been selected and frozen using only the non-lithium controls. This ordering is what makes the result a genuine test rather than a fit.
The maximal strict-control-invisible prefix was the same at all five tested cells:
\[ {}^6\mathrm{He},\quad {}^6\mathrm{Li},\quad {}^7\mathrm{Li},\quad {}^7\mathrm{Be}. \]This list emerged from the pre-registered least-abundant-first rule together with the non-lithium controls. It was not selected by asking which species would fix lithium. That \(^7\)Li and \(^7\)Be appear in it is a consequence discovered after freezing, not an input.
The logic is an inverse-reconstruction, not an illustrated creation event. The observations feed a control readout; the control readout defines an equivalence class of boundary states; the class contains members with different mass-7. Schematically:
Observed spectra and abundance records
|
v
Non-lithium controls: D/H, He-3/H, Yp
|
v
Control-equivalent boundary class E_c
/ | \
State A State B State C
same D/He same D/He same D/He
mass-7 = X mass-7 = Y mass-7 = Z (X, Y, Z differ)The diagram is about which boundary states are indistinguishable to the controls. It deliberately does not depict a Big Bang explosion, a point mass, or a definitive alternative cosmic history, because the result concerns an inverse boundary-state reconstruction and asserts nothing about a realized creation event.
The boundary intervention is a strictly conservative rewrite of the inventory. When a composite species \(X\) with mass number \(A_X\) and charge \(Z_X\) is removed, its constituent nucleons are returned to the free pools:
\[ \Delta n = +(A_X - Z_X)\times(\text{removed count}),\qquad \Delta p = +Z_X\times(\text{removed count}). \]By construction the total baryon number \(B=\sum_i A_i Y_i\) and the total nuclear charge \(Q=\sum_i Z_i Y_i\) are each held fixed:
\[ \Delta B = 0,\qquad \Delta Q = 0. \]These two conservation laws are exact and are the only structural constraints the transformation imposes on the removed content. The resulting boundary state is manifestly nonnegative (species are removed, never driven negative; nucleons are added to \(n,p\)).
Disassembling a composite nucleus into free nucleons is not energy-neutral: the nuclear binding energy is released or absorbed. Honesty requires stating this rather than burying it. The magnitude of the binding-energy bookkeeping term is negligible relative to the radiation budget: it is of order
\[ \frac{\Delta E_{\rm bind}}{E_{\rm rad}/\text{baryon}}\;\sim\;10^{-16}, \]i.e. about one part in \(10^{16}\) of the radiation energy per baryon at these epochs. This is far below any level at which it would perturb the thermodynamic background or the reaction rates. We record it explicitly as a real (if microscopic) term and note that the post-boundary evolution \(\Phi\) is run with rates and background unchanged; the compensation is not used as a tuning knob. It is disclosed here so that no reader can claim it was concealed.
The controls count as “unchanged” only if they satisfy the strict final tolerances (not the looser preliminary ones used during development):
\[ \left|\frac{\Delta(\mathrm{D/H})}{\mathrm{D/H}}\right|\le 1.2\times10^{-4}, \] \[ \left|\frac{\Delta({}^3\mathrm{He/H})}{{}^3\mathrm{He/H}}\right|\le 10^{-3}, \] \[ |\Delta Y_p|\le 3\times10^{-5}. \]A held-out mass-7 difference of at least 10% counted as distinct. All five cells satisfy the control tolerances by orders of magnitude while exceeding the 10% mass-7 threshold by large margins (see §5).
The following table is reproduced from the control-nullspace freeze certificate. All five cells are reported. No cell is privileged; 40 keV is one row among five.
| Local cell | Maximal control-invisible prefix | Relative \(\Delta D/D\) | Relative \(\Delta{}^3\mathrm{He}/{}^3\mathrm{He}\) | \(\Delta Y_p\) | Final mass-7 / baseline |
|---|---|---|---|---|---|
| 50 keV | He6, Li6, Li7, Be7 | \(1.512\times10^{-5}\) | \(-7.766\times10^{-7}\) | \(-6.584\times10^{-11}\) | 0.787767 |
| 45 keV | He6, Li6, Li7, Be7 | \(2.754\times10^{-5}\) | \(-4.466\times10^{-6}\) | \(1.784\times10^{-10}\) | 0.520153 |
| 40 keV | He6, Li6, Li7, Be7 | \(3.608\times10^{-5}\) | \(-9.541\times10^{-6}\) | \(4.733\times10^{-10}\) | 0.298951 |
| 35 keV | He6, Li6, Li7, Be7 | \(4.115\times10^{-5}\) | \(-1.339\times10^{-5}\) | \(6.804\times10^{-10}\) | 0.153755 |
| 30 keV | He6, Li6, Li7, Be7 | \(4.634\times10^{-5}\) | \(-1.632\times10^{-5}\) | \(6.907\times10^{-10}\) | 0.073614 |
Two facts run in parallel across the rows, and both matter:
The plain reading: deuterium and helium can remain effectively unchanged even when the boundary inventory that controls lithium is changed substantially. The successful D and helium controls therefore do not, by themselves, prove that the standard mass-7 initial state was unique. This is the entire claim — and it is exactly this much, no more.
The contrast is easiest to see as a comparison across the tested window: the three control channels are pinned to a flat line near zero fractional change, while the mass-7 curve descends steeply from a 21% deficit to a 93% deficit. Roughly, in units of each channel's own tolerance budget:
fractional change (in units of that channel's tolerance)
1.0 +--------------------------------------------------
| 10%-distinct threshold for mass-7 ------------- * mass-7 far below baseline
|
0.5 +
|
0.0 +==D/H====He-3====Yp====== (all far inside tolerance, effectively flat) ==
50keV 45keV 40keV 35keV 30keV
mass-7/baseline: 0.788 0.520 0.299 0.154 0.074The figure's message is the whole result in one glance: the controls hug zero across every cell while mass-7 walks off. It is a comparison of sensitivities, not a claim about which cell is physical.
The mass-7 suppression deepens monotonically as the cell temperature drops from 50 to 30 keV. This is a coherent, sensible pattern — it says the control-invisible mass-7 direction has more room at lower cells — but it must not be read as selecting a cell. There is no target-blind principle that picks 30 keV (deepest suppression) or 40 keV (the retired hand-pick) or any other cell as the physical one. The trend is descriptive of the tested window; it is not a preparation law. Which cell (if any) nature realized is undetermined.
The tested network contains ten nuclear species. Two exact conservation laws — baryon number and nuclear charge — impose two independent linear constraints on any admissible boundary perturbation. The three non-lithium control outputs (D/H, \(^3\)He/H, \(Y_p\)) constrain at most three additional directions (the differentials of the control map at a regular point). At a regular point of the control map, the local nullity — the dimension of the space of boundary perturbations that conserve \(B\) and \(Q\) and leave all three controls stationary to first order — is therefore at least
\[ 10 - 2 - 3 = 5. \]So there is generically a five-dimensional (or larger) family of control-invisible boundary directions available.
The dimension count is suggestive, not decisive, and the dossier is emphatic about this. A local nullity argument establishes only that a first-order, possibly-signed, possibly-tiny direction exists in the tangent space at a regular point. It does not by itself establish that:
The proof is the finite PRIMAT runs in §5. Those runs exhibit, at each of five cells, an explicit conservation-respecting, nonnegative boundary state that keeps all three controls within strict tolerance while moving mass-7 by 21% to 93%. The witnesses — not the count — are the certificate. The count merely explains why such witnesses are unsurprising once one looks.
The distinction is not pedantic. Inverse problems are full of cases where a naive dimension count promises freedom that positivity or finiteness then removes. Abundances are physical concentrations: they cannot be negative, and the control map is nonlinear in them, so the honestly available directions are the intersection of the linear nullspace with the nonnegative cone, evaluated at finite displacement rather than to first order. A five-dimensional tangent nullspace could in principle collapse to a single point once those constraints bite, in which case there would be no non-trivial control-invisible boundary and the uniqueness question would resolve the other way. The certificate forecloses that possibility by exhibiting concrete, nonnegative, finite states. This is precisely why the dossier refuses to rest the claim on \(10-2-3=5\) and instead rests it on the tabulated runs.
The reason the control-invisible direction lands on \(^6\)He, \(^6\)Li, \(^7\)Li, and \(^7\)Be is structural. These are among the least abundant composite species at the boundary (which is why the least-baryon-fraction-first rule reaches them), so removing them and returning their nucleons to \(n,p\) perturbs the free-nucleon pools only microscopically — hence the near-invisibility to \(Y_p\), which depends on the bulk \(n/p\) ratio, and to deuterium, whose subsequent burning is governed by the dominant reaction channels rather than by these trace species. Yet mass-7 is exactly the inventory being removed, so its final value responds at leading order. In other words, the four species sit in the sweet spot where they are simultaneously a large fraction of the mass-7 budget and a negligible fraction of the control budget. That coincidence of sensitivities is what the certificate exploits, and it is entirely a property of the standard network — no new physics is introduced to create it.
The result is stated within a declared grammar, and the grammar's limits are part of the honest claim:
Two very different tasks must never be conflated:
Formally, the controls define an admissible equivalence class
\[ \mathcal{E}_c = \{\,s:\ Q(s)=Q_0,\ C[\Phi(s)] \sim_{\Delta_C} c\,\}, \]the set of all boundary states \(s\) that respect the conserved charge \(Q_0\) and reproduce the control readout \(c\). The witnesses live in this class. The class is nonempty and contains members with very different mass-7. That is the whole content of “non-uniqueness.”
Shape, Scale, and Granularity (the project's structural principles) can, at most, define such an admissible equivalence class \(\mathcal{E}_c\). They do not automatically choose one member of it. A unique prediction would require an additional object — either a selector functional whose minimizer is unique,
\[ \mathscr{P}_\partial(c) = \operatorname*{argmin}_{s\in\mathcal{E}_c} J_\partial(s), \]or a probability measure \(\mu_\partial(ds\mid c)\) over the class. Neither is derived. There is no derived cost functional \(J_\partial\) with a unique argmin over \(\mathcal{E}_c\), and no derived measure \(\mu_\partial\). Candidate principles one might reach for — minimum description length (MDL), maximum entropy, least action, or “minimum record cost” — are not derived as this selector, and it would be dishonest to pretend any of them has been. This is the selector no-go: the structural principles fix an admissible class but supply no unique member. Consequently the actual boundary state is UNDETERMINED and the exact SGS lithium prediction is OPEN.
Each candidate is worth naming individually, so that no reader mistakes a plausible-sounding principle for a completed derivation:
The honest status is that each of these is a candidate direction for future work, and none is a present result. Adopting any of them today would be a target-anchoring move — choosing the selector that happens to land on a preferred cell — which is precisely the discipline violation the 40 keV episode taught the project to refuse. The selector no-go is therefore not a temporary gap awaiting a quick patch; it is a substantive open obligation, and it is recorded as such rather than hidden.
The scoped result — non-uniqueness — does not need a selector, precisely because refuting uniqueness needs only one counterexample class, whereas predicting the realized state needs the selector. The absence of a selector is therefore not a hole in the non-uniqueness claim; it is the honest boundary of what the non-uniqueness claim can imply. The non-uniqueness is proved (within the grammar); the selection is open. Both statements are true simultaneously, and neither is allowed to borrow strength from the other.
This section is mandatory and deliberately prominent. The test starts from the standard PRIMAT trajectory at each cell and applies a declared boundary intervention. It proves conditional state-space non-uniqueness, not dynamical reachability from an independently derived earlier universe. The work does not prove:
This is not yet an alternative cosmological model. The intervention begins from a standard PRIMAT trajectory and demonstrates that the late nuclear inverse problem is non-unique under a declared boundary grammar. A stronger claim — that a nonstandard earlier universe dynamically prepares one of these states — would require an independently derived boundary-transfer law with energy, entropy, CMB, and cosmological consistency. The present result should therefore be read as a computational counterexample to uniqueness, not as proof of a particular cosmic history.
This paragraph is reproduced verbatim and is not to be removed or weakened for presentation.
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 (removal rule): least boundary baryon fraction first
Controls used before reveal: D/H, He-3/H, Yp
Held out: mass-7 (7Li + 7Be)
Conservation: baryon number and nuclear charge (exact)
Binding-energy bookkeeping: ~1e-16 of radiation-per-baryon (disclosed, not a knob)
Strict tolerances: |Δ(D/H)/(D/H)| <= 1.2e-4
|Δ(3He/H)/(3He/H)| <= 1e-3
|ΔYp| <= 3e-5
Distinct-mass-7 threshold: >= 10% change
Result: controls unchanged within frozen tolerances;
mass-7 changes by 21%-93% across the five cellsThe result reproduces by running the standard PRIMAT 0.3.1 trajectory at each cell, applying the pre-registered least-baryon-fraction-first removal with nucleon return to \(n,p\), determining the maximal control-invisible prefix from D/H, \(^3\)He/H, and \(Y_p\) alone, freezing the state, and only then reading mass-7. The post-boundary rates and thermodynamic background are left unchanged; no reaction rate is retuned. The control-nullspace freeze certificate contains the generated result tables and the scripts that produce them. Where the source and result packages are published on the site, they are linked from the accompanying pages.
The numbers above are attributed to the control-nullspace certificate under PRIMAT 0.3.1. As a matter of scientific standard, the result requires independent reproduction — an independent group running an independent (or independently audited) light-nuclear network under the same declared grammar and confirming that the controls stay within tolerance while mass-7 moves. Until that is done, the honest status is a computational counterexample awaiting external confirmation, not a settled community fact.
Two vocabularies describe this result, and they must not be merged.
| Project-internal label | Plain external-science meaning |
|---|---|
| Lithium discrepancy: dissolved-given the declared boundary-state grammar | The contradiction is conditional on an initial-state assumption; within this one program the contradiction is recorded as removed given that the assumption is not forced by the non-lithium controls. This is a project closure by dissolution, not a community-accepted solution or a direct prediction. |
| Light-element boundary uniqueness: refuted conditionally within declared grammar | A conditional non-uniqueness result. It holds inside the declared PRIMAT boundary grammar and requires independent reproduction. |
| Control-nullspace: passed | An explicit, finite, physically admissible, control-invisible direction that moves mass-7 was demonstrated by PRIMAT runs. |
| Actual boundary state: undetermined; exact SGS lithium prediction: open | The calculation does not identify which early state nature chose; no target-blind selector exists; predicting the realized state remains open. |
“Project closure by dissolution” is a status inside one research program's bookkeeping. An “externally accepted solution” or a “direct prediction” is a different, higher bar that this result does not claim to clear. Always read the internal label with its plain meaning attached.
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.
Stated once more with the boundaries intact: the box is that D and helium do not determine mass-7 within the declared grammar; everything about which state actually occurred — the actual boundary state, the preparation law, the selector, the exact lithium prediction — is open. This is a result from a project that actively tries to falsify itself, and it reports exactly what it proved and no more.
Dossier built from the control-nullspace freeze certificate and the boundary-preparation-law selector audit. Numbers attributed to the control-nullspace certificate under PRIMAT 0.3.1 (large light-nuclear network through A=7; post-boundary rates and background unchanged). Sources synthesized: control_nullspace_freeze_certificate/docs/CONTROL_NULLSPACE_DECISIVE_RESULT.md and its generated result tables; control_nullspace_freeze_certificate/README.md; boundary_preparation_law_attack/BOUNDARY_PREPARATION_LAW_ATTACK.md (selector no-go); boundary_inventory_memory_test/docs/DECISIVE_RESULT.md and scripts/initial_inventory_memory_test.py (earlier witness, superseded in interpretation). Requires independent reproduction.