# Field-dependent nuclear stability: experimental suite E24–E35

**Status:** Proposed research protocols, not completed simulations or evidence for new field phases.

**Prepared:** 29 September 2026.

## Objective

Determine whether a specified, observationally viable change of a persistent field background can move spin–isospin-resolved nuclear systems across binding or decay thresholds, and whether accessible reaction pathways then produce materially different nuclear histories.

The immediate target is not a proof that life becomes impossible. The target is an independently testable chain:

$$
\boldsymbol\phi
\longrightarrow \mathbf C(\boldsymbol\phi)
\longrightarrow \{a_i,r_i,\text{mixing parameters},B_i,\Delta_{np},g_A,\ldots\}
\longrightarrow \{Q_r,\sigma_r(E),\Gamma_r\}
\longrightarrow \mathbf Y(t).
$$

Here the middle quantities belong to one matched theory. They cannot be tuned independently in order to make the final result interesting. Existence, production, survival, and observational viability are separate tests.

A shallow bound state is not necessarily metastable; a virtual-state pole is not a long-lived nucleus. Long-lived nuclear excitations and a metastable field background are separate possible sources of persistence. The two-nucleon and isomer programs below keep those meanings distinct. [R03, R20]

## Scope and numbering

E24–E33 form the principal program. E34 and E35 are optional branches that address genuine excited-state or collective metastability. They extend the earlier E00–E23 program rather than replace its field-potential, gravitational, spectroscopy, and observer-conditioned spatial-history calculations.

Resource labels describe implementations, not promised runtimes: **entry** means analytic work and small numerical models; **intermediate** means substantial software and uncertainty analysis; **advanced** means specialist nuclear theory, coupled channels, stellar evolution, or high-performance computation.

---

## E24 — Calibrate the spin–isospin channels in our phase

**Question:** Can the implementation reproduce known few-nucleon observables before any background is changed?

**Priority/resources:** First; entry to intermediate. Use an instructional potential for verification, then a calibrated effective interaction for predictions.

### Targets and inputs

Treat the neutron–proton coupled ${}^3S_1$–${}^3D_1$ deuteron channel separately from the ${}^1S_0$ neutron–proton, neutron–neutron, and proton–proton channels. Include Coulomb interactions explicitly for the proton pair. Antisymmetry and total spin/isospin labels should be automated and unit-tested. [R02, R03]

Use measured scattering observables, deuteron binding and electromagnetic observables, evaluated masses, and source-level uncertainties. NN-OnLine provides data and partial-wave-analysis products; these are not statistically independent copies of the same measurements. AMDC and CODATA provide mass references. [R01, R07, R08]

### Calculations

1. Verify a square-well or regulated contact model against its analytic bound-state and scattering solutions.
2. Fit a low-energy interaction to selected observables; reserve independent observables for validation.
3. Implement the coupled deuteron channel with a tensor interaction when the selected order/formulation requires it. A schematic representation is

$$
H=T+V_{01}P_{01}+V_{10}P_{10}+V_T S_{12}P_{10}+V_{\rm Coulomb}+\cdots,
$$

where $P_{SI}$ project spin $S$ and isospin $I$, and the dimensionless coordinate-space tensor operator is

$$
S_{12}=3(\boldsymbol\sigma_1\cdot\hat{\mathbf r})(\boldsymbol\sigma_2\cdot\hat{\mathbf r})-\boldsymbol\sigma_1\cdot\boldsymbol\sigma_2.
$$

4. Include electromagnetic currents at an order consistent with electromagnetic observables.
5. Compare at least two regulators or calibrated formulations; estimate truncation uncertainty and test low-energy validity. Bayesian pionless-EFT calibration provides an existing methodological benchmark. [R02]

### Controls and acceptance

Numerical error must be demonstrably smaller than the physical uncertainty being interpreted. Do not demand that a truncated effective theory reproduce arbitrarily precise data outside its expected accuracy. Do not treat the deuteron D-state probability as a directly measured target: it depends on representation, unlike consistently calculated observables. [R05]

**Output:** A frozen baseline with data provenance, parameter covariance, held-out predictions, and phase-shift/binding plots.

**Failure meaning:** Failure here invalidates dependent simulations; it is not a negative result about alternative physics.

---

## E25 — Track binding and virtual-state thresholds with scattering poles

**Question:** Which changes genuinely create or remove a nuclear bound state?

**Priority/resources:** First-stage core; entry to intermediate. Depends on E24.

For a neutral low-energy S wave,

$$
f_0(k)=\frac{1}{-1/a+(r_e/2)k^2-ik}.
$$

The shallow bound-state pole has $k=i\kappa$ and satisfies

$$
\kappa-\frac1a-\frac{r_e}{2}\kappa^2=0,
\qquad B=\frac{\hbar^2\kappa^2}{2\mu}.
$$

These relations are valid within the effective-range expansion. Use a Coulomb-modified amplitude for charged channels. The physical distinction between a bound pole and a virtual pole must be retained. [R03]

### Runs

- Scan inverse scattering lengths through zero while recording effective ranges and other relevant parameters.
- Perform independent-channel scans only as response diagnostics.
- Reproduce a published tensor-strength deformation of the deuteron as a controlled Hamiltonian experiment. It is not yet a field-theory prediction. [R04]
- Replace the diagnostic scans by E27's correlated field trajectories when available.
- Use adaptive sampling near pole crossings and quantify uncertainty in each crossing.

### Controls

Track the analytic continuation and the Riemann sheet, not only the sign of a fitted scattering length. Reject deep roots generated by a truncated expansion outside its validity. Do not identify a negative finite-box eigenvalue with an infinite-volume bound state without a volume or amplitude analysis. Test volume, cutoff, fitting-window, and higher-order sensitivity.

A bound state existing in a potential does not imply that a gas populates it; E29 handles production.

**Output:** Pole trajectories in complex momentum/energy and a map of bound, virtual, resonant, and unresolved regions. Plot uncertainty and effective-theory breakdown, not just central boundaries.

**Strengthening result:** Different validated formulations predict the same crossing along a physically matched trajectory.

**Weakening result:** Crossings disappear under consistent calibration, or lie outside the justified theory range. The latter is an unresolved extrapolation, not proof that no crossing exists.

---

## E26 — Map beta-decay and hydrogen-burning energy balances

**Question:** Does a newly bound nucleus survive weak decay, and which reactions are energetically favorable?

**Priority/resources:** First-stage core; entry for energy balances, advanced for matrix elements. Depends on E24 and ultimately E27.

Use nuclear rest energies with $c=1$, and define

$$
\Delta=m_n-m_p,\qquad B_d=m_n+m_p-M_d,\qquad B_{nn}=2m_n-M_{nn}.
$$

A positive $B_{nn}$ describes a hypothetical bound dineutron. A negative placeholder called a binding energy is not a substitute for an unbound-state scattering calculation.

At negligible initial kinetic energy, negligible neutrino mass, and neglecting atomic binding where appropriate:

| Process | Rest-energy release |
|---|---|
| $n\to p+e^-+\bar\nu_e$ | $Q_n=\Delta-m_e$ |
| $p+p\to d+e^++\nu_e$ | $Q_{pp}=B_d-\Delta-m_e$ |
| $p+e^-+p\to d+\nu_e$ | $Q_{pep}=B_d-\Delta+m_e$ |
| $d\to p+p+e^-+\bar\nu_e$ | $Q_{d\beta}=\Delta-m_e-B_d$ |
| $(nn)\to d+e^-+\bar\nu_e$ | $Q_{nn\beta}=\Delta-m_e+B_d-B_{nn}$ |

These are algebraic mass balances, not lifetime formulas. Use CODATA masses to test the ordinary limits. The fixed-input checks are approximately $Q_n=0.782$ MeV, $Q_{pp}=0.420$ MeV, $Q_{pep}=1.442$ MeV, $Q_{d\beta}=-1.442$ MeV, and $Q_{nn\beta}=3.007\ \mathrm{MeV}-B_{nn}$. [R08]

### Runs

1. Generate diagnostic maps in $(B_d,\Delta,m_e,B_{nn})$; then overlay E27 trajectories.
2. Include electron/positron capture and neutrino-induced processes in the appropriate medium.
3. Calculate weak matrix elements with consistent nuclear wavefunctions, axial coupling, and required two-body currents.
4. Integrate the actual phase space; do not apply a $Q^5$ approximation outside its regime or hold neutron lifetime fixed while changing its inputs.
5. Include electron occupancy, atomic binding, or degeneracy only where the environment requires them.

### Important analytic control

For ordinary positive $\Delta>m_e$, the interval

$$
\Delta-m_e<B_d<\Delta+m_e
$$

allows a deuteron stable against the displayed beta-breakup while pp fusion is endothermic and pep remains exothermic. An endothermic collision reaction is not absent at all temperatures: its thermally populated initial energies must be included.

**Output:** A binding-and-decay diagram with separate surfaces for existence, energy balance, and calculated lifetime. No single surface is a habitability boundary.

---

## E27 — Match background fields to correlated nuclear responses

**Question:** Are the interesting threshold crossings reachable in a specific, observationally allowed field theory?

**Priority/resources:** Begin model specification immediately; advanced matching. Runs in parallel with E24–E26.

Use independent dimensionless inputs, for example

$$
\mathbf C=\left(\alpha,\frac{\hat m}{\Lambda_{\rm QCD}},\frac{m_d-m_u}{\Lambda_{\rm QCD}},\frac{m_e}{\Lambda_{\rm QCD}},G_F\Lambda_{\rm QCD}^2,\theta_{\rm QCD}\right),
$$

and specify which subset the candidate model changes. Derive the changes rather than varying all entries independently. A Higgs/scalar path and an axion-angle path should be separate model families. Existing calculations connect the QCD vacuum angle to light nuclei and nucleosynthesis. [R10]

### Runs

- Match the field to hadronic masses, scattering parameters, tensor/mixing observables, weak currents, and three-body couplings at the stated order.
- Separate experimentally fitted baseline constants from theoretical derivatives with respect to fundamental parameters.
- Use both local derivative estimates and finite matched changes, with a validation range.
- Propagate uncertainty jointly; record correlations that cause thresholds to move together.
- Apply applicable spectroscopy, force, particle, and cosmological constraints before interpreting the extent of the alternative regime.
- Reuse the earlier background-potential and gravitational checks. A two-nucleon calculation does not establish the formation or longevity of field domains.

### A new lattice input worth investigating

Chakraborty and collaborators' 2026 preprint reports finite-volume energies of the deuteron, dineutron, helium-3, and helium-4 with physical sea quarks and several valence masses. It is relevant response information, but the paper states that definitive binding determinations require a finite-volume amplitude analysis. Its partially quenched mass variation must not be silently equated with a universe in which a field changes the physical light-quark masses everywhere. Use it to inform matching and identify missing calculations, not as a ready-made table of alternate-world binding energies. [R06]

If additional lattice work is warranted, prioritize multiple volumes, adequate operator bases, scattering amplitudes, and a physically matched mass variation. Request raw correlators/covariances from authors when not public; do not invent them or fabricate correlations from plots.

**Output:** Field trajectories through E25/E26 with observational and theoretical validity masks. A plotted path must have a reproducible Lagrangian and matching prescription.

---

## E28 — Test three- and four-nucleon consistency

**Question:** Do the proposed two-body changes remain compatible with a controlled few-body theory?

**Priority/resources:** Core; advanced. Depends on E24 and feeds E29/E30.

Calculate tritium, helium-3, helium-4, and neutron–deuteron observables with a suitable Faddeev, variational, or other validated few-body method. Carry the two-body posterior and field responses into these calculations.

### Controls

- Include the three-body interactions required at the chosen order and regulator.
- State which independent data fix the three-body sector in our phase.
- Use held-out few-body observables as tests, not additional invisible fitting conditions.
- Test order-by-order and cutoff dependence; do not hold an unrenormalized three-body term fixed during a scan.
- Conversely, do not refit an unconstrained three-body interaction at every alternate background simply to force agreement with our phase's data. Its field response is a model prediction or an explicit uncertainty.

Hammer and König's dineutron study provides a useful test case: introducing a required electromagnetic three-body counterterm at next-to-leading order changed the inference available from the triton–helium-3 binding difference. Their scoped conclusion is not proof that a free dineutron is observed. [R03]

**Output:** Correlated light-nucleus predictions and a list of observables that distinguish candidate regimes. This step guards against an attractive two-body story built on inconsistent larger nuclei.

---

## E29 — Calculate allowed formation and destruction rates

**Question:** If a new bound state exists, is there an accessible mechanism that actually populates it?

**Priority/resources:** Core; intermediate to advanced. Depends on E24–E28 as applicable.

For a stationary background, a pair must dispose of energy and momentum through an allowed radiative or collision-assisted process. Binding alone supplies neither a production cross section nor a population.

### Initial network candidates

$$
n+p\leftrightarrow d+\gamma,
$$

$$
n+n\leftrightarrow(nn)+\gamma,
$$

$$
p+(nn)\leftrightarrow d+n,
$$

$$
d+(nn)\leftrightarrow{}^3\!H+n,
$$

plus weak conversion, tritium production, reverse reactions, and helium channels required by the selected regime. This is a candidate list, not a claim that every channel has a leading unsuppressed amplitude. The dineutron BBN paper estimated several novel rates from analogies and explicit uncertainty; those approximations should be reproduced and then improved. [R11]

### Selection-rule audit

Enumerate allowed entrance partial waves, total angular momentum, parity, isospin, and electromagnetic multipoles. For a hypothetical spin-zero S-wave dineutron, a $J=0$ S-wave pair cannot make a $0\to0$ single-real-photon transition. Higher partial waves and other processes must be evaluated rather than declaring the entire capture reaction either unsuppressed or nonexistent.

The ordinary neutron–proton capture amplitude cannot simply be copied to neutron–neutron capture. Calculate matrix elements and consistent electromagnetic/weak currents; include required short-distance operators with independently constrained coefficients.

### Rates and controls

For a two-body entrance channel,

$$
\langle\sigma v\rangle(T)=
\sqrt{\frac{8}{\pi\mu}}(k_BT)^{-3/2}
\int_0^\infty\sigma(E)E e^{-E/k_BT}\,dE.
$$

Respect reaction thresholds, identical-particle factors, and spin degeneracies. Derive reverse rates by detailed balance using the same masses, partition functions, and couplings. Compare production, photodissociation, weak decay, and environmental-expansion times; test whether an equilibrium assumption is attained rather than imposing it.

**Output:** Reaction tables with uncertainty and flow diagrams weighted by calculated integrated flux. A large binding energy with negligible formation is a meaningful counterexample to the proposed abundance effect.

---

## E30 — Reproduce and extend dineutron Big Bang nucleosynthesis

**Question:** Which matched changes leave an allowed primordial inventory, and which are observationally excluded?

**Priority/resources:** Core for any phase present during BBN; conditional for purely late phases. Intermediate to advanced. Depends on E26–E29.

### Three successive analyses

1. **Historical reproduction:** Reproduce Kneller–McLaughlin using its fixed-input assumptions and historical observational choices. Its approximately 2.5 MeV result is conditional on that setup, not a universal current bound. [R11]
2. **Updated stationary backgrounds:** Insert matched nuclear masses, strong and weak rates, uncertainties, and an explicitly documented current abundance likelihood.
3. **Time-dependent backgrounds:** Evolve an actual phase history, including changes to thermal evolution, expansion, and energy transfer where implied by the model.

PRyMordial provides a public Python framework for BBN and beyond-standard-model variations; PRIMAT is an independent baseline reference. Neither automatically supplies the novel nuclear rates or a valid field history. [R13, R14]

### Controls

Recover standard BBN before modifications; preserve baryon and charge accounting; use consistent forward/reverse reactions. Include deuterium and helium-4 as primary abundance tests, with explicit treatment of astrophysical assumptions for additional abundances. Reevaluate cosmological input priors when the same field affects the epochs from which they were inferred.

Reproduce the qualitative compensation explored by MacDonald and Mullan: making dineutrons/diprotons bound does not automatically consume all primordial hydrogen when correlated changes affect the deuterium bottleneck. [R12]

If a phase has never occupied our observed primordial region, do not apply our measured abundance directly as though it came from that alternate phase. In an inhomogeneous BBN calculation, compare domain scales with particle diffusion before treating regions as independent boxes.

**Output:** Abundance likelihoods, dominant flows, and a distinction between viable alternative inventories and histories inconsistent with our observed region. Do not infer life from a single abundance cutoff.

---

## E31 — Follow hydrogen ignition and stellar response in the new regime

**Question:** Does a changed two-nucleon regime prevent long-lived energy sources, or reorganize them?

**Priority/resources:** Core for stellar-opportunity claims; advanced. Requires credible E29 rates and E30 compositions where applicable.

Begin with pp-chain, pep, capture, and weak-rate network tests. Then follow self-consistent stars with the equation of state, energy release, reaction rates, and other microphysics changes implied by the same field model.

### Comparisons

- Ordinary deuteron binding with a new dineutron channel.
- A bound but weaker deuteron, including the region where pp is endothermic but pep is exothermic.
- An unbound-deuteron regime, with the continuum and alternative formation processes explicitly treated.
- A bound diproton only if the same matched Hamiltonian predicts one.
- Phase changes before ignition, during hydrogen burning, and after fuel has already been processed.

Use the appropriate primordial composition; do not insert an unexplained seed population of heavy elements to rescue a pathway. Track luminosity, duration, neutrino losses, ejecta, and when material becomes available to later systems. Include ordinary stellar uncertainties and thermal compensation.

Adams and Grohs investigated alternatives in universes without stable deuterium, including gravitational contraction and pathways to subsequent nuclear burning. Their work is a useful counterexample benchmark, not proof of universal habitability. [R15]

**Output:** Viable stellar histories and element-release distributions. Closing one reaction does not establish the absence of stars; demonstrating one alternative does not establish life.

---

## E32 — Evolve nuclei through a changing field background

**Question:** What happens when a nucleus encounters a transition that changes its binding or decay thresholds?

**Priority/resources:** Directly relevant to the latency/passage idea; entry for controlled wave packets, advanced for matched multi-channel physics. Depends on E25–E29 and an independently justified field profile.

Solve

$$
i\hbar\frac{\partial\psi}{\partial t}=H[\boldsymbol\phi(\mathbf x,t)]\psi.
$$

A first local approximation may replace the spatial profile by a time history along the center-of-mass trajectory, but only when gradients across the nucleus are negligible. Record and test that scale separation. Wall width, velocity, and crossing time must be defined in the same frame.

### Runs

- Bound state becoming unbound.
- Unbound scattering wave packet entering a background that supports a bound state.
- A bound state persisting while a weak channel opens or closes.
- Forward and reverse sweeps, with and without a specified environment.

The bound fraction is

$$
P_{\rm bound}(t)=\langle\psi(t)|\Pi_{\rm bound}(t)|\psi(t)\rangle.
$$

Track outgoing continuum flux, kinetic-energy spectra, and work by the background. For unitary evolution with a specified time-dependent Hamiltonian,

$$
\frac{d\langle H\rangle}{dt}=\left\langle\frac{\partial H}{\partial t}\right\rangle.
$$

Weak or radiative channels require an enlarged Hilbert space or a justified open-system treatment; their energy and charge exchanges cannot disappear from the accounting.

### Controls

Test finite-volume reflections and numerical absorbers. At a binding threshold the discrete–continuum gap closes, so a naive gapped adiabatic approximation or two-level avoided-crossing formula is not sufficient. Asymmetry between two arbitrary preparations is not automatically hysteresis. Demonstrate persistence of an observable memory under specified preparation and environmental dynamics.

**Output:** Dissociation, capture, and decay probabilities versus a physically specified crossing timescale, with an energy budget. Do not animate a Euclidean bounce as real-time nuclear motion.

---

## E33 — Find observables that distinguish the competing nuclear models

**Question:** Which measurements actually discriminate the parameter paths, and which leave them degenerate?

**Priority/resources:** Begin sensitivity work early; intermediate to advanced for reaction modeling. Combines E24–E32.

Use a joint likelihood for directly measured scattering observables, deuteron properties, few-body data, and astronomical quantities appropriate to the phase and epoch. Keep evaluated data and derived fits from being counted twice. NN-OnLine and EXFOR provide starting data infrastructure. [R01, R09]

### An analytic identifiability check

At leading zero-range order in a neutral S wave,

$$
|f_0(k)|^2=\frac{1}{a^{-2}+k^2}.
$$

This magnitude does not distinguish $a$ from $-a$. A selected low-energy cross-section curve alone therefore need not distinguish a shallow bound pole from a virtual pole. This limited ambiguity is not evidence that a free dineutron exists. [R03]

### Runs

- Test discrimination using bound-state-specific signals, deuteron photodisintegration, polarization-sensitive observables, and neutron–deuteron breakup modeled consistently.
- Generate synthetic measurements including normalization, resolution, correlations, and missing-channel systematics.
- Measure false-positive rates and recover known injected models before interpreting real residuals.
- Propagate nuclear-model and field-matching uncertainty into the proposed observational signal.
- Select additional measurements by expected reduction in uncertainty about a threshold or rate, not by the largest nominal fractional sensitivity alone.
- Overlay spectroscopy, force, weak-interaction, and cosmological restrictions with the correct place/time assumptions from the earlier program.

**Output:** An identifiability report and a small set of well-specified measurement proposals. Existing-data reanalysis is computational; acquiring new nuclear or precision-measurement data requires a suitable experimental collaboration.

---

## E34 — Optional: calculate a field-dependent nuclear-isomer lifetime

**Question:** Can a specified background coupling change genuine excited-state metastability?

**Priority/resources:** Separate branch; advanced. This is not the ground-state dineutron problem.

Select an isomer whose level scheme, decay branches, and transition multipolarities are sufficiently characterized and whose nuclear structure is tractable at the chosen accuracy. ENSDF and the Atlas of Nuclear Isomers provide reference information. [R19, R20]

For a specified electromagnetic multipole $XL$, the radiative width contains a dependence of the form

$$
\Gamma(XL)\propto E_\gamma^{2L+1}B(XL).
$$

Calculate changes in both transition energy and reduced transition strength. Include competing beta decay, internal conversion, environmental ionization, and thermally accessed intermediate states where relevant.

The background interaction has its own selection rules. A spatially homogeneous rotational scalar cannot directly connect states of unequal total angular momentum. It can still change same-$J$ mixing or energies and thereby indirectly affect allowed radiative pathways. Derive that pathway rather than adding arbitrary off-diagonal entries to a level matrix.

**Output:** A controlled lifetime response and a separation of field-induced effects from ordinary environmental effects. A large change in a rare isomer's lifetime is not automatically important to habitability.

---

## E35 — Optional: test collective nuclear phases

**Question:** Do matched changes produce competing many-nucleon arrangements, not just different few-body bound states?

**Priority/resources:** Separate heavy branch; high-performance many-body calculations.

Reproduce a restricted version of the lattice result for an alpha-particle gas versus a nuclear liquid, then insert the same interaction variations justified by E27. The published calculation provides evidence of a first-order transition in its studied nuclear system; it does not supply cosmic field domains or their lifetimes. [R21]

Calculate phase competition as a function of density, composition, and temperature within the interaction's validity. Test finite-size scaling, clustering, and the dependence on multi-nucleon interactions. Distinguish real phase coexistence from a numerical solver changing between approximate solutions.

If there are two persistent phases, calculate an interface cost and a dynamical transition mechanism. A many-body ground-state-energy crossing alone does not determine nucleation or a cosmological spreading speed.

**Output:** A nuclear-matter phase diagram with stated environmental applicability. A dense-matter transition does not automatically take place in diffuse space or planetary material.

---

## Execution sequence

| Stage | Tasks | Decision |
|---|---|---|
| 1. Verified baseline and exact controls | E24, E25, E26; specify E27; start E33 identifiability checks | Is the threshold structure numerically and physically meaningful? |
| 2. Physically matched nuclear prediction | E27, E28, E29; retain uncertainty and apply early external constraints | Is there a valid field trajectory with distinguishable production or decay effects? |
| 3. Time and environment | E30, E31, E32 | Do those effects survive actual formation histories, stellar adjustment, and background passage? |
| 4. Integrated evidence | E33 plus the earlier field and spatial-history modules | Is one model viable and distinguishable, and does it affect opportunities conditional on our history? |
| Optional branches | E34 or E35, only after a specific mechanism justifies them | Does genuine excited-state/collective metastability add anything not present in ground-state thresholds? |

## First achievable milestone

Produce a matched nuclear-stability map that overlays:

1. The deuteron, dineutron, and diproton bound-state boundaries where applicable.
2. Beta-decay and pp/pep energy-balance surfaces.
3. A specific field trajectory with a justified uncertainty region.
4. Validity and applicable observational exclusions.
5. Calculated formation and survival times for at least one distinct regime.

This would improve on an independently varied dineutron-binding-energy study. Its scientific result could be a surviving regime, a cancellation, an inaccessible threshold, or a demonstrated missing nuclear input. Only the first of those is a positive mechanism result; the others are not to be disguised as either proof or disproof of all possible models.

## Shared acceptance rules

Every run must preserve input provenance, versioned code, units, regulator/order, parameter convention, numerical convergence, raw results, uncertainty assumptions, and which observed region/epoch a constraint concerns.

Do not label an effective parameter scan as a field theory. Do not call a virtual state metastable. Do not infer a reaction rate from binding alone. Do not infer life from a rate. Do not infer local solitude from global phase rarity. Do not change the underlying Hamiltonian while retaining inconsistent currents or reverse rates.

No new lattice data, stellar tracks, transition simulations, or observational fits were produced in preparing this document.

---

## Sources and acquisition notes

References below are research inputs, not a statement that their numerical datasets have all been acquired. Request unavailable source data or record the missing input; do not fabricate it. The papers using independently varied nuclear parameters provide sensitivity experiments, not automatically consistent field histories.

[R01] **NN-OnLine, Nijmegen nucleon–nucleon resources.** Experimental data, phase-shift analyses, and deuteron properties. https://nn-online.org/NN/

[R02] **J. M. Bub et al., Bayesian analysis of nucleon-nucleon scattering data in pionless effective field theory** (2024). Baseline calibration and uncertainty methodology. https://arxiv.org/abs/2408.02480

[R03] **H.-W. Hammer and S. König, Constraints on a possible dineutron state from pionless EFT** (2014). Two/three-body sensitivity, pole interpretation, and order-dependent counterterm effects. https://arxiv.org/abs/1406.1359

[R04] **S. Wang et al., Tensor-force effects on nuclear matter in relativistic ab initio theory** (2024). Controlled tensor-force deformation and deuteron-threshold benchmark. https://arxiv.org/abs/2403.14474

[R05] **Breakup reactions and their ambiguities**, European Physical Journal A (2021). Discussion of scheme-dependent deuteron D-state probabilities versus observables. https://link.springer.com/article/10.1140/epja/s10050-021-00446-3

[R06] **D. Chakraborty et al., Quark-Mass Dependence of Light-Nuclei Masses from Lattice QCD and Trace-Anomaly Contributions to Nuclear Bindings** (2026 preprint). Finite-volume, partially quenched response information; retain its stated limitations. https://arxiv.org/abs/2603.28872

[R07] **Atomic Mass Data Center.** Evaluated masses and associated releases; preserve atomic/nuclear mass conventions and covariance where available. https://www-nds.iaea.org/amdc/

[R08] **NIST CODATA constants.** Particle masses and ordinary-phase numerical checks. https://physics.nist.gov/cuu/Constants/Table/allascii.txt

[R09] **IAEA EXFOR and database documentation.** Source-level experimental nuclear reaction data. https://www-nds.iaea.org/exfor/ ; V. V. Zerkin and B. Pritychenko, https://arxiv.org/abs/1802.05714

[R10] **D. Lee et al., theta-dependence of light nuclei and nucleosynthesis** (2020). Alternative field-to-nuclear parameter direction. https://arxiv.org/abs/2006.12321

[R11] **J. P. Kneller and G. C. McLaughlin, The Effect of Bound Dineutrons upon BBN** (2004; preprint 2003). Historical network and fixed-input bound. https://arxiv.org/abs/astro-ph/0312388

[R12] **J. MacDonald and D. J. Mullan, Big Bang Nucleosynthesis: The Strong Nuclear Force meets the Weak Anthropic Principle** (2009). Correlated changes and surviving hydrogen as a counterexample benchmark. https://arxiv.org/abs/0904.1807

[R13] **A.-K. Burns, T. M. P. Tait, M. Valli, PRyMordial: the first three minutes, within and beyond the standard model.** Public Python BBN implementation; check the documented supported inputs before extending it. https://pmc.ncbi.nlm.nih.gov/articles/PMC11266446/ ; https://github.com/vallima/PRyMordial

[R14] **Cyril Pitrou, PRIMAT.** Independent BBN baseline. https://www2.iap.fr/users/pitrou/primat.htm

[R15] **F. C. Adams and E. Grohs, On the Habitability of Universes without Stable Deuterium** (2016/2017). Alternative stellar pathways and their assumptions. https://arxiv.org/abs/1612.04741

[R16] **S. Borsanyi et al., Ab initio calculation of the neutron-proton mass difference** (2014/2015). Correlated QCD/electromagnetic mass-difference input. https://arxiv.org/abs/1406.4088

[R17] **A. Ekström and L. Platter, Quantifying the breakdown scale of pionless effective field theory** (2024). Guidance on validity and uncertainty; do not treat the inferred scale as universal under arbitrary parameter changes. https://arxiv.org/abs/2409.08197

[R18] **Masatsugu Sei Suzuki, Deuteron / graduate quantum-mechanics notes.** Pedagogical derivations identified by the user. Lecture index: https://bingweb.binghamton.edu/~suzuki/QuantumMechanics.html ; direct PDF: https://bingweb.binghamton.edu/~suzuki/QM_Graduate/Deuteron.pdf . The direct PDF timed out during this preparation; no numerical dataset from it was extracted.

[R19] **NNDC ENSDF.** Evaluated nuclear levels and decays. https://www.nndc.bnl.gov/ensdf/

[R20] **S. Garg et al., Atlas of Nuclear Isomers — Second Edition** (2022). Isomer spectroscopy, half-lives, decay modes, and original references. https://arxiv.org/abs/2208.01028

[R21] **S. Elhatisari et al., Nuclear binding near a quantum phase transition** (2016). Collective nuclear-phase benchmark, not evidence of cosmological field domains. https://arxiv.org/abs/1602.04539