# HBF scientific research basis — 2026-08-13

## Scope and evidence policy

This release is based on a targeted review of authoritative public material:
peer-reviewed primary papers, official government and intergovernmental data
services, official scientific-software repositories, and laboratory teaching or
benchmark material. It is not a claim to have searched literally every page,
thesis, private database, or unpublished dataset. Private or access-controlled
material was neither accessed nor inferred.

Evidence was accepted only when it could change a defined software gate and be
implemented without inventing missing measurements. Search results, review
articles, vendor claims, and secondary summaries were used only to locate the
primary source. Every executable model has a domain, maturity, uncertainty
statement, claim boundary, artifact hash, and tests in
`packages/model-registry/models.json`.

## Research-to-implementation trace

| Gate | Public primary/official basis | Implemented artifact | Deliberate boundary |
|---|---|---|---|
| Phase 2 covariance propagation | IAEA Nuclear Data Services guidance on experimental covariance construction and EXFOR uncertainty components | `packages/reactivity/covariance.py`; `content/sources/sikora-weller-2016/derived-covariance.json` | The matrix is assumption-derived: pointwise statistical errors are independent and the published 3.4% normalization systematic is fully correlated. It is not a source-released covariance. |
| Phase 3 kinetic distributions | Liu et al. (2026) on non-Maxwellian p–¹¹B distributions and the sustaining/recirculating-power trade-off | `scientific-core/kinetics/isotropic_distributions.py` | Positive isotropic distributions and the full two-species angular integral only; no Fokker–Planck time evolution or sustaining power. |
| Phase 3 radiation | NRL Plasma Formulary; Putvinski, Ryutov & Yushmanov (2019); Mlodik et al. (2023) | `scientific-core/radiation/radiation_models.py` | Relativistic bremsstrahlung and optically thin synchrotron emission. Net synchrotron loss abstains without absorption, geometry, reflectivity, transport, and tail physics. |
| Phase 3 stability | Canonical ideal-MHD interface theory and PPPL MHD material | `scientific-core/stability/ideal_mhd_interface.py` | Exact magnetized Rayleigh–Taylor interface dispersion only; not a global device eigenmode or confinement-stability result. |
| Grad–Shafranov independent comparison | Official FreeGS open-source solver and documentation | External gate and preregistration package | The shipped solver is internally verified against the analytic Solov'ev solution. No FreeGS/CHEASE result is claimed until another operator publishes it. |
| Phase 4 handoff | Existing HBF evidence schema plus reproducible command, environment, and hash capture | `external-validation/` | Software can make validation reproducible; it cannot establish operator identity, institutional independence, or experimental truth. |

## Phase 2 finding: covariance without fabrication

The Sikora–Weller table provides pointwise statistical errors and a 3.4%
systematic normalization uncertainty, but the carried publication artifact does
not provide a point-to-point covariance matrix. IAEA documentation explains
that EXFOR often contains components rather than covariance matrices, and its
X4Covar workflow permits an evaluator to construct an approximate covariance
under explicit assumptions. The release therefore uses

`C = diag(s_stat²) + s_sys s_sysᵀ`

and propagates it with `C_y = J C Jᵀ`. A seeded multivariate-normal linear
response calculation checks the analytic standard deviation. Unknown energy
correlations, model-form effects, calibration correlations, and transcription
error remain unavailable—not zero. A future source-released covariance must be
stored as a separate artifact and compared; it must never silently replace or
be conflated with this approximation.

## Phase 3 finding: complete the scoped gates, not the reactor

The current kinetic literature makes the missing term clear: a non-Maxwellian
tail can alter reactivity, but maintaining it requires power. The implemented
framework therefore supports a structurally positive two-temperature mixture,
normalization and moment checks, and a full isotropic relative-velocity fusion
integral. It does not calculate gain.

For radiation, the implementation separates emitted channel power from net
loss. Bremsstrahlung includes the relativistic electron–ion and
electron–electron fit. Synchrotron uses a numerically evaluated
Maxwell–Jüttner momentum moment. Because high-energy tails, absorption and
spectral transport can materially change escape, the software returns no net
synchrotron-loss value.

For stability, a canonical exact dispersion was selected because it has clear
analytic limits: the hydrodynamic result, a neutral critical field, no magnetic
tension for a perpendicular field, and stable heavy-below layering. Passing
those tests closes the defined stability-module software gate. It does not
answer global stability for a torus, mirror, FRC, stellarator, or any proposed
HBF device.

## Phase 4 finding: readiness and validation are different metrics

The reproducibility package now contains a one-command runner, environment and
artifact-hash capture, a run-result schema, preregistration template, independent
sign-off template, browser-side structural precheck, benchmark inputs and
expected outputs, and an issue/reporting path. That completes all eight
validation-readiness gates.

Independent validation remains 0/3 until all of the following are public and
accepted: a third-party reproduction, an external benchmark result, and an
independent institutional sign-off. An internal rerun cannot satisfy these
gates, even if every test passes.

## Primary and official sources used

- Sikora & Weller, *A New Evaluation of the ¹¹B(p,α)αα Reaction Rates*,
  DOI [10.1007/s10894-016-0069-y](https://doi.org/10.1007/s10894-016-0069-y).
- IAEA Nuclear Data Services, [EXFOR](https://www-nds.iaea.org/exfor) and
  [Development of Web Tool for constructing a covariance matrix from EXFOR uncertainties](https://nds.iaea.org/nrdc/nrdc_2012/working/wp2012-42rev.pdf).
- Smith & Otuka, [Experimental Nuclear Reaction Data Uncertainties](https://www-nds.iaea.org/nrdc/india/ws2017/epnrdm2017/smith.pdf), Nuclear Data Sheets.
- Liu et al., *A zero-dimensional kinetic study of p-¹¹B fusion gain via the
  non-Maxwellian proton distribution*, DOI
  [10.1088/1361-6587/ae72c9](https://doi.org/10.1088/1361-6587/ae72c9).
- Richardson, [NRL Plasma Formulary (2019)](https://www.nrl.navy.mil/Portals/38/PDF%20Files/NRL_Plasma_Formulary_2019.pdf).
- Putvinski, Ryutov & Yushmanov, *Fusion reactivity of the pB¹¹ plasma
  revisited*, DOI
  [10.1088/1741-4326/ab1a60](https://doi.org/10.1088/1741-4326/ab1a60).
- Mlodik et al., *Sensitivity of synchrotron radiation to the superthermal
  electron population in mildly relativistic plasma*, DOI
  [10.1063/5.0140508](https://doi.org/10.1063/5.0140508), with the
  [PPPL author copy](https://w3.pppl.gov/~fisch/fischpapers/2023/Mlodik.sensitivity.POP2023.pdf).
- PPPL, [General Plasma Physics II: Magnetohydrodynamics](https://w3.pppl.gov/~hji/GPPII_Lecture_Notes_10-07-24.pdf).
- [FreeGS official repository](https://github.com/freegs-plasma/freegs), an
  open-source free-boundary Grad–Shafranov solver reserved for the external
  cross-code gate.

## Non-claims

This research and software do not demonstrate ignition, scientific gain,
engineering gain, net electric power, reactor feasibility, experimental
validation, or safety of an HBF device. The word “complete” in the phase
scorecard means only that the explicitly listed internal acceptance tests ran
and passed within their declared domains.