ANULUM / SCPN Reactor Systems / Compare
Anchors across the six families
Six families, twenty device cores, one question asked of each: which printed numbers of a filed source does the core give back, and how closely. This page puts every answer side by side. Nothing is computed here: each row is transcribed from the level-0 physics section of the core’s own VALIDATION.md, and the status is the one the core gives itself. A row with a green status is a number the core returns exactly; an orange one is a printed number the source’s own figures do not give back, which the core records instead of absorbing into a tolerance. No row describes, approximates or validates any real machine.
Status vocabulary, the cores’ own
Anchor, exactthe core returns the printed value exactly, or at every digit the source prints
Anchor, within tolerancereproduced within the tolerance the core declares and states the reason for
Consistentagrees with a printed floor, range or statement without being a printed value
Identity or relationa printed relation, scaling or model identity verified, no printed number involved
Impliedwhat the source's other printed values require of a quantity it never prints
Reconstructedrecovered from printed values by a round trip; proves arithmetic, not the design
Measured, recordedan offset, rounding or truncation the core measured and asserts instead of an equality
Not reproduceda printed value the source's own numbers do not give back; used as an anchor nowhere
Declaredan input no source prints; the record says it is declared
No level-0 physicsthe core owns configuration and clock semantics only; nothing is anchored
Every anchor, side by side
| Core | Filed source | Quantity | Source prints | Core recovers | Status | Note |
|---|---|---|---|---|---|---|
| Closed magnetic confinementphysics · explorer · sources | ||||||
| SCPN-TOKAMAK-CORETokamak · device page | Greenwald 2002, eq. 1.3 | Greenwald density limit | n_G = I_p / (π a²) in 10²⁰ m⁻³ | the implemented relation, same form and units | identity | verifies a relation already on the configuration; no number is printed |
| Peng and Strickler 1985 | spherical regime pairing | aspect ratio 1.5 with elongation 2 | fixture at exactly A = 1.5, κ = 2 (radii 1.5 and 1.0, so the ratio is exact in binary) | consistent | conventional fixture above A = 2.5 with κ below the 1.4 the source calls natural there | |
| Peng and Strickler 1985 | normalised-current ceiling | about 7 MA/(m T) | both fixtures under it | consistent | ||
| both sources | major radius, field, current | not printed; only relations among them | declared, and said to be declared | declared | Pappus volume checked to one ulp against the theorem | |
| SCPN-STELLARATOR-COREStellarator · device page | none on file | no level-0 | two capabilities: device configuration model, diagnostic and clock semantics | |||
| SCPN-RFP-COREReversed-field pinch · device page | Paccagnella, arXiv:1509.07307, eqs. 4–5 | reversal threshold Θ_rev | the model's identity j₀,₁ / 2 = 1.2024… | 1.2024…; the configuration's advisory 1.2 proven to be its rounding | identity | F_bfm(Θ_rev) = 0 exactly in double arithmetic |
| Paccagnella 2015 | product identity B₀ J₁(2Θ) = ⟨B_φ⟩ Θ | identity of the model | holds to 1e-15 relative | identity | ||
| NIST DLMF 10.21; OEIS A115368, A115369 | Bessel zeros j₀,₁ and j₁,₁ | printed constants | |J₀(j₀,₁)| and |J₁(j₁,₁)| at or below 1e-14 through the pinned kernel library | exact | the anchors are identities of the model and printed zeros, not correlations with data | |
| SCPN-SPHEROMAK-CORESpheromak · device page | Wood et al. 2005, UCRL-JRNL-214703 | Taylor eigenvalue of the SSPX conserver, 1 m diameter by 0.5 m high | 9.9 m⁻¹ | 9.91 m⁻¹ (0.1 %, declared tolerance 1 %) | within tolerance | |
| PPPL-2257 (1985) | eigenvalue scaling | inverse radius at fixed shape | doubling both extents halves λ and both wavenumbers exactly | identity | ||
| separation form (derived here) | relaxed-state field | curl B = λ B, div B = 0 | wall B_r, B_θ vanish to 1e-15 B₀; curl and divergence by central differences to 1e-6 | identity | the cylindrical eigenvalue's own citation, Turner et al. 1983, is not on file | |
| Wood 2005 | formation disposition | hollow / relaxed / peaked operating rule | restated against a declared tolerance | consistent | predicts nothing about any discharge; magnetic axis, helicity–energy relation, tilt criterion and decay time not evaluated (no filed source) | |
| SCPN-FRC-COREField-reversed configuration · device page | Zhu and Wu, arXiv:2607.11908, Table I (Yingguang-1) | coil inner diameter, active length, coil count and pitch, fill density | 12.4 cm; 36 cm; 8 coils on 4.5 cm; 2e15 cm⁻³ | reproduced from the built objects; 0.124 / 2 = 0.062 and 8 × 0.045 = 0.36 exact in binary | exact | |
| Bala et al., arXiv:2204.07978, eq. 14 | kinetic-scale bound S* / E | below 3.5 | the verdict turns exactly at the bound | identity | a configuration inside the bound is not claimed stable | |
| Zhu and Wu 2026 | separatrix radius, length, external field | radius printed as a simulation result, approximately 1 cm; no field printed | declared; the printed radius is not used as an anchor | declared | ||
| Open and non-toroidal magnetic confinementphysics · explorer · sources | ||||||
| SCPN-MIRROR-COREMagnetic mirror · device page | Endrizzi et al. 2023 (WHAM), eq. 3.4 | classical confinement at n₂₀ = 1, 100 keV, R_m = 10 | 250 ms | 250 ms | exact | |
| Endrizzi 2023 | gain from β = 0 to 0.9 | "only 50 %" | factor 1.5 at R_vac = 10 | exact | ||
| Endrizzi 2023, eq. 3.5 | gas-dynamic time coefficient | 5.2 | 5.09 at 2.5 proton masses (3 %) | within tolerance | matched only to the stated 3 % | |
| Endrizzi 2023, eqs. 3.1–3.3 | engineering forms at unit inputs; τ_s = τ_ii | 5 ms, 1/8 ms, 5.8 µs; "about E_i / 10" | reproduced; equality at T_e = E_i / 40^(2/3) to 1e-14, between E_i / 12 and E_i / 10 | consistent | ||
| Endrizzi 2023, eq. 3.7 | FLR worked case a / ρ_i = 4, L_p / a = 10 | m_crit = 0.8, all m ≥ 2 stabilised | 0.8; disposition switches at 2 | exact | the m = 1 mode is not assessed | |
| Endrizzi §3.6; Frank et al. 2025, eq. 3.3 | adiabaticity α; tandem eq. 3.3 | no printed number (the α ≈ 10 case prints no L_B) | record digest pinned as an immutability fixture | no level-0 | no printed numerical anchor exists | |
| SCPN-MAGNETIC-CUSP-COREMagnetic cusp · device page | none on file | no level-0 | two capabilities; the polywell's cusp topology is presented in the electrostatic family | |||
| SCPN-LEVITATED-DIPOLE-CORELevitated dipole · device page | Garnier et al. 2006, FED 81, 2371 | resonant field at 6.4 GHz | 0.23 T | 0.228633 T | exact | exact at two significant figures |
| Garnier 2006 (two pages) | F-coil charge at 300 A C-coil | 930 kA-turns | 933.19 kA-turns through flux conservation and the printed 716 turns | exact | two inductances and a charging current printed on two different pages | |
| Garnier 2006 | ampere-turns at the operational current | "> 1.2 MA" | 1.303 MA-turns | consistent | ||
| Garnier 2006 | "over 1.5 MA turns" | 1.5 MA-turns | 1.303 at the operational current; 1.322 at the maximum charge | not reproduced | checked where the numbers are largest; anchors nothing | |
| Garnier 2006 | levitation field B_r | printed form uses the average diameter; no value printed | 0.986 mT as printed, 1.973 mT by the loop force balance; ratio carried, neither adjusted | measured | the source disagrees with the standard balance by exactly two | |
| Garnier 2006 | operational current | 1820 A | 1846.4 A induced by the printed inductances at the printed maximum charge (1.4 %) | measured | reported and gated nowhere | |
| Garnier 2006 | axial field gradient at the floating coil | printed nowhere | derived so the printed 560 kg is balanced at a margin of exactly one | declared | ||
| Self-magnetic and pulsed pinchesphysics · explorer · sources | ||||||
| SCPN-Z-PINCH-COREZ-pinch · device page | Pease 1957, Braginskii 1958, in Klíř 2005 eq. 2.20 with NRL coefficients | Pease–Braginskii current, hydrogenic, ln Λ = 10 | ≈ 1.4 MA (literature) | 1.37 MA; √(ln Λ) scaling | consistent | |
| Haines 2011 §5; Kadomtsev 1966 | m = 0 criterion on the Bennett profile | sausage-unstable at every radius for γ = 5/3 | reproduced; the reduced criterion flips exactly at γ = 2 | identity | ||
| Shumlak and Hartman 1995 | sheared-flow threshold | dv_z / dr > 0.1 k v_A | disposition of the declared shear; the static class reports none | identity | ||
| Bennett 1934; Haines 2011 §2 | Bennett equilibrium | integral pressure balance, profiles, Ampère | closed to machine precision; I², 1/N, m_i^-1/2 scalings | identity | ||
| SCPN-THETA-PINCH-CORETheta-pinch · device page | Quinn et al. 1973, LA-UR-73-1053, Fig. 2 | required field-ratio product, 5-m sector (β 0.85, a 0.7 cm, R 2.375 m, h 0.19 /cm) | −0.0064 measured, ≈ −0.0065 plotted | −0.0059 (declared 10 %) | within tolerance | the quotient forms of the excursions are the ones that reproduce it |
| Quinn 1973, eq. 6 | wall example a = 3 cm, β = 0.8, h a = 0.13 | a / b = 0.4 | 0.399 (0.40 ± 0.01) | within tolerance | ||
| Quinn 1973, eq. 4 | m = 1 growth rate of the 5-m sector | calculated 1.0 MHz | within a factor of two | within tolerance | order of magnitude by design: the source does not print every input | |
| Quinn 1973, p. 16 and Table I | end-loss times, Scylla IV-1 and IV-3 | 2.13 µs, 9.67 µs | within 1 % (normalised to Scyllac 5 m, 2.7 keV, 11.5 µs) | within tolerance | an empirical three-device fit | |
| SCPN-DENSE-PLASMA-FOCUS-COREDense plasma focus · device page | Saw and Lee 2017, IAEA-TECDOC-1829, Table 1 | E₀ and t_rise, PF1000 / NX3 / INTI / PF400J | table columns | within 2.5 % and 2 % (the table's rounding) | within tolerance | |
| TECDOC Table 1 | terminal snowplow speed vs peak v_a | table column | within 15 %, overestimating every row by 7–14 %; the sign is asserted | measured | ||
| Lee 2014, eq. 28 | ratio at c = 3.4 | "typically 2.5" | 2.40 (5 %) | within tolerance | ||
| TECDOC eqs. 5–6, items (a)–(k) | fast-ion-beam chain | PF1000, NX3, INTI, PF400J columns | within 3 %; PF400J within 12 % (two-digit pinch radius enters as r_p⁻²) | within tolerance | ||
| TECDOC eqs. 1–2; Lee 2012 | neutron identity; scaling-law calibration | constants differing by 0.5 %; 7e9 at 0.5 MA | identity to 1 %; calibration within 10 %, refused outside 0.1–1 MA | within tolerance | ||
| TECDOC Table 1 | T_pinch and n_i | tabulated | not reproduced by eqs. 41 and 43 at the tabulated inputs (factors about 3 and 5) | not reproduced | the tabulated values are outputs of the integrated code | |
| TECDOC Table 1 | drive parameter SF | PF1000, NX3 rows | within 1 %; INTI excluded, its printed SF does not follow from its own inputs | measured | ||
| Inertial confinementphysics · explorer · sources | ||||||
| SCPN-ICF-LASER-CORELaser ICF · device page | Craxton et al. 2015 (review) | 40 µm coefficient of the hot-spot radius ceiling | 40 µm | the same IEEE double from the two pressure coefficients and the reference radius | exact | |
| Craxton 2015, 1.5 MJ design | absorbed energy at 95 % | 1425 kJ | 1425 kJ exactly; inner radius and IFAR point exact from three printed lengths | exact | ||
| Craxton 2015 | shell kinetic energy from η_hydro and absorbed fraction | one significant figure | reproduced to that figure | exact | ||
| Craxton 2015 | closure of the three ignition coefficients on f_k E_k = 2π P_hs R_hs³ | an equality | 0.53 % high, the same at every energy from 1 kJ to 1 MJ; pressure coefficient from the floors 115 Gbar where 100 is printed | measured | the rounding of the printed coefficients | |
| Craxton 2015 | worked example of the energy-form pressure floor | "120 to 180 Gbar" | 112 to 125 Gbar at the stated inputs | not reproduced | ||
| Craxton 2015 | one-dimensional gain | 48 | about 57 from the printed geometry and burnup at standard solid density | not reproduced | neither figure is an anchor; a quoted burnup applies to the fuel that assembles | |
| SCPN-ICF-BEAM-COREBeam ICF · device page | Ho, Harte and Tabak 1994 | capsule masses from the printed radii and densities | printed radii and densities | 25.45 mg ablator, 3.87 mg solid fuel, 0.0073 mg vapour | exact | heavy-ion sources only; nothing is evidence about the electron-beam configuration |
| Callahan-Miller and Tabak 1998 | effective spot radius √(ab) | 2.7; 1.67 | 2.7331; 1.6673 | exact | at the precision each printed answer carries | |
| Ho 1994 | capsule gain | 430 MJ from 1 MJ | 430 exactly; beam counts 8 and 16 per side double into the printed 16 and 32 | exact | ||
| Ho 1994 | burn-up fraction; conversion efficiency | never printed | 0.3286; 0.8859 | implied | what the printed quantities require of the fifth | |
| both sources | driver energy of the capsule design | not printed | printed yield over printed system gain | reconstructed | recovering the gain from it is a round trip | |
| Callahan 1998 | printed gains 58, 55, 132 | 58, 55, 132 | 58.27, 55.81, 132.12: floors, not rounded values | measured | no single power law joins the three range–energy pairs (exponents 1.1200, 1.2544, 1.1926) | |
| SCPN-ICF-IMPACT-COREImpact ICF · device page | LA-8000-C (1979), plane scheme | plate areal density; face energy; compression ratio | 0.052 g/cm²; 1.04 MJ/cm²; 420 | exact; to one ulp; exact | exact | values read off pages rendered at 170 dpi, never off the text layer |
| LA-8000-C, convergent scheme | target areal density | 2 g/cm² | 2.13 g/cm² at the one figure printed | exact | ||
| LA-8000-C | plate thickness; compressed fuel thickness | 2.7e-3 cm; 2.3e-3 cm | 2.7659e-3; 2.3810e-3: the volume truncates rather than rounds | measured | rounding would give 2.8e-3 and 2.4e-3 | |
| LA-8000-C | gas state, 10 bar at 300 K | 0.01 of cryogenic density | 0.009466 (5.3 %) by the ideal-gas law | consistent | a consistency instrument, an anchor nowhere | |
| LA-8000-C | convergent sphere mass; one-gram burn | 0.84 mg; "nearly 400 GJ" | 0.8922 mg at the printed cryogenic density; 337.5 GJ (19 %) | not reproduced | no filed source pairs the two schemes | |
| Magneto-inertial and magnetised-target systemsphysics · explorer · sources | ||||||
| SCPN-MIF-COREFRC compression · device page | release portal | no level-0 | released software with its own evidence pages; no capability inventory of this kind | |||
| SCPN-MIF-MAGLIF-COREMagLIF · device page | SAND2021-3239B (related public chapter) | liner 10 mm tall, 5 mm OD, 0.5 mm wall; 10 T; 0.5 kJ preheat; 18 MA | six printed values | all six reach the composed record; aspect ratio exactly 5.0 | exact | not the cited Phys. Plasmas 17 (2010) 056303, which is not on file |
| SAND2021-3239B | peak implosion velocity | 70 to 100 km/s (a range) | declared inside it; liner density, convergence ratio and γ declared | declared | ||
| SCPN-MIF-PLASMA-JET-COREPlasma-jet liner · device page | Hsu et al., arXiv:1201.1879 | per-jet mass | 300 mg over 30 jets | 10 mg exactly | exact | |
| Hsu 2012 | total kinetic energy | 376 kJ | 375.0 kJ (0.27 %, asserted at half a per cent) | within tolerance | ||
| Hsu 2012 | launch radius | not printed; density 6.63e-4 kg/m³ and a 3 m chamber are | 0.60 m declared; the printed density comes back to better than 0.1 % | declared | the printed array covers about five per cent of the sphere, asserted | |
| SCPN-MIF-LINER-COREMechanical or liquid liner · device page | LA-7686-MS (1979), Table II-I | initial liner energy, two design points | 0.336 GJ; 0.756 GJ | both to 0.83 % from an annular copper shell at 1e4 m/s (asserted at 1 %); 1e3 m/s misses a hundredfold | within tolerance | the velocity's superscript is lost in the extraction; settled against the table |
| LA-7686-MS abstract | characteristic time r₀ / v | implosion 20 to 40 µs | 20 and 30 µs | consistent | ||
| shell mechanics | annulus vs thin shell | d / (2r + d) | 0.74 % at the filed design point, asserted exactly | identity | ||
| Electrostatic, beam-target and hybrid systemsphysics · explorer · sources | ||||||
| SCPN-IEC-COREIEC and polywell · device page | Wulfkühler et al. 2024 (Sci. Rep.) | bridge angles of the grid-angle table | 1.146°, 0.573°, 0.382°, 0.229° | all four to the three decimals printed | exact | dropping the arctangent reproduces the same digits; the table cannot settle its own equation |
| Wulfkühler 2024 | globe-grid apertures; globe family range | 50; 8 to 220 | 50; both endpoints | exact | ||
| Wulfkühler 2024; Radel, UWFDM-1325 | symmetric grids 3 / 6 / 9 / 15 rings | 8 / 24 / 48 / 120 apertures | every row; the nine-ring Wisconsin cathode's 48 crosses two documents | exact | ||
| SCPN-BEAM-TARGET-COREBeam target · device page | NRL Plasma Formulary 2019, p. 44 | ten Maxwellian D–T rates, 1 to 1000 keV, from the Duane coefficients | table | every one to the printed two figures (residual at most 1.4 %, the table's rounding) | exact | averaging the fit verifies all six coefficient tuples |
| NRL 2019, p. 44 | m_e / m_D and m_e / m_T; printed square roots | 2.72e-4 = 1/3670; 1.82e-4 = 1/5496; 1.65e-2 = 1/60.6; 1.35e-2 = 1/74.1 | each recovers the other; both roots from the ratios | exact | ||
| equal-mass kinematics | equivalent stationary-target energy | four times the beam energy | exact; the exact D–T mass ratio 1.669 reported beside the 2 in force | identity | ||
| SCPN-FUSION-FISSION-HYBRID-COREFusion–fission hybrid · device page | ORNL/PPA-79/3, eq. 17 | denominator | 1.33 | the same IEEE double | exact | values read off the rendered page; the OCR layer mangles digits |
| ORNL/PPA-79/3, eq. 19; p. 26 | R_o; Q′ for electrical self-sufficiency | 68; ~1.4 | 68.15; 1.396 | within tolerance | ||
| ORNL/PPA-79/3, p. 10 | thorium over uranium blankets; effect of ~3 % fissile buildup | 3–5×; roughly halves the reactor number | 4.70 fresh, 4.03 exposed; 2.08 uranium, 2.42 thorium | consistent | the ceiling statement is asserted as the identity Q′B / (1 + Q′B) | |
79 rows across 21 device cores: 23 anchor, exact, 13 anchor, within tolerance, 9 consistent, 11 identity or relation, 1 implied, 1 reconstructed, 7 measured, recorded, 5 not reproduced, 5 declared, 4 no level-0 physics. The three cores without a level-0 anchor say why in their row. Every source named is on file in the core’s repository, and the explorer of each family reproduces the rows marked exact or within tolerance from the same relations.