Updated 25 October 2026 PDT. The closed experiment log now contains 1,529 new designs, 1,435 completed routine relaxations and 790 verified new-design Ouro hull calculations. Forty-six initial endpoints are below 20 meV/atom. The energy–magnetization comparison remains at 220 endpoints, including historical candidates, repeats and controls. These are not counts of independently novel frameworks. Four additional Fe–B–C designs have completed Orb relaxation and endpoint verification but still await hull, novelty and magnetic screening; they are shown separately from the closed-log totals.
Since the 23 October snapshot, the closed log has added 639 designs, 250 hull calculations, seven initial below-threshold endpoints and 52 comparison points. No fully qualified framework family has been added in that interval. Since the immediately preceding update, ten completed designs and two hull results have been added, with no new under-20 endpoint or magnetic comparison point. The leading candidates and numerical Pareto frontier are unchanged.
Latest experiments: useful negative results, with a new chemistry test pending
All ten newly closed designs converged. Two Fe28B12 networks built from rotated or screw-related quadrants, and four compact Fe9B / NdFe8B ring networks, lost tetragonal symmetry. Two host-site B-pair replacements in a ZrFe4Si2-derived scaffold also lost tetragonality. The two ligand-site replacements retained tetragonal geometry, but Ti2Fe8B8 and Nd2Fe8B8 gave 382.578 and 310.229 meV/atom above the hull. These fixed recipes are retired. No magnetic prediction was allocated and missing magnetization is not plotted as zero.
Two existing near misses, Fe14B8 and Nd8Fe92B8, received finite Orb force-response diagnostics using 1×1×2 supercells at Γ and q=(0,0,½). Neither showed an imaginary mode beyond the declared −0.1 THz significance threshold at those sampled points. This supplies no unstable mode to follow in that limited search; it does not establish full-zone dynamical stability or lower their existing hull energies of 29.460 and 29.432 meV/atom.
The pending Fe–B–C test replaces four B atoms with C on complete site orbits of two existing Cr23C6-derived vacancy frameworks. Two site choices each give Fe92B18C4 and Fe90B20C4. All four unconstrained relaxations converged and passed the endpoint geometry, 3D-connectivity, primary P4/mmm symmetry and chemical-history checks. Their hull energy, routine novelty result and magnetic prediction are still pending. This is a matched ligand-chemistry experiment on existing frameworks; carbon substitution alone earns no new-framework credit.
Candidates to retain
A–J link to the exact public CIFs associated with each pair of hull and magnetic values. All ten are Orb-relaxed tetragonal endpoints below 20 meV/atom; their novelty and confirmation evidence differs. Jₛ is the predicted local-moment density assuming ferromagnetic alignment, expressed in tesla. It does not establish magnetic order, MAE, coercivity or permanent-magnet performance.
ID | Candidate / exact CIF | Hull (meV/atom) | Predicted Jₛ (T) | Evidence / priority |
|---|---|---|---|---|
A |
The compact junction is a useful new direction
B, Fe₂₆Si₄B₁₂, is a 42-atom GPAC-authored junction between Cr₅B₃-derived and V₈SiB₄-derived blocks. Its exact relaxed endpoint gives 3.359 meV/atom and 1.2896 T. Two independently strained and rattled starts return 3.358 and 3.357 meV/atom, with 1.2892 and 1.2894 T. This supports a reproducible model basin while keeping its known parent-block ancestry explicit.
Its selected AFLOW database check completed all 826 frozen references with no positive or unresolved comparisons. That is a completed finite subset, not full framework qualification: other atom counts, distorted smaller-parent relations, metal-only equivalence and broader literature remain outside it. We have assigned no new-framework credit. The P-filled junction gives 8.640 meV/atom and 1.2366 T; a B-site variant Fe₂₆Si₂B₁₄ gives 19.407 meV/atom and 1.3729 T. Both also reproduce in two independent checks, and are retained as members of the same design family.
The retained magnetic tradeoffs
The C16 fixed-period registry D gives 15.958 meV/atom and 1.7471 T; its two repeats both give 15.956 meV/atom, with 1.7467–1.7474 T. Fe₄₀B₁₈ reaches 1.7599 T at 19.710 meV/atom but has little threshold margin. These retain a known C16 metal backbone and unresolved occupied-framework novelty. The separate selected C16 audit remains incomplete.
C, the earlier Fe₆₀Co₂B₃₂ intergrowth, remains a strong historical comparison at 7.518 meV/atom and 1.6419 T. I, the Fe-rich Fe₁₂₆W₁₁B₄₀ tau derivative, gives 9.264 meV/atom and 1.5645 T; two independent repeats return 9.263–9.265 meV/atom and 1.5650–1.5655 T. Framework novelty remains unresolved for that tau endpoint.
A, Fe₁₂₀Al₆W₁₁B₄₀, remains the 1.042-meV/atom, 1.4143-T energy benchmark. The researcher reported low MAE for the “1 meV aluminum candidate,” without saved numerical results, easy axis or exact DFT-input verification. We retain that qualitative feedback and lower its hard-magnet priority; it does not supply a numerical MAE or rule out related compositions. G, H and J preserve diversity and prior finite-scope review evidence.
The rare-earth track now has exact-CIF magnetic values
The refined clustered and screw Nd₁₆Fe₁₁₂B₄ vacancy structures now have their own magnetic predictions: 12.435 meV/atom and 1.6741 T for E; 13.614 meV/atom and 1.6736 T for the screw ordering. These values replace the previous publication’s “not recalculated” status for the refined CIFs. They do not represent two new frameworks or a meaningful improvement over the original rounded magnetic values.
Both structures retain the Nd₂Fe₁₄B metal scaffold. The selected clustered-endpoint AFLOW library audit terminated with 1,976 complete negative comparisons and 325 unresolved comparisons out of 2,301 frozen representatives. It is not a novelty pass, and its result does not transfer to the screw variant. Rare-earth orbital moments and sublattice alignment are not validated by the local-moment proxy.
The updated Pareto chart
Open the updated Project 14 Pareto figure
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User-requested 25 October 2026 frozen research update: 220 comparison endpoints, separate magnet tracks, exact-CIF magnetic results, failed confirmations, ten newly closed designs, two finite mode diagnostics and four separately pending Orb endpoints. Orb/Ouro screening; no synthesis or hard-magnet guarantee. SHA256 316ef04ce8058f511b89efd19cbeff5217e51df098533871609d1d11a2674511
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The chart keeps the rare-earth-free and rare-earth-containing tracks separate, using the Project 14 blue and pink palette. Dashed lines show the numerical tradeoff among all measured endpoints, including known controls. Solid lines show the subset previously qualified within declared finite scopes. Filled X markers identify original endpoints whose independent confirmations failed or were mixed. Small faint points are repeats, not additional discoveries.
Open the searchable 220-endpoint report
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User-requested 25 October 2026 frozen research update: 220 comparison endpoints, separate magnet tracks, exact-CIF magnetic results, failed confirmations, ten newly closed designs, two finite mode diagnostics and four separately pending Orb endpoints. Orb/Ouro screening; no synthesis or hard-magnet guarantee. SHA256 ff6706dbee1568aa877b62c179647e72fecabb1e3780cc4ad34d59b31649a813
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Download the frozen comparison data (JSON)
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User-requested 25 October 2026 frozen research update: 220 comparison endpoints, separate magnet tracks, exact-CIF magnetic results, failed confirmations, ten newly closed designs, two finite mode diagnostics and four separately pending Orb endpoints. Orb/Ouro screening; no synthesis or hard-magnet guarantee. SHA256 3f187aaf63b7a8fbd96d32a9baaea65e76aebc0e37e8e3c0efe1c208acc8b2ef
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What did not hold up
The recent Cr₂₃C₆-derived Nb and Mo substitutions initially looked attractive: Fe₈₄Nb₈B₂₂ at 18.373 meV/atom and 1.6106 T, and Fe₈₄Mo₈B₂₂ at 17.572 meV/atom and 1.6172 T. All four independent strain/rattle repeats instead relaxed to orthorhombic Pmmm under the unchanged primary symmetry gate. The original energy values remain in the log, but these are not robust tetragonal finalists. We have not relaxed the symmetry tolerance or projected their endpoints back to tetragonal symmetry.
The previous six LiNi₁₆-derived B-site-deletion designs all converged. Only two retained tetragonal symmetry, at 131.698 and 135.695 meV/atom, so the batch adds no below-threshold candidate or magnetic point. Convergence alone is not the bottleneck; retaining the desired symmetry and obtaining favorable energy together is harder. The exact negative recipes are retired, with their starting structures, compositions and outcomes preserved.
The six Nd/Sm pair-center designs also converged, but only three retained tetragonal symmetry. Their verified hull values were 32.622, 49.444 and 55.048 meV/atom. The lowest-energy member, Nd₆Fe₅₈Si₈B₁₆, gives a predicted 1.2538 T and joins the comparison as an above-target result. It is dominated in energy and magnetization by existing rare-earth candidates, so the numerical frontier is unchanged. This batch adds no under-20 endpoint or newly qualified framework; its six exact recipes are retired.
The six chimney-ladder Fe–Co–B / Fe–B designs all converged under unconstrained Orb relaxation, but every endpoint became triclinic P1 at the unchanged primary symmetry gate. They passed the other geometry checks, including periodic 3D connectivity. No endpoint was sent for hull or magnetic screening, and their six exact recipes are retired. This is a symmetry failure, not evidence that these unmeasured compositions have zero magnetization or unfavorable hull energy. The 220-point comparison and its numerical frontier are unchanged by this batch.
An earlier six-design batch used ScB12-derived cage geometry with an Fe24 skeleton, Zr/Nd/Sm host sites and either single-B or axial B-pair fillings. All six converged, retained 3D connectivity and passed the other geometry checks, but relaxed from I4/mmm to triclinic P1 or P-1. Their cell volumes contracted by 17–24%. No hull or magnetic calculations were allocated to these non-tetragonal endpoints. These exact recipes are retired and remain in the experiment log; the measured Pareto comparison is unchanged. This limits this particular inverse cage-chemistry construction, not all 3D cage frameworks.
Coordination diagnostic: can relaxation repair a poor starting environment?
We revisited six previously unrelaxed Sc₅Co₄Si₁₀-derived Fe/Ti/Nd boride inputs that had failed only the starting coordination check. The inputs, compositions and final acceptance gates were unchanged. All six converged under unconstrained Orb, repaired the low B coordination and retained periodic 3D connectivity. Five lost tetragonal symmetry; Fe₃₀B₄ retained P4mm and passed the full endpoint geometry checks.
The exact Fe₃₀B₄ CIF then gave 222.921 meV/atom above the Ouro hull, with zero missing references. This is far outside the target, so no magnetic prediction or independent finalist confirmation was allocated. The routine novelty route found no published same-formula match; that does not establish a new underlying framework or outweigh the high energy. These six experiments add no under-20 candidate, magnetic point or framework credit.
The useful learning is about the initial filter: low coordination in a starting CIF can repair during relaxation, so it is not proof that the final geometry will fail. This six-case test does not establish a better global acceptance threshold. Future exceptions should be bounded, supported by a plausible local rearrangement and judged by the unchanged relaxed-endpoint gates. The exact negative recipes are retired.
Earlier follow-up: Nd and Pr junctions repair geometry but miss the energy target
Two previously unrelaxed junctions derived from the published La4Co9.6Al3.4 intergrowth were tested with Nd4Fe30B2 and Pr4Fe30B2 compositions. Both converged, increased B coordination from two to six neighbors and retained 3D connectivity. Both satisfy P4/mbm at the unchanged 0.01 Å symmetry tolerance, although the tighter 0.005 Å diagnostic resolves lower symmetry.
The exact relaxed CIFs give 114.886 and 115.450 meV/atom above the Ouro hull, respectively, with zero missing references and no further relaxation inside the hull calculation. Their balanced hull decompositions are Fe plus Nd2Fe14B or Pr2Fe14B. They are well outside the target, so no magnetic predictions or finalist repeats were allocated. The routine lookup labels both “new composition”; their known parent metal scaffold prevents interpreting that as proof of framework novelty.
Across all eight coordination diagnostics, every structure repaired its starting B coordination, three retained tetragonal geometry and none met the energy target. This supports narrowly testing physically plausible exceptions to the initial coordination filter, while keeping the final geometry and energy gates unchanged. All eight exact recipes are retired. The table includes unmeasured properties explicitly; these experiments do not add points to the energy–magnetization chart.
Starting composition | B coordination before → after | Relaxed symmetry | Hull (meV/atom) | Magnetization |
|---|---|---|---|---|
Fe₃₄B₄ | 2–2 → 6–8 | P1 | Not screened | Not screened |
Higher magnetization is possible, but costs energy
Above-target comparison points now include Fe₈₈Mo₄B₂₂ at 25.038 meV/atom and 1.8357 T, and the Fe₉₂B₂₂ depletion endpoint at 30.274 meV/atom and 2.0523 T. A native Fe₄B database control gives 37.671 meV/atom and 2.0802 T, with no new-framework credit. Ti₂Fe₁₈B remains 36.343 meV/atom and 1.8816 T. These explain the upper-right tradeoff in the plot; none meets the under-20-meV target.
Ti₂Fe₁₈B CIF — 36.343 meV/atom; 1.8816 T. Above-target comparator with published ancestry.
Fe₈CoGe₄B₂ CIF — 19.055 meV/atom; 0.8757 T. Finite-scope reviewed Ni9Si4B2-derived comparator.
What the next search should build on
The objective remains distinct tetragonal boride frameworks with low model hull energy and high predicted Jₛ, in both magnet tracks. The most useful structural changes so far preserve locally credible boride coordination while changing junctions or occupied-site arrangements. This is a working interpretation of a deliberately selected search, not a controlled comparison proving one generator is best. Further composition sweeps should be bounded and site-specific, with matched controls and independent finalist checks.
Ouro novelty is the routine lookup, accompanied by local history and ancestry checks. “New composition” is not evidence of a new underlying framework. We continue to distinguish chemical prototype, full occupied framework, metal scaffold and literature ancestry, with selected finite AFLOW audits for exceptional candidates. Extending a defect period solely to lower meV/atom is not a discovery criterion.
The log retains both successes and failures. It separately records 64 independent confirmation relaxations, 12 earlier continuation diagnostics, eight initial-coordination diagnostic relaxations and two finite mode diagnostics. The four completed Fe–B–C relaxations remain an open batch awaiting remote screening. No new simulation was launched to prepare this publication. REMAG remains paused; selective MAE screening stays with the researcher. All numerical screening results here are Orb/Ouro model predictions. Near-hull energy, including a reported zero, does not guarantee synthesis.