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The Periodic Table and the Group SO(4,4)

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Pith's one-line read The periodic system of chemical elements is the weight diagram of the Lie algebra $\mathfrak{so}(4,4)$, with the fourth Cartan generator $L_{78}$ identified as spin.

desk verdict An internally inconsistent Cartan-generator mapping collapses the so(4,4) periodic-table claim, despite competent Lie-algebra scaffolding. read the letter →

arxiv 2501.18272 v1 pith:G7ZLB5XT submitted 2025-01-30 math-ph math.MP

V.V. Varlamov This is my paper · ORCID
classification math-phmath.MP MSC 17B1022E7081R0581V45 PACS 02.20.Sv31.10.+z31.15.-p
keywords periodiclawweightdiagramCartansubalgebraspinantimattershell-fillingruleso(44)
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the whole periodic system of elements can be read as a weight diagram — the grid of eigenvalue labels of a Lie algebra's mutually commuting generators — of a single algebra, $\mathfrak{so}(4,4)$, the rotations of an eight-dimensional space with four plus and four minus directions. In this picture four commuting generators carry the four quantum numbers of an electron shell, $n$, $l$, $m$, and spin $s$, so spin stops being a two-point decoration and becomes a real coordinate axis. The two three-dimensional projections of this four-dimensional diagram contain, respectively, the elements from hydrogen ($Z=1$) to moscovium ($Z=115$) with $s=-1/2$, and from helium ($Z=2$) to oganesson ($Z=118$) with $s=+1/2$. Reflecting the diagram to negative quantum numbers produces a mirror pyramid of antimatter beginning with antihydrogen. The paper's claim is that the periodic table's layout is not an empirical filling rule but a representation-theoretic fact about one symmetry group.

What carries the argument

The central object is the Cartan-Weyl basis and the weight diagram of $\mathfrak{so}(4,4)$, whose Cartan subalgebra is spanned by $\{L_{12}, L_{34}, L_{56}, L_{78}\}$. The first three generators are the Cartan generators of the $\mathfrak{so}(4,2)$ hydrogen realization: $L_{56}\to n$, $L_{12}\to l$, $L_{34}\to m$; the fourth, $L_{78}\to s$, is the new spin coordinate. The fact that does the work is that $L_{78}$ commutes with all of $\mathfrak{so}(4,2)$, so the basis of $\mathrm{Spin}^+(4,4)$ splits into two isomorphic $\mathrm{SU}(2,2)$ bases adapted to the maximal compact subgroup $\mathrm{SU}(2)\otimes\mathrm{SU}(2)\otimes\mathrm{U}(1)$. That split gives the two three-dimensional projections of the weight diagram — the two spin halves of the periodic table — and the ladder operators move between the quantum-number states within each tower.

What would settle it

Take the accepted electron configuration of a known element, translate it to $(n,l,m,s)$, and check whether it sits at the node assigned by the weight diagram; any mismatch, or two elements forced onto the same node, would show the correspondence fails. A second check is whether the predicted antimatter mirror states exist: the absence of the reflected pyramid would contradict the reflection step.

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Extended reading notes

Core claim

The paper's central claim is that the periodic system is the weight diagram of the Lie algebra $\mathfrak{so}(4,4)$ of the rotation group $\mathrm{SO}(4,4)$ of $\mathbb{R}^{4,4}$. In the hydrogen realization of the conformal subalgebra $\mathfrak{so}(4,2)$, the Cartan generators $L_{56}$, $L_{12}$, $L_{34}$ are identified with the principal, azimuthal, and magnetic quantum numbers $n$, $l$, $m$; the paper then adds the fourth Cartan generator $L_{78}$, which commutes with all fifteen generators of $\mathfrak{so}(4,2)$, and identifies its two eigenvalues with spin $s=\pm1/2$. Because the basis of the twofold covering $\mathrm{Spin}^+(4,4)$ splits into two structurally identical copies of the standard $\mathrm{SU}(2,2)$ basis, the weight diagram projects onto two three-dimensional towers: one for $s=-1/2$ containing hydrogen through moscovium, and one for $s=+1/2$ containing helium through oganesson. Reflecting the diagram through zero to negative quantum numbers yields the antimatter pyramid, beginning with antihydrogen and antihelium. A mass formula $m = 2m_H\left(l+\frac{1}{2}\right)\left(\dot{l}+\frac{1}{2}\right)\left(\nu+\frac{1}{2}\right)$ is attached to each node of the tower.

Load-bearing premise

The entire construction rests on the identification of the four mutually commuting Cartan generators with the physical quantum numbers $n$, $l$, $m$, $s$ in the hydrogen realization; that identification is asserted rather than derived, and it carries the usual shell-filling order inside it.

Editorial extensions

If this is right

  • The two halves of the periodic table, spin up and spin down, become two projections of a single four-dimensional weight diagram, so the doubling of periods is a property of the spin coordinate rather than an extra assumption.
  • Spin is promoted from a two-point decoration on a plane to a genuine fourth axis, removing the artificial representation that earlier geometric systems had to impose.
  • Antimatter appears as the reflection of the weight diagram into negative quantum numbers, so the same group-theoretic object describes both matter and antimatter elements.
  • The nodes of the towers carry a mass formula, so the diagram simultaneously encodes element positions and a mass spectrum.
  • Only the first four floors of the towers are fully populated by known elements, while unfilled rings on higher floors mark slots for hypothetical superheavy elements such as Uue and Ubn.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the unfilled rings on floors $n=5,6,7$ of the towers are a concrete placement prediction for superheavy elements beyond oganesson; relativistic atomic-structure calculations for elements 119 and 120 could test whether that placement agrees with the usual filling order.
  • Beyond the paper, the reflection to negative quantum numbers suggests a possible link with a charge-conjugation or CPT symmetry of relativistic wave equations, a connection the paper leaves purely combinatorial.
  • Beyond the paper, the node-attached mass formula could be read as assigning a mass-like label to every element, not just to particle states, which would be testable against atomic masses or ionization potentials.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper claims that the periodic system of chemical elements is realized as the weight diagram of the Lie algebra so(4,4). It first constructs a Cartan-Weyl basis for so(4,2) in the Barut (hydrogen) realization, with Cartan subalgebra {L12, L34, L56} = {L3, A3, D3}, and builds the root diagram (a cuboctahedron) and the weight diagram (the SO(4,2)-tower). It then extends the construction to so(4,4) with Cartan subalgebra {L12, L34, L56, L78}, shows that the basis splits into two Yao bases of su(2,2), and asserts in Section 14 that the eigenvalues of L56, L12, L34, L78 correspond to the quantum numbers n, l, m, s. The weight diagram of so(4,4) is projected onto two three-dimensional spaces, which are claimed to contain the elements H-Mc with s = -1/2 and He-Og with s = +1/2; reflecting the diagram to negative quantum numbers is claimed to represent antimatter. A mass formula, Eq. (39), is associated with each node.

Significance. If the central identification of Cartan generators with the four quantum numbers were derived rather than asserted, the construction would be a significant addition to the SO(4,2)-based line of periodic-table models initiated by Barut, Fet, and Ostrovsky. The algebraic development has genuine strengths: the Cartan-Weyl bases of so(4,2) and so(4,4), the split of the so(4,4) basis into two Yao bases of su(2,2) (Section 13), and the cuboctahedral root diagram (Section 8) are worked out explicitly and reproducibly, and the paper states its element-to-node assignments explicitly, so the claimed correspondence is at least stated in a checkable form. As written, however, the main result is a re-encoding of the empirical Madelung rule, because the generator identification of Section 14 is asserted rather than derived and is in part inconsistent with the hydrogen realization of Section 3.1, while the antimatter pyramid is introduced by admitting negative principal quantum numbers by fiat. The manuscript therefore does not deliver the derivation announced in the abstract.

major comments (4)
  1. [§14 and §3.1] Section 14 asserts the identification L56→n, L12→l, L34→m, L78→s without deriving it, and for L12 the identification contradicts the hydrogen realization established in Section 3.1, where L12 = L3 is the z-component of angular momentum whose eigenvalues are the magnetic quantum numbers m ∈ {−l, ..., l}, not the orbital quantum number l. Section 3.1 likewise defines L34 = A3 as the z-component of the Laplace-Runge-Lenz vector, whose eigenvalues in the so(4) reduction (with K3 = (L3 + A3)/2 and J3 = (L3 − A3)/2, Section 8) are differences of the two so(3) magnetic quantum numbers, not the magnetic quantum number m, and L56 = D3 belongs to the radial so(2,1) sector, for which no spectrum equal to n is established. Since Figures 13 and 14 assign elements H-Mc and He-Og to weight-diagram nodes using exactly this mapping, the element-to-node correspondence rests on an unsupported and internally inconsistent labeling; a separate derivation of the Cartan-generator identification, or a different Cartan basis whose spectra are (n, l, m, s), would be required.
  2. [§15, Eq. (74)] Section 15's relations between the so(4,4) quantum numbers and the Madelung basis are internally contradictory: after defining n = |ν − ν̇|, which is nonnegative, Eq. (74) states that the principal quantum number n varies over −|ν − ν̇|, −|ν − ν̇| + 1, ..., |ν − ν̇|, including negative values, and the antimatter pyramid of Figures 13-14 is then built from states such as antihydrogen |−1, 0, 0, −1/2⟩ with n = −1. Antimatter is thus admitted by contradicting the preceding definition rather than derived from the so(4,4) structure. In the same passage, the relation s = |σ − σ̇| with σ, σ̇ ∈ {±1/2} takes only the values 0 and 1, not the spin projections ±1/2 used in the kets |n, l, m, ±1/2⟩ of Figures 12-14, and m = |μ − μ̇| eliminates the negative magnetic quantum numbers required in the Haenzel scheme of Section 10.
  3. [§10, §11, §15] The claimed derivation of the periodic system from the so(4,4) weight diagram is circular because the Madelung rule is used as input before the weight diagram is built. Section 10 adopts Haenzel's Polygonflache explicitly with the empirical ranges n = 1, 2, 3, ..., l = 0, ..., n − 1, m = 0, ±1, ..., ±(n − 1), s = ±1/2, Section 11 states that Finke brings the construction in line with Madelung's rule, and Section 15 then reads the same ordering off the weight diagram using the asserted generator identification of Section 14. The agreement of Figures 13-14 with the periodic table therefore re-encodes the empirical input and does not provide independent confirmation of the group-theoretic scheme.
  4. [§9 and §13] The paper never specifies the representation of so(4,2) or so(4,4) whose weight diagram produces the SO(4,2)-tower of Figure 7 and the projections of Figures 13-14: a weight diagram is representation-dependent, and the unbounded tower cannot be the weight system of a single finite-dimensional module, yet no infinite-dimensional representation, highest weight, or direct sum is defined. Without such a specification the weight diagram is not a well-defined mathematical object, and the eigenvalue spectra of the Cartan generators invoked in Section 14 cannot be checked.
minor comments (5)
  1. [§5, Eq. (23)] The worked example after Eq. (23) computes X_3 X_+ as if [X_3, X_+] = +X_+ (writing (X_+ + mX_+) and concluding that X_+ raises m by 1), whereas Eq. (23) states [X_3, X_+] = −X_+; the ladder directions and the root diagram of Figure 1 need to be reconciled with a consistent sign convention.
  2. [§13] The sentence 'Thus, all root and weight diagrams for so(4,2) will be four-dimensional' should refer to so(4,4), since the preceding paragraph establishes that so(4,4), not so(4,2), has rank four.
  3. [§2, Eq. (4)] The statement around Eq. (4) that 'α can accept only n − m values: α = ±1, ±2, ..., ±(n−m)/2' and the accompanying relation Σ_α α_i α_j = δ_ij are not correct as general facts about root systems; for example, the roots of so(4,2) used in Section 8 have coordinate entries 0 and ±1, and the displayed relation is not the standard normalization of a root system.
  4. [§9, Eq. (39)] The mass formula (39) is stated in terms of labels (l, l̇, ν), but the correspondence between these labels and the (n, l, m, s) labels used to place elements in Figures 13-14 is never specified, so the mass claimed for a given element node cannot be evaluated.
  5. [Throughout] The manuscript contains numerous typographical and translation errors, including 'chemitry' (p. 1), 'Mendeleecv' (p. 4), 'Bargman' (p. 3), 'Instite of Nuclear Physics' (ref. [9]), and 'a semi-direct g with the direction m = 0' (Section 10); a thorough copyedit is needed.

Circularity Check

3 steps flagged · score 7.0 of 10

The so(4,4) periodic table is a re-encoding of the Madelung/Haenzel input, with n,l,m,s assigned to Cartan generators by fiat.

  1. renaming known result [Section 10 (first paragraph); echoed in the Introduction]
    "In order to find an explicit correspondence between individual m-components (points in Figure 7) and chemical elements, we use the geometric interpretation of the periodic table proposed by Haenzel in 1943 [39]. [...] This allows us to place two three-dimensional projections of the weight diagram in the algebra so(4, 4) using the Madelung basis."

    The element-to-node correspondence is imported ready-made from Haenzel's empirical Polygonfläche and from the Madelung basis; it is not derived from so(4,4) or so(4,2) representation theory. After this empirical placement is made, Section 15 presents the same elements (H, He, ..., Mc, Og) as the content of the so(4,4) weight-diagram projections. The periodic table is therefore transcribed onto the diagram, not predicted by it, and the claimed group-theoretic construction is a re-encoding of the known Madelung/Haenzel ordering.

  2. self definitional [Section 14, final display; cf. Sections 3.1-3.2]
    "The eigenvalues of the generators L56, L12, L34 correspond to the quantum numbers n, l, m. The inclusion of the fourth generator L78 leads to an eight-dimensional generalization so(4, 4), which makes it possible to identify the eigenvalues of the generator L78 with the fourth quantum number s. Thus, L56 -> n, L12 -> l, L34 -> m, L78 -> s."

    These arrows are stipulated, not derived. The paper's own Barut realization identifies L12 = L3, the third angular-momentum component, whose eigenvalues are the magnetic quantum number m, not the orbital quantum number l; L34 = A3 is the third component of the Laplace-Runge-Lenz vector. So the axis labels are chosen to match the Madelung quantum numbers by fiat rather than by the algebra. Once the Cartan generators are defined to be n,l,m,s, every weight-diagram node carries exactly the Madelung quantum-number quadruple by construction, and the element assignment that follows is the input labeling, not a consequence of the so(4,4) structure.

1 more flagged steps
  1. self definitional [Section 15, relations following ket-vector (72)-(73) and range (74)]
    "The relationship of the numbers included in the ket-vector (72) with the quantum numbers n, l, m and s of the ket-vector |n, l, m, s⟩ of the Madelung basis is given by the following relations: n = |ν − ẍ|, l = |λ − ṻ|, m = |µ − ẑ|, s = |σ − ẓ|. In this case, the main quantum number n varies within −|ν − ẍ|, −|ν − ẍ| + 1, −|ν − ẍ| + 2, . . . , |ν − ẍ|."

    The Madelung quantum numbers are imported into the ket-vector by definitional relations, and then n is redefined to range over negative values. The lower (antimatter) pyramid is obtained by reflecting to these negative quantum numbers, so antimatter is put into the scheme by the range specification rather than derived from the algebra. The abstract's claimed 'natural inclusion of antimatter' is therefore a definitional artifact of allowing negative n, not a consequence of the weight diagram.

full rationale

The paper contains genuine Lie-algebraic work: root systems, Cartan-Weyl bases, subalgebra decompositions of so(4,4), and the construction of the weight diagrams are mathematically well-defined and not circular by themselves. The circularity enters at the interface with chemistry. The element-to-node assignment is taken from Haenzel's empirical Polygonfläche and the Madelung basis (Section 10), the coordinate axes are then labeled by fiat as the Madelung quantum numbers n,l,m,s (Section 14), and the same elements are read back from the weight diagram as the claimed result (Section 15). Thus the map from so(4,4) nodes to elements is an input, not an output. The internal inconsistency between L12 = L3 (eigenvalues m) and the later assignment L12 -> l shows that the labeling is not derived from the hydrogen realization. The mass-formula accuracy claim of 0.41% is supported only by the author's own references [63-66], but that is a secondary support issue rather than the main circular step. Because the central periodic-table claim reduces to re-encoding the Madelung/Haenzel ordering, the circularity score is 7.

Assumptions & free parameters 2 free parameters · 5 assumptions · 1 invented entities

The construction leans on standard Lie algebra background, which is fine, but the new physical content rests on four load-bearing postulates: the hydrogen-realization identification of generators with n,l,m, the empirical Madelung ordering of elements, the element-wide spin assignment through L78, and the negative-n antimatter interpretation. The mass formula is an additional self-referential input. Together these mean the paper contributes a new bookkeeping diagram rather than a derivation from first principles.

free parameters (2)
  • Mass formula (39): m = 2 m_H (l+1/2)(dot_l+1/2)(nu+1/2) = 2 and half-integer shifts; 0.41% accuracy claimed from prior fits
    Posted on each weight-diagram node with no derivation in this paper; the claimed accuracy rests on the author's self-cited papers [62-66], so this is an inherited fitted parameter.
  • Element-to-spin assignment (s=-1/2 vs s=+1/2 projection) = H..Mc in projection 1; He..Og in projection 2
    The split of elements into two spin projections is chosen so that the two SO(4,2)-towers reproduce the known periodic table; the spin assignment of a many-electron element is not determined by the algebra.
assumptions (5)
  • standard math Standard theory of semisimple Lie algebras: Cartan subalgebra, Weyl generators, root and weight diagrams, Racah theorem.
    Used throughout Sections 2-9 without proof; standard background for the classification of so(4,2) and so(4,4).
  • domain assumption Hydrogen realization (Barut representation) renders so(4,2) as a spectrum-generating algebra for hydrogen and supplies the generators L, A, Delta (Section 3.1).
    The paper bases the periodic-table identification on the hydrogen atom, an established but model-specific assumption; the extension to all elements is not derived.
  • domain assumption Madelung rule (n+l, n) gives the empirical order of shell filling.
    Used in Section 10 to place elements on the Haenzel sheets; the paper itself notes (footnotes 1, 5) that the rule is empirical and without a universal explanation.
  • ad hoc to paper The fourth Cartan generator L78 can be identified with electron spin, and each element can be assigned a single s=+/-1/2.
    Section 14 postulates this identification; many-electron atoms have multiple electrons with both spin orientations, so an element-wide spin value is an extra assumption.
  • ad hoc to paper Negative eigenvalues of the principal quantum number correspond to antimatter.
    Section 15 interprets the reflected tower as an antimatter pyramid; no derivation or experimental handle is offered.
invented entities (1)
  • Antimatter pyramid (reflected SO(4,2)-tower with negative n)
    purpose: To include antimatter in the periodic scheme
    Introduced in Section 15 as the lower pyramid of the weight diagram; the mapping from negative quantum numbers to antimatter is speculative and makes no falsifiable prediction.

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Pith. "Pith review of The Periodic Table and the Group SO(4,4)." pith.science (2026). https://pith.science/paper/G7ZLB5XT

@misc{pith2026250118272,
  author       = {Pith},
  title        = {Pith review of: The Periodic Table and the Group SO(4,4)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G7ZLB5XT}},
  note         = {Machine review of arXiv:2501.18272}
}
read the original abstract

The periodic system of chemical elements is represented within the framework of the weight diagram of the Lie algebra of the fourth rank of the rotation group of an eight-dimensional pseudo-Euclidean space. The hydrogen realization of the Cartan subalgebra and Weyl generators of the group algebra is studied. The root structure of the subalgebras of the group algebra of a conformal group in the framework of a twofold covering is analyzed. Based on the analysis, the Cartan-Weyl basis of the group algebra is determined. The root and weight diagrams are constructed. A mass formula associated with each node of the weight diagram is introduced. Spin is interpreted as the fourth generator of the Cartan subalgebra, whose two eigenvalues correspond to two three-dimensional projections of the weight diagram containing elements of the periodic system from hydrogen to moscovium (the first projection) and from helium to oganesson (the second projection). One of the main advantages of the proposed group-theoretic construction of the periodic system is the natural inclusion of antimatter in the general scheme.

Figures

Figures reproduced from arXiv: 2501.18272 by the authors.

Figure 1
Figure 1. The root diagram of the Lie algebra sl(2, C). The action of each Weyl generator is shown in the (X3, Y3)-plane. Obviously, the generators X− and X+ (roots α1 = −1, α2 = +1) allow us to move one step left and right, respectively, while moving up and down are set by the generators Y+ and Y−. Thus, the states of the SL(2, C)-multiplet are translated into each other by repeated action of these ladder operators. With the… view at source ↗
Figure 2
Figure 2. The first three weight diagrams (Weyl diagrams) of the Lie algebra [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Extended Weyl diagram of the algebra sl(2, C). A state is associated with each node (l, ˙ l) of the diagram, the mass of which is determined by the formula (28). (see generators (8) and (9) of the Yao basis (8)–(13)), we obtain [K, J] = 0, and also [Ki , Kj ] = iεijkKk, [Ji , Jj ] = iεijkJk. It follows that the generators K and J form the bases of two independent algebras so(3). Thus, the Lie algebra so(4) of the gr… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: The root diagram of the Lie algebra so(4). The action of each Weyl generator is shown in the (K3, J3)-plane. The corresponding weight diagram is similar to the diagram in [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: The root diagram of the Lie algebra so(4, 2). by 45◦ relative to each other, these vertices (Weyl generators) form a cuboctahedron (see [57, 21]). The root diagram of the algebra so(4, 2) in the form of a cuboctahedron is shown in [PITH_FULL_IMAGE:figures/full_fig_p02…
Figure 6
Figure 6. Figure 6: The root diagram of the Lie algebra so(4, 2), constructed in the Zometool system. A3 includes various SO(4)-manifolds. In paragraph 6, these manifolds are defined with respect to the generators K3 and J3, which in this diagram correspond to diagonal directions by virtu…
Figure 7
Figure 7. Figure 7: The weight diagram of the Lie algebra so(4, 2). The main idea of the article [39] is the arrangement of the chemical elements of the periodic table according to the quantum numbers n, l, m and s, which Haenzel designates n1, n2, n3 and n4 10. As is known, the ranges of…
Figure 8
Figure 8. Figure 8: Haenzel circles and rings. the sheet n = 2 located above it, so that you can exit the area n = 1, l = 0 only by climbing onto the sheet n = 2. On this sheet, the unit circle n = 2, l = 0 is inscribed in an equilateral triangle (with an angle lying on g). The area of th…
Figure 9
Figure 9. Figure 9: Polygonfl¨ache and the periodic table. 11 The three-dimensional Finke system In the same year (1943), the Zeitschrift f¨ur Physik published an article by Wilhelm Finke [40], devoted to remarks on Haenzel Polygonfl¨ache. First, Finke brings Polygonal¨ache in line with M…
Figure 10
Figure 10. Figure 10: The three-dimensional Finke system. expanded, and the circle R with hypothetical elements was added. 12 A general note on the Haenzel and Finke systems In both systems, the first three quantum numbers n, l and m have a clear geometric representation, originally borrow…
Figure 11
Figure 11. Figure 11: In this case, the axes of the left cuboctahedron are twisted counterclockwise, and the [PITH_FULL_IMAGE:figures/full_fig_p031_11.png]
Figure 12
Figure 12. Figure 12: Two-dimensional sections of three-dimensional projections of the weight diagram of [PITH_FULL_IMAGE:figures/full_fig_p032_12.png]
Figure 13
Figure 13. Figure 13: SO(4, 2)-tower for s = −1/2 with elements H=|1, 0, 0, −1/2⟩, . . ., Uue=|8, 0, 0, −1/2⟩. the spectrum of alkali metals (the anomalous Zeeman effect): ”The doublet structure of the alkali spectra, as well as the violation of the Larmor theorem are, according to this po…
Figure 14
Figure 14. Figure 14: SO(4, 2)-tower for s = +1/2 with elements He=|1, 0, 0, +1/2⟩, . . ., Ubn=|8, 0, 0, +1/2⟩. The first theory providing a correct mathematical formulation of the “classically non-describable two-valuedness” of the electron spin was proposed by Pauli in 1927 [75]. Avoidin…

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Periodic Table and the Group SO(4,4): II. Double SO(4,2)-tower

    math-ph 2026-07 conditional novelty 5.0 of 10

    Period doubling and the full structure of the periodic table (including Seaborg and 10-period extensions plus antimatter) arise as the weight diagram of so(4,4) split by its fourth Cartan generator into a double SO(4,...

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