He–He = SO(4) | Li–Og = SO(3,1) ⨁ SO(4) | Iachello | 2025 Split-Symmetry Periodic Table (SSPT-34)

[Scott Hutcheon]

Hello all,

Knowing Eric and René (and probably many/most of you) have studied group theory in relation to symmetry and periodicity, the following combines several themes into a new PT. Very aware everyone has limited energy and time bandwidths, so tried to make it rewarding:

A. Symmetry and Group Theory Forever Wars

One Expert (which the scientific 10,000-hour rule bestows on them) believes that symmetry and group theory exists as actual entities -- and they are completely correct.

Another Expert believes that believing in symmetry and group theories as physical realities or actual entities or substantial things is untenable and quite frankly, ridiculous -- and they are completely correct.

How can they both be right?

When working within a less scientifically evolved paradigm there will always be paradoxes that cannot be reconciled -- and which will inevitably result in Forever Wars between Experts (as with the Scylac-Scylur Skirmish that requires the breaking of the d-block to resolve). In fact, unresolvable Forever Wars between Experts is a clear sign that the current paradigm is wrong/incomplete and needs to be shifted.

Per the RSPT paper, utilizing the heuristic device of German mathematician Kurt Goëdel’s unprovable axioms within any system level -- where the inability to find a solution (proof) at the more complex level is evidence that it might only be found at a more fundamental level -- suggests that something that cannot be solved at the level of Physics could find a resolution at the deeper level of Information. 

An example of this is Scottish physicist James Maxwell’s Demon, which could never have been resolved within Physics but was explainable at the Information level even with our very initial exploratory steps. Similarly, the irreconcilability of Physic’s Gravity and Quantum Mechanics will only be unified at the Information level, which is understood to be below and underneath the Planck scale.

To achieve this paradigm shift, we simply remove the unnecessary Catholic Priest religious belief "proof of God" singularity (which was entirely invented by admittedly and openly combining the pagan Ancient Greek primeval atom and the Aquinas instant universe, then gussied up with math to match the then recent breakthrough astronomical observations) from the current 100-year-old paradigm of singularity → evolution. 

Just as the luminiferous aether/ether and epicycles were once removed as unnecessary to advance science through more scientific paradigms.

Left with only evolution, we realize an Emergent Universe where evolution began with and continues through Information → Physics → Chemistry → Biology.

This also resolves the paradox for the two Experts. Yes, group theory and symmetry as actual entities or things is unacceptable at the level of Physics (physical reality). And yes, group theory and symmetry are most definitely real things or actual entities at the level of Information (emergent orderings and symmetries through informational evolution). Simple informational symmetries must undergo spontaneous symmetry breaking as they emerge into the much more complex level of Physics and the physical universe (where everything in physical reality, chemical reality, and biological reality is asymmetrical).

Information (simplest, cleanest, most fundamental, most symmetrical) → 
Physics (more complex, messy, asymmetrical) → 
Chemistry (much more complex, messier, more asymmetrical) → 
Biology (most complex, messiest, most asymmetrical).

B. Iachello | He–He = SO(4)  |  Li–Og = SO(3,1) ⨁ SO(4)

Iachello's work on hydrogen and helium helps provide a group-theoretical explanation for why the first period is truly unique, moving beyond the standard Quantum Mechanical description. Applying dynamical symmetry and algebraic model techniques to atomic physics, he reveals that the H–He period isn't just the first step in a repeating pattern... but rather a fundamentally different symmetry class.

His group-theoretical framework describes quantum systems by their dynamical algebra, a Lie group whose representations encompass all possible states of the system. The observed states (the orbitals/charge densities and their energies) correspond to a specific chain (the system's dynamical symmetry) of sub-algebras within this larger group. For scientific (universal) periodic tables, the key is that different periods of the table are characterized by different dynamical symmetry chains -- where the relevant dynamical algebra is SO(4,2) ⊕ SO(2).

1. The H-He Distinct Dynamical Symmetry | SO(4):

• The hydrogen atom (one electron in a 1/r potential) has a famous 'accidental' degeneracy, where all orbitals with the same principal quantum number n (e.g., 3s, 3p, 3d) have the same energy, and this high level of near-perfect symmetry is described by the group (or its Lie algebra ) SO(4), which is a rotation group in four dimensions; and
• An entire shell (e.g., the n=1 shell, the n=2 shell) forms a single irreducible representation of the SO(4) group, with the n-Shell as a multiplet, where the n=1 shell is one specific representation, the n=2 shell is a larger one, and so on; and
• While the near-perfect SO(4) symmetry is broken in helium by the electron-electron repulsion, the underlying algebraic structure remains the same, and the two electrons of helium still occupy the first and only orbital of the n=1 SO(4) multiplet, with the system still described by the SO(4) chain, just with a modified Hamiltonian; and
• The first period is therefore defined by the complete filling of the first SO(4) multiplet, and this multiplet has a very small, fixed size, and is a closed, finite system.

2. The  Distinct Dynamical Symmetry for Later Periods | SO(3,1) ⊕ SO(4):

• For atoms with more electrons (starting with Lithium in Period 2), the dynamical symmetry changes, where the relevant group is no longer just SO(4), and a more appropriate chain involves SO(3,1) ⊕ SO(4); and
• The group SO(3,1) is the Lorentz group, and, in this context, it is associated with the radial quantum number, where this symmetry chain beautifully generates the entire Madelung rule (the order of orbital filling: 1s, 2s, 2p, 3s, 3p, 4s, 3d...) which governs the structure of all subsequent periods; and
• This SO(3,1) ⊕ SO(4) symmetry is what produces the repeating pattern of s- and p-blocks, with the d- and f-periods inserted in a predictable way (what I've described before as a pushing out or displacing of the earlier p-period type), where each period corresponds to filling a set of orbitals/charge densities generated by this specific symmetry chain.

3. The 'Group Contraction' and the Quantum Phase Transition | the transition from the first period to the second:

• A group contraction is a mathematical limit where one group, like SO(3,1), transforms into a different, often simpler, group like the Euclidean group E(3) under a specific parameter going to a limit; and
• The symmetry of the first period SO(4) is a contraction of the symmetry governing the later periods SO(3,1) ⊕ SO(4), and, as we move from the multi-electron atoms back to helium, the symmetry 'contracts' down to the simpler SO(4) form; and
• This isn't just a mathematical curiosity, as it signifies a quantum phase transition in the periodic table; and
• The H-He 'phase' is governed by SO (4), and characterized by the filling of a single, isolated n-shell, where the chemistry is dominated by this fundamental 1s orbital/charge density; and 
• The 'many-electron' phase is governed by SO(3,1) ⊕  SO(4), and characterized by the complex interplay between angular and radial motion described by the Madelung Rule, leading to the repeating patterns of the later s-, p-, d-, and f-periods.

To clarify, Iachello's work provides a formal proof that the first period is not merely the first one, but is instead a distinct quantum phase of any scientific periodic table, governed by different laws of symmetry than the elements that follow. This group-theoretical framework is the deepest known answer to why the first period does not, and cannot, repeat:

1. Hydrogen and helium belong to one dynamical symmetry class (SO(4)), while all other elements belong to another (SO(3,1) ⊕ SO(4)); and
2. Period 1 (1s) is the manifestation of the smallest representation of the  SO(4) algebra, and is a self-contained, closed, finite system; and
3. The move from Helium to Lithium isn't just adding a proton and electron, but a fundamental shift in the underlying symmetry of the atom, akin to a phase transition; and
4. The later periods repeat or double (2-8-8-18-18-32-32) because they are all generated by the same dynamical symmetry chain (SO(3,1) ⊕ SO(4)), whereas the first period does not repeat because it is generated by a different, contracted symmetry.

C. The 2025 Split-Symmetry Periodic Table (SSPT-34)

This new (as of today) SSPT-34 combines my research in cosmology (where H and He cannot be placed with any other group) with support from the incredible work of Iachello. It maintains the known periods (2-8-8-18-18-32-32) as well as expected orbital/charge density filling orders (1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p →), and has no artificial gaps (per the Van den Broek-Moseley sequential atomic numbering breakthrough), and contains most of the requirements of the RSPT paper (though claiming the reactivity of F and Cl as evidence of an extended Group/Column of Instability might be a stretch).

It has nearly inclusive vertical Döbereiner-Scerri Triads (horizontal triads are mandatory after Van den Broek-Moseley), leaving out only H and He -- though if Chemistry's Periodic Table can be combined with Physics' Standard Model, this would be resolved. As always, only the correct d- and f-period orientation (breaking the d-block) allows for all d- and f-elements to be included in vertical triads.

It also interconverts with the equivalent cylinder wraparound 'Working Chemistry variation' which has 100% of elements in vertical triads and very strong matches for most chemical and/or physical property trends for both Periods (horizontal) and Groups (vertical):

With this 'Working Chemistry variation' also an interconverted variation for the recent Right-step Triadic Periodic Table (where all elements are within vertical triads):

Which is also the case for the recent Split-P Periodic Table:

Which may mean that the ungainly 'Working Chemistry variation' that interconverts for all three of these recent PTs is more correct, as it's also the interconversion (equivalent cylinder wraparound) for the 2021 corrected standard table (CSPT-32 and CSPT-18) included in the RSPT paper and which originally fixed the standard iconic PT!

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[Scott Hutcheon]

Apologies, section B second paragraph should have ended with "where the relevant dynamical algebra is SO(4,2) ⊕ SU(2)." Was typing out SO too many times.

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[johnmarks9]

Dear Scott,

Wow! What a panoramic vista of science you present! Your view is corroborated by Solms & Friston´s latest interpretation of Freud using the analogy between information and thermodynamics. There are now popular, accessible accounts of this by Mark Solms [1] and PCW Davies [2] who show that Maxwell´s demon is the Markov [3] blanket, viz. the “atom” of homœostasis or Lenz´s “atom of inertia” [4].  As Kant [5] observed, we (our physical  brains) created all this!

Your “Working Chemistry” variation is excellent and further improved by Scerri´s relocation of Arima (& Iachello)´s  H - He pair (and its group analogues, the halogens and the inert gases) on the left so that the sp-block beyond remains intact with their d- and f- subgroups falling felicitously in corresponding columns (Leach´s database, PT 1279: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1279

Back at the level of “messy” chemistry, there seems to be a convergence between Brauner´s [6] internal periodicity and Kibler´s [7,8] SO(4,2) X SU(2) PT. Interesting is the naturally arising division of the ten d-elements into 4+6 and the 14 f-elements into 6+8. The f-division yields the geochemical phenomenon of the division of the rare earths into “ceric” and “yttric” earths, viz. La-Sa and Eu-Yb:

  

It would appear the d-equivalent is Sc-Cr and Mn-Zn:

But I´m not clear whether this is so. Is there any division of d- analogous to the division of f- into ceric and yttric earths?

In both cases, the divisions yield internal mini-triads:

For f-, 7-triads: La-Gd-Lu, Ce-Tb-Hf, Pr-Dy-Ta, Nd-Ho-W, Pm-Er-Re, Sa-Tu-Os (or Cs-Sa-Tu), Ba-Eu-Yb (or Eu-Yb-Pt).

For d-, 5-triads: Sc-Fe-Ga, Ti-Co-Ge, V-Ni-As, Cr-Cu-Se (or K-Cr-Cu), Ca-Mn-Zn (or Mn-Zn-Br).

Is there any chemical validity in such observations?

John

REFS:

1. Solms M: “The Hidden Spring” Profile Books, London 2021

2. Davies PCW: “The Demon in the Machine” Penguin Books, London 2019

3. Markov AA: “Распространение закона больших челноков на величины, зависящие друг от друга” Proc. Maths-Phys. Soc. Kazan, 1906, 2: 155-156

4. Lenz HFE: "Über die Bestimmung der Richtung der durch elektodynamische Vertheilung erregten galvanischen Ströme” Annalen der Physik und Chemie 1834, 107: 483–494

5. Kant I: “Kritik der reinen Vernunft” Johann Friedrich Hartknoch, Riga 1781

6. Brauner B: “Über die Stellung der Elemente der seltenen Erden im periodischen System”, Z. f. Elektroch. 1908, 14: 525-527

7. Kibler M: “Classifying Chemical Elements” ex. DH Rouvray & RB King: “The Periodic Table into the 21st century”, Proc. 2nd Int. Conf. on the Periodic Table 2003 1, 11: 313-314. Research Publishing, Baldock 2004

8. Kibler M: “A Group-Theoretical Approach to the Periodic Table” ex. DH Rouvray & RB King: “The Mathematics of the Periodic Table”, Proc. 2nd Int. Conf. on the Periodic Table 2003 2, 11: 251-252. Nova Science, New York 2004

[Scott Hutcheon]

Thanks John,

As per above (10,000-hour rule), I would ask René, who is much more the Expert for your question about the earths and chemical property periodicities and trends than I'll ever be.

Yes, I'm warming up to the 2025 Split-Symmetry Periodic Table (SSPT-34), as the Cosmology version of the interconverted series (equivalent/cylinder wraparounds) especially after realizing (today) that, per the RSPT paper, the complete shells of the He-Octet Gases 'ending' each Period makes a lot more sense than placing He (1s2) over p6 Octet Gases.

Per the RSPT paper, the conflation of the Duplet Rule (Helium) and Octet Rule is entirely artificial -- especially considering there are 10 additional element orbital/charge densities between 3s/4s and Kr/Xe and 24 extra between 6s/6s and Ra/Og (rendering the Octet rule meaningless).

A. Require shifting p-periods for interconversion -- non-expected/untraditional Groups

SSPT-34 Group Theory interconversion

• 2-8-8-18-18-32-32 | 7 Periods
• Precisely follows Madelung Rule
• Döbereiner-Scerri vertical triads for all but H-He
• Supported by astronomy/Emergent Universe evolution/Iachello
• Supported by inert gases as end of Periods/filled orbitals/charge densities
• Rang-Vernon B-Al-Sc-Y-La-Ac extended properties Group
• RSPT Column of Instability, though extended here to include reactive F and Cl
• Van den Broek-Moseley continuous atomic numbering
• Interconverts with the CSPT-32/Working Chemist variation

STPT-32 Triadic interconversion

• 2-8-8-18-18-32-32 | 7 Period
• Follows Madelung Rule with artificial gaps (versus  Van den Broek-Moseley)
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines (wraparound)
• Döbereiner-Scerri vertical triads for 100% of elements
• Rang-Vernon B-Al-Sc-Y-La-Ac extended properties Group
  
• RSPT Column of Instability
• Supported by inert gases as end of Periods/filled orbitals/charge densities
  
• Interconverts with the CSPT-32/Working Chemist variation

B. Require shifting s- and p-periods for interconversion -- non-expected/untraditional Periods

RSPT-32 Cosmology interconversion

• 2(1-1)-2-8-18-18-32-32-6 | 7 Periods
• Supported by astronomy/Emergent Universe evolution
  
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines
• Döbereiner-Scerri vertical triads for all but B-C-N-O
• Standard p-Groups
• RSPT Column of Instability
• Van den Broek-Moseley continuous atomic numbering
  
• Interconverts with the CSPT-32/Working Chemist variation

SHPT-34 Broken Octet interconversion

• 8-8-18-18-32-32-2 | 7 Periods
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines
• Döbereiner-Scerri vertical triads for all but B-C-N-O
• Standard p-Groups
• RSPT Column of Instability
• Interconverts with the CSPT-32/Working Chemist variation

RTPT-32 Triadic interconversion

• 8-8-18-18-32-32-2 | 7 Periods
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines
• Döbereiner-Scerri vertical triads for 100% of elements
• Rang-Vernon B-Al-Sc-Y-La-Ac extended properties Group
  
• RSPT Column of Instability
• Van den Broek-Moseley continuous atomic numbering
  
• Interconverts with the CSPT-32/Working Chemist variation

C. Working Chemist variation for researchers and experimenters

Corrected Standard Periodic Table (CSPT-32) -- aka Working Chemist variation

• 2-8-8-18-18-32-32 | 7 Periods
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines (wraparound)
• Döbereiner-Scerri vertical triads for all but B-C-N-O
• RSPT Column of Instability
• Supported by inert gases as end of Periods/filled orbitals/charge densities
  
• Least modified and most familiar in both 32- and 18-column formats

While of all the above recent work, the Split-Symmetry might be the best fit for Corrected Cosmology/Group Theory, it breaks many traditional chemistry Groups (at least at standard temps and pressures).

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[johnmarks9]

Thanx for your re-cap, Scott.

What is your view of Brauner´s internal periodicity and Group Theory´s prediction of the split of d- into 4+6 and f- into 6+8?

Is there any chemical evidence for this aside from the ceric-yttric split in f- ?

John

[Scott Hutcheon]

Checked to see if other authors had used Group Theory to create Periodic Tables.

M. Kibler's Group Theory Periodic Table, based on SO(4,2) ⨁ SU(2) and without the Iachello contraction, does not continue Madelung's Rule and Van den Broek-Moseley atomic numbering starting with the octet gas element 18 (Ar):

V. Varlamov's Group Theory PeriodicTable, based on SO(2,4) ⨁ SU(2) ⨁ SU(2)' and without the Iachello contraction, does not continue Madelung's Rule and Van den Broek-Moseley atomic numbering starting with the octet gas element 18 (Ar):

Both look like visually elegant solutions to Groups, but do not contain sequential Periods (Madelung's Rule and Van den Broek-Moseley continuous atomic numbering) starting after the octet gas element 18 (Ar). 

Finding the 'one' solution -- including filling, atomic numbering, Periods, Groups, and chemical and/or physical property trends -- becomes an exponentially more complex/difficult issue for all periodic table variants starting after element 18.

Whereas, creating visually and Group appealing periodic tables is much simpler/less complex without the requirement of following Madelung's Rule and Van den Broek-Moseley continuous atomic numbering -- example here where I use the Iachello contraction SO(4) H-He | SO(3,1) ⨁ SO(4) Li-Og):

Which is visually/traditional Group trend appealing, but only works for sequential atomic numbering up to element 20 (Ca).

[René]

On 22 Nov 2025, at 06:52, Scott Hutcheon <scotth...@gmail.com> wrote:

Checked to see if other authors had used Group Theory to create Periodic Tables.

M. Kibler's Group Theory Periodic Table, based on SO(4,2) ⨁ SU(2) and without the Iachello contraction, does not continue Madelung's Rule and Van den Broek-Moseley atomic numbering starting with the octet gas element 18 (Ar):

Scott, your depiction of Kibler (1st image) does not match with Kibler as he presented it (2nd image), here: https://arxiv.org/pdf/quant-ph/0503039

René

[René]

On 22 Nov 2025, at 06:52, Scott Hutcheon <scotth...@gmail.com> wrote:

Checked to see if other authors had used Group Theory to create Periodic Tables.

M. Kibler's Group Theory Periodic Table, based on SO(4,2) ⨁ SU(2) and without the Iachello contraction, does not continue Madelung's Rule and Van den Broek-Moseley atomic numbering starting with the octet gas element 18 (Ar):

Scott, what is a lachello contraction?

[Scott Hutcheon]

Thanks René, good catch on the f-periods being up a further period/row, further breaking down sequential radioactivity periodicity unless there was something else I missed:

The Kibler is an example of mathematical-theoretical (Information-level) symmetries that cannot exist in asymmetrical chemical reality. Looks like the 1928 Corbino -- https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=989 -- which also does not adhere to Van den Broek-Moseley sequential numbering. See also the Tsimmerman ADOMAH rehabilitations.

At the Information level, the Standard Model is also mathematically symmetrical (anti-particles, etc.) but physical reality emerges asymmetrically through spontaneous symmetry breaking.

The Varlamov looks like a 1928 Janet -- https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=152 - flipped into a right-step (rotated in the paper) by also not adhering to Van den Broek-Moseley sequential atomic numbering.

Iachello contraction is described in thread -- while coming from more of a physics background where attribution is often generous and named in honour of the initial author's breakthrough works.

[Scott Hutcheon]

As I champion removing the obscuring factors enabling the non-evolution of the standard periodic table (hidden Column of Instability, correct d- and f-period orientation, etc.), realized the problems with Van den Broek-Moseley sequential numbering for these last three theoretical Group Theory PTs can be better clarified visually:

[ERIC SCERRI]

Please provide references to the papers by Iachello.

Eric Scerri 

On Nov 19, 2025, at 2:29 PM, Scott Hutcheon <scotth...@gmail.com> wrote:

Thanks John,

As per above (10,000-hour rule), I would ask René, who is much more the Expert for your question about the earths and chemical property periodicities and trends than I'll ever be.

Yes, I'm warming up to the 2025 Split-Symmetry Periodic Table (SSPT-34), as the Cosmology version of the interconverted series (equivalent/cylinder wraparounds) especially after realizing (today) that, per the RSPT paper, the complete shells of the He-Octet Gases 'ending' each Period makes a lot more sense than placing He (1s2) over p6 Octet Gases.

Per the RSPT paper, the conflation of the Duplet Rule (Helium) and Octet Rule is entirely artificial -- especially considering there are 10 additional element orbital/charge densities between 3s/4s and Kr/Xe and 24 extra between 6s/6s and Ra/Og (rendering the Octet rule meaningless).

A. Require shifting p-periods for interconversion -- non-expected/untraditional Groups

SSPT-34 Group Theory interconversion

• 2-8-8-18-18-32-32 | 7 Periods
• Precisely follows Madelung Rule
• Döbereiner-Scerri vertical triads for all but H-He
• Supported by astronomy/Emergent Universe evolution/Iachello
• Supported by inert gases as end of Periods/filled orbitals/charge densities
• Rang-Vernon B-Al-Sc-Y-La-Ac extended properties Group
• RSPT Column of Instability, though extended here to include reactive F and Cl
• Van den Broek-Moseley continuous atomic numbering
• Interconverts with the CSPT-32/Working Chemist variation

<Interconverted PTs r2 - triads.png>

STPT-32 Triadic interconversion

• 2-8-8-18-18-32-32 | 7 Period
• Follows Madelung Rule with artificial gaps (versus  Van den Broek-Moseley)
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines (wraparound)
• Döbereiner-Scerri vertical triads for 100% of elements
• Rang-Vernon B-Al-Sc-Y-La-Ac extended properties Group
  
• RSPT Column of Instability
• Supported by inert gases as end of Periods/filled orbitals/charge densities
  
• Interconverts with the CSPT-32/Working Chemist variation

<Interconverted PTs r2 - triads6.png>

B. Require shifting s- and p-periods for interconversion -- non-expected/untraditional Periods

RSPT-32 Cosmology interconversion

• 2(1-1)-2-8-18-18-32-32-6 | 7 Periods
• Supported by astronomy/Emergent Universe evolution
  
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines
• Döbereiner-Scerri vertical triads for all but B-C-N-O
• Standard p-Groups
• RSPT Column of Instability
• Van den Broek-Moseley continuous atomic numbering
  
• Interconverts with the CSPT-32/Working Chemist variation

<Interconverted PTs r2 - triads3.png>

SHPT-34 Broken Octet interconversion

• 8-8-18-18-32-32-2 | 7 Periods
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines
• Döbereiner-Scerri vertical triads for all but B-C-N-O
• Standard p-Groups
• RSPT Column of Instability
• Interconverts with the CSPT-32/Working Chemist variation

<Interconverted PTs r2 - triads2.png>

RTPT-32 Triadic interconversion

• 8-8-18-18-32-32-2 | 7 Periods
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines
• Döbereiner-Scerri vertical triads for 100% of elements
• Rang-Vernon B-Al-Sc-Y-La-Ac extended properties Group
  
• RSPT Column of Instability
• Van den Broek-Moseley continuous atomic numbering
  
• Interconverts with the CSPT-32/Working Chemist variation

<Interconverted PTs r2 - triads5.png>

C. Working Chemist variation for researchers and experimenters

Corrected Standard Periodic Table (CSPT-32) -- aka Working Chemist variation

• 2-8-8-18-18-32-32 | 7 Periods
• Schwarz backbone H-Halogens/He-Octets/Alkalis/Alkalines (wraparound)
• Döbereiner-Scerri vertical triads for all but B-C-N-O
• RSPT Column of Instability
• Supported by inert gases as end of Periods/filled orbitals/charge densities
  
• Least modified and most familiar in both 32- and 18-column formats

<Interconverted PTs r2 - triads7.png>

While of all the above recent work, the Split-Symmetry might be the best fit for Corrected Cosmology/Group Theory, it breaks many traditional chemistry Groups (at least at standard temps and pressures).

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On Mon, Nov 17, 2025 at 7:25 AM johnmarks9 <johnm...@hotmail.com> wrote:

Dear Scott,

Wow! What a panoramic vista of science you present! Your view is corroborated by Solms & Friston´s latest interpretation of Freud using the analogy between information and thermodynamics. There are now popular, accessible accounts of this by Mark Solms [1] and PCW Davies [2] who show that Maxwell´s demon is the Markov [3] blanket, viz. the “atom” of homœostasis or Lenz´s “atom of inertia” [4].  As Kant [5] observed, we (our physical  brains) created all this!

Your “Working Chemistry” variation is excellent and further improved by Scerri´s relocation of Arima (& Iachello)´s  H - He pair (and its group analogues, the halogens and the inert gases) on the left so that the sp-block beyond remains intact with their d- and f- subgroups falling felicitously in corresponding columns (Leach´s database, PT 1279: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1279

Back at the level of “messy” chemistry, there seems to be a convergence between Brauner´s [6] internal periodicity and Kibler´s [7,8] SO(4,2) X SU(2) PT. Interesting is the naturally arising division of the ten d-elements into 4+6 and the 14 f-elements into 6+8. The f-division yields the geochemical phenomenon of the division of the rare earths into “ceric” and “yttric” earths, viz. La-Sa and Eu-Yb:

  <image_2025-11-17_151746268.png>

It would appear the d-equivalent is Sc-Cr and Mn-Zn:

<image_2025-11-17_151835784.png>

To view this discussion visit https://groups.google.com/d/msgid/PT-L/CANbBqwi-D%2BYPT7xV%2B6uwzCL_hco%2BBGjnEbHtOXzcsgjS4kyxEg%40mail.gmail.com.

ERIC SCERRI PhD

UCLA

Website: http://www.ericscerri.com
PhilPeople https://philpeople.org/profiles/eric-scerri
Google Scholar https://scholar.google.com/citations?hl=en&user=8w1T5bEAAAAJ
ResearchGate https://www.researchgate.net/profile/Eric-Scerri

Editor-in-Chief of Foundations of Chemistry https://link.springer.com/journal/10698