Triad Periodic Tables (including new variations with 100% Döbereiner-Scerri Triads)

[Scott Hutcheon]

Moving these Triadic Periodic Table variations into a separate email chain for clarity. The attached newly discovered PTs are variations of the RSPT-32 and RSPT-36 (Right Step Periodic Table) and contain Döbereiner-Scerri Triads for 100% of the elements.

A. 2025 Right-step Triadic Periodic Table (RTPT-32) Pros:

1) The RTPT-32 contains the Column of Instability (Mn–125, and related Island of Stability connection), as well as Schwarz's "backbone of the periodic table" with the connected H-Halogen Group (as per René also), the He-Octet Gases Group, and the Alkali Metals and Alkaline Earth Metals Groups; and

2) Contains the mandatory Sc-Y-La-Ac, as well as the B-Al-Sc-Y-La-Ac Group extension/relation that René has extensively researched, rehabilitated, and referenced; and

3) Contains periods of 8-8-16-16-32-32; and

4) Continues the RSPT idea of later orbital/charge density types 'pushing out' or displacing earlier orbital types, where here 4p and 5p are also displaced by 3d and 4d, and 6p and 7p are also displaced by 4f and 5f which naturally displaces 5d and 6d; and

5) As far as I'm aware, this is the only table that satisfies Eric's research on triads, René's research on the trends of the potential extended Group B-Al-Sc-Y-La-Ac, and the RSPT paper. Peace descended on the village and there was much rejoicing.

2025 Right-step Triadic Periodic Table (RTPT-32) Cons:

• This PT entirely breaks up the traditionally stacked p-block into three p-periods:This follows the mandatory breakup of the d-block into separate d-periods for any scientific (universal) periodic table in order to correctly incorporate the Column of Instability (and related Island of Stability, as well as the proper relationship for the REE elements), however, it appears too radical based on electronic/charge density periodicities; and
• Not aware of as much recent detailed work as René's on p1 B-Al-Sc-Y-La-Ac to justify these later p2- through p4-element headed Groups as sharing chemical and/or physical properties...
• Though this may be acceptable as p1- through p4-element groups of the p-block have always been an illogical and fundamentally unexplainable mixed-bag of chemically and/or physically unrelated elements, and René has provided detailed trend justifications for at least the p1-element headed Group containing B-Al-Sc-Y-La-Ac...
• Whereas p5 (Halogens) and p6 (Octet Gases) are uncontroversial Groups; and
• Comes preloaded with the obvious dismissal as the Split-p or Split-p Soup table -- though it has precedent with the 1934 VRPT-32 (Victor Romanoff Periodic Table) split-d periodic table that interests René: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=290

• 
  

B. 2025 Split Triadic Periodic Table (STPT-16):

This further variation of the RSPT and Right-step Triadic Periodic Table moves the p5 Halogens and p6 Octet Gases to the right (as per understood 'cylinder' aspect of periodic tables). Though I'm never satisfied with artificial gaps in PTs (here between the first four p-periods and their split p5 and p6 counterparts), the chemical and/or physical properties seem as near as perfect as possible for periods and groups.

C. 2025 Perfect Triadic Periodic Table (PTPT-16) aka the Maple Leaf Periodic Table (MLPT-16):

With the discovery of the RTPT-32, naturally the challenge was then to find a 'perfect' triadic table where every single element exists within perfect triads both vertically and horizontally. Per the RSPT paper and the Bell Curve Rule -- where focusing entirely on one aspect or entirely ignoring one aspect (such as triads) while ignoring chemical and/or physical properties leads to artificial tables -- the most interesting bit for me about this curiosity is that the first naturally occurring radioactive element (Bismuth) forms a group with the first unnaturally occurring element (Einsteinium). Though the expected Mn–125 Column of Instability forms with anti-rule artificial gaps in it (as Selenium and Tellurium and Iridium are not radioactive/unstable). Note: the RSPT paper predicts that the lone not-currently-considered-radioactive isotope of Mn (Manganese) will turn out to be around as unstable, at similar orders of magnitude, as the recently understood single primordial Bismuth (Bi) isotope is now known to be.

As always, commentary, critiques, and concerns are always welcome (what doesn't kill a table makes it stronger)!

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[Scott Hutcheon]

As I'm sure anyone who has or has had a long-term partner can relate, my wife took one look at the 'perfect triadic periodic table' and gleefully (with entirely too much joy and satisfaction) pointed out that two sets of elements (Chlorine 17–20 Calcium and Iodine 53–61 Promethium) do not form exactly perfect vertical triads (each part of 2/3 vertical triads instead of the required 3/3).

Changing the name of the more mathematical curiosity to the 2025 Maple Leaf Triadic Table (MLTT-16) and shelving it as it also does not contain the expected periodicities of a scientific PT.  

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[johnmarks9]

Calm down, Scott.

She´s wrong:

Each set forms perfect 18-triads:

Cl-Br-J, Ar-Kr-Xe, K-Rb-Cs, Ca-Sr-Ba, are all Döbereiner triads

Sc-Y-La, Ti-Zr-Ce, V-Nb-Bz, Cr-Mo-Ty, Mn-Tc-Pm, are all Sommerfeld triads.

Beylkin´s PT shows this clearly:

So enjoy your final glee . . .

John

[Scott Hutcheon]

After reviewing hundreds of related PTs, it's beginning to look more and more that Right-Step formulations are mandatory for scientific/universal PTs (which will be added to the RSPT paper Periodic Table Rules). This right handedness is necessary to include 100% of elements in Döbereiner-Scerri Triads, the Vernon Group 3 Sc-Y-La-Ac or extended B-Al-Sc-Y-La-Ac, the Schwarz backbone of the connected Halogens-Octets-Alkalis-Alkalines (and the related Vernon H-Halogens and He-Octets), and the Column of Instability (Mn, Tc, Pm, Np, 125).

Though humans have chased symmetry for thousands of years, we now know that reality is entirely asymmetrical at all levels and directly connected to handedness (or there wouldn't be a universe, physics, chemistry, or biology including us), and it seems therefore logical that a certain handed PT would necessarily be more scientifically-realistically-observationally-experimentally correct and less religious-philosophical-mathematical-theoretical.

What follows are examples and notes:

The 1953 Mendoza Right-Step PT (1953 MRPT-33) has 33 columns as the author searches to find a way to keep H naturally separate from the rest of the elements, contains the Vernon rehabilitated B-Al-Sc-Y-La-Ac, the Column on Instability, and has no artificial gaps, but breaks apart the Schwarz backbone connected (and Vernon) He-Octets and Alkalis and Alkalines from the Halogens and does not contain 100% Döbereiner-Scerri Triads .

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=407

The near ideal example of the primacy of handedness for scientific (universal) PTs is the 2002 Gutierrez-Samanez Right-step Periodic Table System A (2002 GSRPT-32A), by Julio, whose mathematical orientation in the Right-Step variant (see bottom image on linked page) includes the Vernon B-Al-Sc-Y-La-Ac, the Column of Instability (Mn-Tc-Pm-Np-125) and connected Island of Instability, has no artificial gaps between elements (correctly includes the Van den Broek-Moseley sequential atomic numbering breakthrough), but does not include the complete Schwarz PT backbone with the connected Halogens and Octet Gases by instead placing H over the Alkalis and He over the Alkaline Earths. The 2002 GSRPT-32B entirely breaks up the Schwarz backbone but keeps the Vernon B-Al-Sc-Y-La-Ac (as part of H-Li) and the Column of Instability (as part of F-Cl).

Conversely, the related 2002 Gutierrez-Samanez Left-Step Periodic Table (2002 GSLPT-32A) contains the Schwarz backbone and Vernon H-Halogens and the He-Octet Gases but does not contain the connected Alkali Metals or Alkaline Earths. The 2002 GSLPT-32B replicates Janet's Left Step Periodic Table (LSPT-32). They do not contain 100% Döbereiner-Scerri Triads:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1100
https://www.monografias.com/trabajos-pdf/tabla-periodica-nuevo-modelo/tabla-periodica-nuevo-modelo.pdf

Shared by René, the 2020 Gutierrez-Samanez Right-Step Periodic Table (GSRPT-32) version contains the Vernon B-Al-Sc-Y-La-Ac and the Column of Instability (but extended with F and Cl) and no artificial gaps, but also e over H and n over Ne (where, according to the RSPT paper, 0s would contain the Free Proton over H and the Alpha Particle over He):

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1303

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=313

Shared by René, the 2003 Rich Right-Step Periodic Table (2005 RRPT-23) contains the complete and connected Schwarz backbone (including René's H-Halogens and He-Octets), but contains the artificial f-periods gap and does not contain either 100% Döbereiner-Scerri Triads or the Column of Instability:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1242

Introduced by René, the closest to a scientific (universal) symmetrical PT is the 2018 Beylkin Symmetrical PT (BSPT-32), who commits the outsider blasphemy of correctly placing the d-periods (but only halfway due to a mathematical focus on symmetry) over the f- periods. This leads to a better PT with the mandatory Mn-Tc-Pm-Np-125 Column of Instability, the Schwarz PT backbone with the connected Halogens, Octets, Alkalis, and Alkalines, but without 100% Döbereiner-Scerri Triads, with the lesser B-Al-Ga-In-Tl (per Vernon's work on the stronger trending B-Al-Sc-Y-La-Ac Group extension), and with artificial gaps between elements (ignoring the Van den Broek-Moseley sequential atomic numbering breakthrough):

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1202

Again, while 20/20 hindsight makes the Column of Instability seem blindingly obvious (per the attribution to Arthur Schopenhauer “All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.”), there have been no known previous proposals or references to such a self-evident Column of Instability and only halfhearted QM attempts to explain the seemingly random positions of Tc and Pm in the current unscientific standard table (SPT-18 and SPT-32).

While it's unbelievable that it took nearly 80 years for the Column (especially after the 1913 breakthroughs regarding atomic number and radioactivity) to be understood as a fundamental pillar for any scientific PT, it was simply a case of being unable to see the forces for the decision trees, as obviously the iconic standard table's Mn-Tc-Re-Bh-artificial gap-Pm-Np seemingly obvious 'column' is nowhere near the same as the Beylkin and Right-Step Tables Mn-Tc-Pm-Np (and extended Mn–125). Further, no such column exists with the SPT-32 (the standard periodic table in its proper 32-column form), and would continue to be missed with an extended SPT-50 (the standard periodic table in its proper extended 50-column form) if g-period elements are added (and the connection to the element 125 Island of Instability would still remain hidden).

As well, when it comes to arguments against breaking the d-block into properly related d-periods and f-periods, it is widely accepted that two rows don't a Group make (which is the excuse given for removing and dropping the f-periods below the standard table) and therefore confusing that so many authors have supplied the Sloppy Sandwich Suggestion of somehow proving all d-periods should remain in an artificially stacked d-block by showing that less than half of the artificially grouped 4d- and 5d-elements (the sandwich filling) show related trends which reduces to near zero related chemical and/or physical property trends down the artificial d-block when including the same vertically grouped 3d- and 6d-elements (the sandwich bread slices) in the artificial d-columns. Just as with the artificially isolated f-periods in the standard table, two rows of elements (here 4d and 5d) cannot be considered Groups with trends.

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[René]

On 13 Nov 2025, at 08:10, Scott Hutcheon <scotth...@gmail.com> wrote:

Hi Scott

Thanks for bringing so much energy to our list.

After reviewing hundreds of related PTs, it's beginning to look more and more that Right-Step formulations are mandatory for scientific/universal PTs (which will be added to the RSPT paper Periodic Table Rules). This right handedness is necessary to include 100% of elements in Döbereiner-Scerri Triads, the Vernon Group 3 Sc-Y-La-Ac or extended B-Al-Sc-Y-La-Ac, the Schwarz backbone of the connected Halogens-Octets-Alkalis-Alkalines (and the related Vernon H-Halogens and He-Octets), and the Column of Instability (Mn, Tc, Pm, Np, 125).

I don’t understand the relevance of triads. Could you explain it to me?

As Philip Stewart said, "Triads are a consequence of the structure of the system, and a consequence cannot determine a structure."

https://www.chemistryviews.org/details/ezine/1247399/At_Last_A_Definitive_Periodic_Table/?utm_source=chatgpt.com

Eric has noted that the LSPT features a certain regularity of triads however no element in period 1 (H, He) of that table is part of a triad whereas this is not the case for all periods thereafter. In contrast, all periods of the traditional table have at least one element that is part of a triad.

Though humans have chased symmetry for thousands of years, we now know that reality is entirely asymmetrical at all levels and directly connected to handedness (or there wouldn't be a universe, physics, chemistry, or biology including us), and it seems therefore logical that a certain handed PT would necessarily be more scientifically-realistically-observationally-experimentally correct and less religious-philosophical-mathematical-theoretical.

I am not sure about the merits of a right step periodic table in terms of asymmetry compared to the conventional periodic table, which is also asymmetric in appearance.

[trim]

Again, while 20/20 hindsight makes the Column of Instability seem blindingly obvious (per the attribution to Arthur Schopenhauer “All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.”), there have been no known previous proposals or references to such a self-evident Column of Instability and only halfhearted QM attempts to explain the seemingly random positions of Tc and Pm in the current unscientific standard table (SPT-18 and SPT-32). 

While it's unbelievable that it took nearly 80 years for the Column (especially after the 1913 breakthroughs regarding atomic number and radioactivity) to be understood as a fundamental pillar for any scientific PT, it was simply a case of being unable to see the forces for the decision trees, as obviously the iconic standard table's Mn-Tc-Re-Bh-artificial gap-Pm-Np seemingly obvious 'column' is nowhere near the same as the Beylkin and Right-Step Tables Mn-Tc-Pm-Np (and extended Mn–125). Further, no such column exists with the SPT-32 (the standard periodic table in its proper 32-column form), and would continue to be missed with an extended SPT-50 (the standard periodic table in its proper extended 50-column form) if g-period elements are added (and the connection to the element 125 Island of Instability would still remain hidden).

In the Column of Instability, bohrium seems to let the concept down. There does not seem to be anything out of the ordinary or notable as far as Bh goes.

As well, when it comes to arguments against breaking the d-block into properly related d-periods and f-periods, it is widely accepted that two rows don't a Group make (which is the excuse given for removing and dropping the f-periods below the standard table)...

The two rows of the f-block are dropped below the main body of the table for space-saving reasons, rather than because two rows don’t make a group.

...and therefore confusing that so many authors have supplied the Sloppy Sandwich Suggestion of somehow proving all d-periods should remain in an artificially stacked d-block by showing that less than half of the artificially grouped 4d- and 5d-elements (the sandwich filling) show related trends which reduces to near zero related chemical and/or physical property trends down the artificial d-block when including the same vertically grouped 3d- and 6d-elements (the sandwich bread slices) in the artificial d-columns. Just as with the artificially isolated f-periods in the standard table, two rows of elements (here 4d and 5d) cannot be considered Groups with trends.

In the d-block, the 5d row is impacted by the lanthanide contraction and the 6d row is expected to be impacted by the actinide contraction. That is why the groups making up the 4d, 5d and 6d rows have, or are expected to have, comparable atomic and ionic radii and hence similar chemical behavior. The 3d row can be thought of as an example of a first-row anomaly.

René

[Larry T.]

I don't understand relevance of triads either. They played important role in the beginning of 19th century, but we are well past those times.

As it was demonstrated long time ago on this list, any tabulated sequence of natural numbers will generated triads.

Larry.

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[johnmarks9]

Dear René,

That´s a fascinating discussion you posted concerning the comments following David Bradley´s article "At last a definitive PT" back in 2011.

At something like the sixtieth comment, Eric asks Bernard Schaeffer why He behaves like an inert gas if it´s an alkaline earth metal in disguise?

One could equally ask why Be isn´t an inert gas in disguise? The argument is usually that the s-p energy gap is low enough that 2s no longer behaves like a full shell, i.e. all the electrons in the L-shell become "hybridized". But it could be argued that this phenomenon continues into the M-shell and that Zn isn´t an inert gas for a similar reason. This is why Scerri´s Sommerfeld triads have predictive periodic properties similar to Döbereiner´s triads. Chemical phenomenology justifies the original ´A´ and ´B´ subgroups.

Further in the debate, Martin Channon makes the point that, like all dynamic systems, the atom is 4-D: three in space plus one in time. Therefore 3-D and even more 2-D representations inevitably fall short. The Dewey decimal system works quite well for libraries despite the innumerable degrees of freedom in the subject matter of books. He links this to a more general problem of epistemology and seems to think there´s an ideal epistemology, which I didn´t find convincing. Stowe´s model shows the disposition of shells rather than periods. Tsimmerman´s formulation of Madelung is intriguing.

On Scott´s Column of Instability, I for one would be grateful, Scott, if you could spell out to dumbos like me its "blindingly obvious" nature, let alone significance. What are you getting at?
John

[René]

On 14 Nov 2025, at 06:11, johnmarks9 <johnm...@hotmail.com> wrote:

On Scott´s Column of Instability, I for one would be grateful, Scott, if you could spell out to dumbos like me its "blindingly obvious" nature, let alone significance. What are you getting at?

John

Hi John, and Scott

Here’s my understanding, bearing in mind Scott that you’ve focussed on Tc, Pm and Np and Ubp. It seems that the picture is broader than that. Thanks Scott (and John) for prompting a closer look at this subject.

The Column (or Axis) of Instability

The Axis of Instability refers to a sequence of unusual or anomalous behaviours that appear when moving down Group 7 and its two f-block shadows, Pm and Np.

In Group 7

Mn—crystallises in a highly complex and radical cubic structure with 58 atoms per unit cell. Four distinct coordination environments occur in α-Mn, each with a different effective atomic radius. This structure is unique among the metals.

Tc—radioactive despite lying among stable neighbours; none of its isotopes are stable, making it the lightest element for which this is true.

Re—the most radioactive of the naturally occurring elements that have a stable isotope. Only 37.4% of natural rhenium is stable (^185Re); the remaining 62.6% is ^187Re with a half-life of 4.16 × 10^10 years.

Bh—too poorly characterised for any firm conclusion.

The f-block shadows

Pm—radioactive despite being flanked on both sides by lanthanides with fully stable isotopic compositions.

Np—the first of the transuranium elements, marking the onset of deliberate artificial synthesis, although later detected in trace natural amounts.

Ubp (Z = 125)

After element 120, the 6f, 7d, and 8p orbitals are expected to lie so close in energy—and to be so strongly affected by relativistic shifts—that no stable orbital-ordering sequence would exist. That said, around Z = 125 (Ubp), the 5g orbital is expected to collapse sufficiently in energy to permit the first appearance of an associated electron.

It is striking that, after the familiar period-opening sequence (each period beginning with an s-block pair—119 and 120 in this case), a naïve extension of that sequence would place element 125 in a position corresponding to Group 7.

General pattern

With one exception, the effect is limited to the d- and f-blocks. The exception is in the p-block, where (unstable) white P crystallises in the alpha-Mn structure, with 58 vibrating P4 tetrahedra. Here, P (15) and Mn (25) are linked by a Z+10 relationship.

All the elements involved have odd-Z and show either:

• half-filled subshells (P: p^3; Mn, Tc, Re, Bh: d^5); or
• a total of seven outer (fs, fds or gds) electrons (Pm, Np, Ubp via a presumed 8s2 7d4 5g1).

The pattern is absent or weak in the s- and p-blocks, and stronger in the other blocks.

Given the existence of nuclear “magic numbers”, one might reasonably ask whether there are mid-shell or “antimagic” numbers where nuclei tend to be less stable. The relevant Z values here are 15 (P), 25 (Mn), 43 (Tc), 61 (Pm), 75 (Re), 93 (Np), and 125 (Ubp).

I don’t know if this pattern has any connection with the unusually complex crystal structure of Mn. It may be coincidence—yet it may hint at a deeper periodicity that extends beyond electronic structure into nuclear structure.

In summary, we are dealing with…

• odd-Z mid-shell instability;
• anomalous crystal structures;
• nuclear-stability irregularities;
• abrupt changes in orbital energetics;
• possible “antimagic” Z-values;
• a delayed 5g collapse; and
• a numerical coincidence placing Z = 125 in the Group-7 slot.

Taken together, the constellation of coincidence and anomalies is truly remarkable—an esoteric manifestation of the periodic law anyone?

Re, "there have been no known previous proposals or references to such a self-evident Column of Instability" I mentioned the Axis of Instability, in 2019, here https://groups.google.com/g/pt-l/c/kATkE6AOCLs/m/Z7tdYjbwAAAJ and in 2013, here https://en.wikipedia.org/w/index.php?title=User%3ASandbh&diff=prev&oldid=556572291

René

[Scott Hutcheon]

Off-thread preface: While many enjoy breaking out the popcorn and watching the show (I'm often guilty of this too), have also received a couple of direct emails over the civility of some responses or comments (which apparently has some history for this group). As replied to those, thanks, but there are no concerns for me as my background is over thirty years in studying cosmology, astronomy, information, physics, and the history and philosophy of science (primarily physics) and this is expected per the Schopenhauer attribution.

Additionally, I have rhino skin as a result of being personally and publicly attacked (face-to-face in classrooms and studios) for seven years at a college and two universities over incredibly intimate and personal creations -- while also knowing that sociopathy cannot be tested until the early/mid twenties as we're nearly all necessarily antisocial at younger ages to allow for intellectual/belief separation and societal/cultural evolution (meaning it required continually defending myself against still-sociopathic students back when pure toxicity was normalized and even expected/encouraged by professors).

Obviously, being accused of naivety, of merely luckily finding coincidence, misdirecting energy, facing assumptions about levels of education-experience-understanding-knowledge, or that reading the RSPT paper is beneath or a waste of time (even if it would have prevented so many repetitive replies in these threads), is minor and trivial compared to Experts viciously criticizing Boltzmann into suicide (for correctly proposing statistical mechanics and the kinetic thoery of gases) or Semmelweis into an asylum and death (for correctly suggesting the paradigm shift of washing your hands before surgery or childbirth). Not that I'm remotely in their league, but they are cautionary tales.

I'm actually instead saddened about the ongoing reality in the sciences of most Experts being unable to adapt to a new paradigm, per German physicist Planck and his "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." It's an unnecessary hangover from attempts to force religious beliefs as eternal truths onto everyone else. Instead, knowing the science behind the 10,000-hour rule, it's much more tragic that so much life and work and energy and time can (even if just partially) be spent within an incorrect/unscientific paradigm after a more scientifically evolved one is proposed but then only briefly skimmed and rejected outright to defend turf rather than be closely examined, fully understood, and then pondered for its consequences.

Obviously not all proposed paradigm shifts can be completely considered as science would quickly mire under the sheer numbers and weight, resulting in non-evolutionary inertia. Experts are fundamentally necessary to both find and share the very evidence that leads to and triggers paradigm shifts, while also acting as funnelling screens to sort out potential shifts. However, believing in only evolution at every level (as a core belief, not a tacked-on educated one) -- and especially completely accepting that there are no eternal truths and only unpredictable universal evolutionary change -- is still not the normal worldwide culture and past-and-present religious beliefs continue to infect, degrade, and undermine scientific advancement (with anti-science, anti-intellectualism, and anti-education beliefs unhappily a growing concern these days).

And, truly, any mild or slight criticisms/shadings here are loving compliments compared to what I'm about to endure after even daring to show Physicists that their science primacy (including lifetime work, legacy, career, stature, and power structure) is being displaced by Information and Cosmologists/Astronomers that they've mostly wasted their intellectual lives, and almost exactly a century of dead-ended/delayed/stalled field progress considering observational and theoretical paradoxes, due to somehow actually believing in the embarrassing paradigm of the Catholic Priest singularity → evolution (Catholic Priest singularity → Physics → Chemistry → Biology) instead of the blindingly obvious, as always with 20/20 hindsight per Schopenhauer's attribution, actually scientific paradigm where evolution began with and continues through the increasing complexity phase transitions of Information → Physics → Chemistry → Biology.

Real scientist English astronomer Fred Hoyle will have his revenge served cold regarding the secularized religious belief hot expansion.

Back to the thread: Thanks René, and I mean this sincerely and honestly due to my deep understanding of and agreement with the 10,000-hour rule, as always your deep expertise around chemical/physical properties of elements and their placements regarding the periodic table is very welcome.

As your Axis of Instability was not peer-reviewed and published, I hadn't known of it. It's interesting and not a coincidence that we arrived at similar names for the relationship coming from completely different interests and backgrounds. Mine in relation to physics/cosmology and the Z ≥126 Island of Stability, while also necessarily including (from first principles) 125 -- which, just like the Column, was hidden in plain sight behind the non-obvious Ubp naming convention.

Since I do not subscribe to shadow property/dotted-line relationships or any concept of recovering both Mn-Tc-Re-Bh and Mn-Tc-Pm-Np within simultaneous bifurcated relationships (similar to the misunderstanding of the cat being in a superposition of both dead and alive), while only accepting Mn-Tc-Pm-Np-125 from first principles as the Column of Instability and it's relation to the Island of Stability, let's revisit the RSPT paper -- which also, in direct relation, addresses the artificial bifurcated simultaneous relationship of Sc-Y-La-Ac and Sc-Y-Lu-Lr.

1. Any Periodic Table that is symmetrical (bilaterally symmetrical) should now be regarded as non-science/nonsense. From Physics, with its recently agreed paradigm shift (that certainly wasn't the case when I was in school) that perceived symmetry is actually impossible within physical, chemical, or biological reality -- asymmetrical gravity, asymmetrical time, asymmetrical baryon matter-antimatter, asymmetrical charges, asymmetrical spins, asymmetrical orbits/orbitals/charge densities, asymmetrical handedness, asymmetrical chirality, etc. -- the use of band-aid/secondary line connections to claim multiple/shadow chemical and/or physical property relationships in order to salvage/rescue symmetrical tables is straightforward evidence of an artificial workaround to sidestep/avoid proof from first principles.

2a. Any salvaging of the current standard periodic table by claiming multiple or shadow or secondary connections for Sc-Y-La-Ac and/or the Mn-Tc-Pm-Np/Mn–125 Column of Instability is belied from first principles:

2b. Any rescuing of the Left-Step (or any left-step) periodic table by claiming multiple or shadow or secondary connections for Sc-Y-La-Ac and/or the Mn-Tc-Pm-Np/Mn–125 Column of Instability is belied from first principles:

2c. Even though it's obscured/hidden by the 18-column's more symmetrically attractive form, it should be clear by now from the 32-column forms that the current standard iconic periodic table is a modified left-step table (cylinder wraparound interconversion/equivalency for chemical and/or physical property relationships) -- and 100% universally wrong for all the same reasons.

3. As historically expected, only outsiders would dare commit the blasphemy (aka paradigm shift) of breaking apart the sacred artificial idol d-block into scientifically correct d- and f-period pieces/relationships -- where, from first principles, there is no possibility of Mn-Tc-Re-Bh and of only Mn-Tc-Pm-Np-125 (and where nothing needs to be recovered or fudged):

While, per the paper, the RSPT may not be the final 'one' of the right-steps -- as it was accidentally realized while solving for H and He Eddington numbers and chemical/physical properties in relation to all other elements, addressing missing Mass 5 and 8, and the underrepresented masses of 2 and 3 as well as Lithium and Beryllium, while also simultaneously finding a way to keep the traditional p-Groups -- it naturally contains, from first principles, the Column of Instability.

As does every scientific right-step:

Right-Step Mendoza: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=407

Right-Step Gutierrez-Samanez: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1100
Right-Step Vernon/Gutierrez-Samanez: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1303

These right-steps necessarily contain correct relationships -- Sc-Y-La-Ac and/or B-Al-Sc-Y-La-Ac, as well as Mn-Tc-Pm-Np-125 -- as an inherent feature from simply following first principles of Van den Broek-Moseley sequential atomic numbering and the Madelung Rule (with corroborating support from the 1913 breakthrough of radioactive periodicity).

Mathematics at the Information level obviously contains symmetries, whereas Physics and Chemistry are asymmetrical, so while the Beylkin and its artificial gaps is halfway correct with five proper d- and f-period relationships, that started with the one proper relationship with Romanoff and its artificial gaps (https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?textfield=Romanoff), only right-step tables fully resolve.

This is supported by the Döbereiner-Scerri triads, where only proper alignment of d- and f-periods allows for full d- and f-element vertical triads (equally one correct for Romanoff, five/half for Beylkin, and 10/complete for right-steps). As stated in another chain, horizontal triads are now trivially obvious after the monumental paradigm shift from atomic weights to Van den Broek-Moseley sequential atomic numbering. But only after the paradigm shift, within the incorrect paradigm Experts blindly hashed out atomic weight anomalies where Mendeleev prevailed by recognizing/intuiting an unverifiable/unfalsifiable (for that paradigm) underlying Information-level triadic relationships.

While similarly, group theories, algebras, and simple vertical triad math relationships may seem (rightfully) ridiculous as entities at the Physics or Chemistry level if you're trapped in the Catholic Priest singularity → Physics → Chemistry → Biology paradigm, they are very real as actual self-organizing emergent Information-level entities in the Information → Physics → Chemistry → Biology paradigm that drives and informs the underlying level from which the spontaneous-symmetry-broken asymmetric relationships and properties we experience as real at the level of Physics and Chemistry arise (including the periodic table).

4a. Unless I'm missing something obvious (always likely), it seems self-defeating/illogical to continue defending the outdated/superseded paradigm of the artificial d-block and arguing against the more scientific/evolved d- and f-period orientations within the right-step periodic table forms, considering they are also the only from-first-principle non-fudge-factored variants that support all the investigatory and research work towards Sc-Y-La-Ac as a better trend fit versus Sc-Y-Lu-Lr as well as the Rang-Vernon B-Al-Sc-Y-La-Ac extended Group as a better trend fit versus B-Al-Ga-In-Tl-Nh.

4b. I'm never interested in winning, or proving I'm right, simply because of the hard-earned realization there is no eternal win, no permanent 'right' -- only permanent wrong (i.e., disproven beliefs). Think of biologic evolution, there is no winning, merely continuing to survive and adapt, versus permanent extinction (wrong for the changing environment). Fundamental evolution means there are never eternal truths, every scientific fact is necessarily incorrect/incomplete, just like the paradigm it was formed within, and will either be discarded as wrong or superseded/made more complete/more evolved by a more fundamental understanding. 

Since ever discovering completely objective reality is not realizable, it's instead the fruitful journey towards the impossible destination. 

[johnmarks9]

Another delightful philosophical deep-dive!

Yes, the cosmos just is.

Physics deals basically with events in space and time - and electromagnetism. 

Chemistry deals with the subset of physics which concerns that quantum phenomenon, the atom.

Biology deals with that subset of chemistry which concerns a phenomenon nicknamed "Maxwell´s demon", demonstrated by the thermodynamic phenomenon known as a "Markov blanket" and realized in the biological unit known as a cell, which nevertheless follows the laws of physics and chemistry, yet grows into humans via that other homœostatic phenomenon, Darwinian evolution.

John

PS "Since ever discovering completely objective reality is not realizable": Well, you may be able to discover it, but can´t ever know that you have! - Popper.

[René]

On 20 Nov 2025, at 09:27, Scott Hutcheon <scotth...@gmail.com> wrote:

1. Any Periodic Table that is symmetrical (bilaterally symmetrical) should now be regarded as non-science/nonsense.

Hi Scott

The attached periodic table has four axes of symmetry; its shape; four block types in each half; metals and nonmetals in each half; and a subatomic particle in each half.

Should it now be regarded as non-science?

René

[Mark Leach]

And, such periodic tables have an honourable history:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1039

Mark Leach

meta-synthesis

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[ERIC SCERRI]

Or the original version due to Thomsen who taught chemistry to Bohr. 

It was also Bohr’s preferred format. 

Eric Scerri PhD

On Nov 24, 2025, at 7:36 AM, Mark Leach <ma...@meta-synthesis.com> wrote:

And, such periodic tables have an honourable history:

To view this discussion visit https://groups.google.com/d/msgid/PT-L/7E087276-85E8-49F3-8F1E-428DF84D014C%40meta-synthesis.com.

[Scott Hutcheon]

Like Periodic Table periods, can only repeat so many times before there's not enough energy available to continue...

Went back and am copying-and-pasting a few parts from a previous thread's fuller reply:

"The step-pyramid periodic table is a bilaterally near visually symmetrical attractive artificial construct that has been rehashed since at least its invention in 1882 by Bayley (true science is built on discoveries that lead to falsifiable theories not beliefs that lead to unfalsifiable invented works of art): https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=66"

"2. Per the RSPT paper, this form claims the electron (e) and the Neutron (N) as Period 0, despite any 0s or Period 0 being the Free Proton and Alpha Particle based on the universal reality of Chemistry (starting at 1s) evolving from Physics"

"5d. Rather than further going into gruelling detail pointing out how forcing artificial bilateral symmetry onto a periodic table can only reinforce a biologically pleasing yet physically shallow understanding of true symmetry, it might be better to show here how little actual symmetry there is between periods, blocks, primary, and secondary (dotted line) relationships (a picture speaks a thousand words and all that):

"

There is no actual (bilateral or otherwise) symmetry in chemical reality. It looks like basic gross generic bilateral symmetry if orientations are visually manipulated to match organizationalist desires (per the RSPT paper), but it's not possible for symmetry to exist at an asymmetrical level like Chemistry. 

Would also strongly recommend not using period blocks as they obscure relationships within periods (between metalloids and other metals for example):

This is the same table as the capstone step-pyramid, just in a more scientific/evolved paradigm format. Favourite scientific (universal) right-steps such as Working Chemist would be interconverted variations of this.

[René]

On 25 Nov 2025, at 06:17, Scott Hutcheon <scotth...@gmail.com> wrote:

There is no actual (bilateral or otherwise) symmetry in chemical reality.

Well, yes there is: in terms of chemical reality, there are metals and nonmetals in each half. The context here is that the metal-nonmetal dichotomy is one of the great foundational aspects of chemistry, well known in terms of the general saying that metals are on the left and nonmetals on the right.

Too, there are four block types in each half. For the chemical reality of blocks, consider the following:

The division into blocks is justified by their distinctive nature: s is characterized, except in H and He, by highly electropositive metals; p by a range of very distinctive metals and non-metals, many of them essential to life; d by metals with multiple oxidation states; f by metals so similar that their separation is problematic. Useful statements about the elements can be made on the basis of the block they belong to and their position in it, for example highest oxidation state, density, melting point ... Electronegativity is rather systematically distributed across and between blocks.

P. J. Stewart

In Foundations of Chemistry, 2017

Would also strongly recommend not using period blocks as they obscure relationships within periods (between metalloids and other metals for example):

I see no basis for such a negative recommendation.

Thus, the diagonal transition from p-block metals to metalloids in the p-block is a beautiful illustration of the culmination of metallic-to-nonmetallic trends across each period, considering that metalloids have a predominately nonmetallic chemistry.

How do you see this now?

René

Stewart, P. J. (7 November 2017). "Tetrahedral and spherical representations of the periodic system". Foundations of Chemistry. 20 (2): 111–120. doi:10.1007/s10698-017-9299-y