RFE July 2026: Ferrites and Barlow packings

[Sean A. Irvine]

Hi

Can someone please compute more terms for the following sequences concerning ferrites and Barlow packings?

A011947, A011963, A011964, A011958, A011961, A011962.

These are the six remaining sequences with the obnoxious keyword combination "easy", "more". The hardest part will likely be obtaining access to corresponding paper by T. J. McLarnan.

Thank you to all those who responded to last month's question. We did not get a complete resolution, but progress was made.

I track these requests for enhancement here:

https://oeis.org/wiki/User:Sean_A._Irvine/Requests_for_Enhancements#Requests_for_Enhancements

Sean.

[Robert McKone]

Hello Sean,

Attached is a short note showing:

A011947(n)=A045683(2n+1)

It gives a direct coding between the Barlow packing condition and the binary necklace condition.  This gives a simple formula for computing a(n).

Mathematica code:

a[n_] := Total[MoebiusMu[#]*2^(((2 n + 1)/# - 1)/2) & /@ Divisors[2 n + 1]];

Sorry for its rough format, I saw your email earlier today when at work and I was thinking about the layers and necklaces since, and only had time to write this up after midnight.

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[Anthony Neves]

Greetings,

Please find the McLarnan paper attached below.

Note that A011947 is found in Table 4; A011958 in Table 5; and A011961, A011962, A011963, and A011964 in Table 7 with parameters N = 4, 6, 8, and 10, respectively.

- AMN

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[brad klee]

https://github.com/bradleyklee/Artifacts/tree/main/19-ferrite-terms/
https://github.com/bradleyklee/Artifacts/tree/main/19-ferrite-terms/reference

This isn't, imo, a good use case for LLMs but one to triage anyways, mainly 

with a focus on autonomous refereeing. 

The setup is that two LLM's testify regarding evidence they've collected and 

the payoff matrix is essentially the one from prisoner's dilemma. 

The best we can do is a minimum sentence for Harm.On.ica and Claude, 

which they did obtain for the data of Table 7. 

I don't know if this is actionable, but the reference implementation looks 

concise enough for a human reviewer in finite time. 

[  ] chaotic disks update :  :

M.F. Hasler also asked for more rigor on the transcendent digits claim, so 

we ran a burner to 50K finding a 4:1 wall:body collision ratio and a very 

strong linear signal over the 10K essential data: 

https://github.com/bradleyklee/Artifacts/tree/main/18-disks-deep

The question we're debating on youtube (lol) is whether these "first terms" 

will ultimately reach a revival with roughly symmetric negative slope guiding

bitwise complexity back toward its crystalline initial condition. 

My opinion or belief is also an Occam's razor argument that once the velocity 

vectors move off an octagonal star, the feedback looping of position and 

momentum can't be expected to reach a logistic turnaround. 

The wildest periodicity conjecture we've come up with is this: 

If the phase volume is essentially zero in the momentum space, and the 

few admissible momentum vectors form a strict D4 star, then we expect periodic 

trajectories in the algebraic position space of a square or maybe rectangular 

container. 

That makes conceptual sense, but it's even more difficult to prove than an 

increasingly complex hierarchy of special case crystalline initial conditions. 

What we're doing is not the same as polygon billiards, so I guess it's not 

also immediately relevant to this recent paper: 

Miranda, Ramos, "Classical Billiards can Compute"

https://arxiv.org/abs/2512.19156

I don't know if any techniques from Veech or Rauzy would be helpful, but 

I can be interested to look more in that direction as necessary. 

Thanks, 

--Brad

[Andrei Zabolotskii]

The author of the paper is alive and well. I got in touch with him after I tried and failed to replicate A011958. We'll see how it goes.

Andrei

суббота, 4 июля 2026 г. в 05:58:01 UTC+1, brad...@proton.me: