The 40-point badge
Asked, not built. What the question is, what would answer it, and which file is missing.
Status
Open. No file in this project defines a 40-point badge: no circle set, no diamond set, no arrangement list, no exclusion table, no count. This page records the question and what would close it, and draws nothing it cannot source.
What is asked
The nuna life oracle carries it as an open question, NL-050: a possible 40-point badge as a larger neighbourhood — what rules make good ornaments with it?
The project notes record the intention alongside it: to experiment with different rule sets around a possible 40-point badge model, and then to find patterns with it.
So the question arrives from nuna life rather than from the filing system. That matters for what an answer has to look like. A neighbourhood needs only a list of which tiles count as neighbours. A badge needs that list to be closed under the exclusion rule, with a legal-combination count and a ceiling, the way the 16-point badge is.
What would settle it
Four things, in order, and the first is the one that makes the rest possible.
- A definition of the forty. Which circles, which diamonds, which arrangements — as coordinates on the lattice, in the form the combination-shapes reference uses for the sixteen.
- The exclusion table, derived rather than drawn. If the rule is still “shares a circle or a diamond”, the table follows from the definition and should never be typed by hand. That is how the 16-point key was checked.
- The count, by tier, with its ceiling. 1,157 in six tiers is what makes the 16-point badge usable. A single total would not be enough.
- An independent re-derivation. The 16-point count is trustworthy because two separate pieces of code return it from the same rule. Nothing less should be accepted here.
What is missing
Nothing with a 40-point badge in it is among this project's files. Earlier work on the question exists in a nuna life session — a lab page with its own neighbourhoods and rule sweeps — but it has not been exported to a file, so nothing from it can be cited here, including whatever counts it reported.
The export that would unblock this page is small: the badge's node list and its arrangement table, as data. With that, this page becomes a reference like the other two in an afternoon.
Note
Aaron's slot.
Open questions
- Is it one badge or two? The name “40” has been used for more than one neighbourhood in the nuna life work — at least one that contains the 24 and one that is the ring beyond it. Those are different objects and they need different names before either is written up.
- Is a 40-point badge a badge at all, or only a neighbourhood? If its tiles do not resolve into circle-and-diamond arrangements under the same rule, it belongs to nuna life and not to this shelf.
- What the ceiling is. The 16-point badge closes at six and that closure is what made the filing system finite. A badge without a known ceiling cannot be filed by.
- Whether the combination pages should carry a 40-point section at all until the above is answered.
Checks
| What | How | Source |
|---|---|---|
| The question, as filed | “A possible 40-point badge as a larger neighbourhood: what rules make good ornaments with it?” | nuna life oracle, NL-050 |
| The intention | Experiment with rule sets around a possible 40-point badge model, then find patterns with it | project note, 40-point badge |
| Neighbourhoods are the badges | 24 by default, 16 by deliberate choice — which is why a third neighbourhood is wanted at all | nuna life oracle, NL-002 |
| A definition of the forty | No file on hand. No circles, diamonds, arrangements, exclusions or counts | — |
| Any count | None citable. Earlier session work exists but has not been exported to a file | — |