The Groundtruth Seam · a finite census
Clutter Number ?
Rename and inspect connected antichains of sets, reproduce every published value of OEIS A293607 through 42, then audit the next weight.
A clutter here is a finite family of nonempty sets. No edge may contain another, every edge must meet the family through a chain of intersections, and only the pattern of membership counts. The names on the vertices do not.
Rename every vertex. Keep the same object.
Choose one of the eight weight-7 examples printed in the OEIS entry, then move the relabeling control. The family below changes its vertex names while its weight, antichain test, connectedness test, and canonical card are recomputed.
Make the OEIS list come back
The browser reads the committed A293607 b-file below, then enumerates every set partition and edge-size partition through weight 9. The next section stays locked unless all ten published cells agree.
The empty object is a stated convention. The non-vacuous reproduction is weights 1 through 9.
Now allow one more weight
waiting for the anchor
We could not find this published as of 2026-08-01, having searched the live OEIS A293607 text, JSON, and b-file records; OEIS sequence search for 23,42,108; exact web searches for A293607 with 108, the sequence values, and the phrases “Number of unlabeled clutters of weight”, “clutters of weight”, and “unlabeled clutters of weight”; OpenAlex; Crossref; and arXiv.
This is an absence report, not a priority claim. An unindexed table, private computation, different terminology, or a later OEIS update could change it.
Make 108 survive two different cuts
selected sum: locked
Change from connected clutters to all antichains
The ordinary Euler transform assembles an arbitrary antichain as a multiset of connected components. Weights 0 and 1 are omitted from the control because agreement there is conventional or true by construction. The genuine published cross-check begins at weight 2.
At weights 2 through 9 the transformed values reproduce the separately published A293606 record. At weight 10, the same operation yields 313. That is a consequence of the connected coefficient 108, not a second independent census and not an additional priority claim.
The check
The browser computes the values in this panel from the embedded copies of the committed records and from the page engine:
| A293607 source record | loading |
|---|---|
| anchor reproduction | loading |
| weight-10 search space | loading |
| audited representatives | loading |
| distinct canonical cards | loading |
| nonzero profiles | loading |
| Euler transform at weight 10 | loading |
- Weight: the sum of edge cardinalities, equivalently the total number of incidences. It is not the number of vertices, number of edges, rank, or ground-set size.
- Antichain: edges are nonempty and pairwise unequal, and neither edge contains the other. Duplicate edges are rejected.
- Connected: the edge-intersection graph is connected. This equals connectedness of the bipartite incidence graph after isolated vertices are excluded.
- Ground set: exactly the union of the edges. Isolated named vertices are not added.
- Unlabeled: vertex names and edge order are erased. The canonicalizer permutes edges and sorts vertex-incidence columns. It never exchanges the vertex and edge sides.
- Empty convention: a(0) = 1. This cell is vacuous as a reproduction test, so the page identifies weights 1 through 9 as the anchor with content.
- Exactness and uncertainty: the counts are integers with no sampling error. The free choices are the definitions above and the cutoff at weight 10. Publication absence is not certain beyond the named searches and date.
Run node research/sequence-extension/verify-sequence-extension.mjs. It independently enumerates through weight 10, executes this page engine, checks both OEIS records, and deliberately corrupts the anchor, a representative, and an Euler-transform coefficient to prove the checks can fail.
Primary records: OEIS A293607, its b-file, OEIS A293606, and the OEIS licence. Fetched 2026-08-01 at 10:50 UTC with HTTP 200. The committed provenance record gives byte counts and SHA-256 hashes.
Weight 11 is still outside the room
This census stops at weight 10. It does not estimate, extrapolate, or claim weight 11. Extending the table again requires another full enumeration, an independent implementation, and a fresh publication search.