RemarkRemark: AI-adaptedProof: Not suppliedSession-authored (Fable 5 assisted)‡ sources checked 2026-08-26‡ not proved here

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

‡ Recorded, not proved here. This statement is included so the library can refer to it honestly, with a citation to the literature. It is not proved anywhere in this library: the track that would prove it has not been developed here yet.

Skolem's construction gives a Steiner triple system of order $6 m + 1$

Statement

The source gives an explicit Skolem construction on $(Z / (2 m)) \times (Z / 3) \cup {\infty}$ and proves that its blocks form a Steiner triple system of order $6 m + 1$ for every $m \geq 1$ .

Remarks

This page uses only that existence statement. The exact block families are not rebuilt here, because the harvested notes and design record for this batch both require that block list to be copied from a verified source rather than reconstructed from memory.

Used by

A Steiner triple system exists exactly for orders v>3 with v≡1 or 3 (mod 6) Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Jonathan Davidson, Steiner Triple Systems (standard reference, not scraped)

Skolem's construction gives a Steiner triple system of order 6m+16m+1