Notes on the scoring, and two corrections made on 2026-08-07
1 — Edge status is now an evidence class, and the grades have changed
The status on each pairwise edge used to be a two-valued field, established or
candidate, and it conflated two different things: how well attested an interaction is, and how
well classified it is. It is now three-valued, and it grades only the second.
- established — a classification theorem exists. That is all the word means here.
It is not a claim about community consensus or about importance.
- phenomenon — observed, named, repeatedly reproduced, and real; but no invariant
classifies it.
- candidate — a proposed connection, neither classified nor agreed as observed.
On that definition three grades change:
| Edge | Was | Now | Ground |
|---|
| S1×S2 — protected criticality | candidate | established |
Mermin 1979 classifies defects in an ordered medium by the homotopy groups of G/H. A classification theorem, and 47 years old. |
| S2×S3 — self-organised criticality | established | phenomenon |
Bak, Tang & Wiesenfeld 1987 is an observation, reproduced very widely. No invariant classifies it. |
| S2×S4 — edge of chaos | established | phenomenon |
Langton 1990 proposed λ as the invariant; Mitchell, Hraber & Crutchfield 1993 deflated it and nothing replaced it. |
S1×S4 keeps established — Kitaev 2003 is a construction. S1×S3 and S3×S4 remain
candidates. This is the reading this series takes, with its evidence stated so it can be argued with; it is
not a claim that the field has settled the question. The full argument, with citations, is on
Broken Symmetry and the S1×S2 Edge.
2 — FQHE no longer scores closure (S3: 1 → 0)
Two copies of this matrix disagreed about one cell: whether the fractional quantum Hall state carries
closure. This copy said 1; the copy frozen in version control as the predictor for an analysis said 0. The
tutorial now matches the frozen predictor. Stack height is computed from the scores, so FQHE's stack
follows automatically; no stack number was edited by hand.
The conservative reading. Closure in this series means a self-sustaining network that
produces its own components from a food set — the RAF condition of Hordijk & Steel 2004, after
Kauffman 1986. The conservative reading holds that a fusion algebra closing on itself is not yet
a food-generated production network in the RAF sense: the algebra says what may combine with what,
which is not the same as a network that manufactures its own components from a supply.
⛔ A correction to how this reading used to be argued (2026-08-10). This paragraph
previously read “Anyons are excitations created by externally perturbing the medium.”
That is false, and it is the one claim here that is settled published physics rather than a
judgement call. Anyonic quasiparticles are collective excitations generated by the
two-dimensional electron gas itself — the substrate produces them under the right conditions;
they are not injected from outside (Nayak, Simon, Stern, Freedman & Das Sarma,
Rev. Mod. Phys. 80, 1083 (2008), doi:10.1103/RevModPhys.80.1083). The companion
tutorial Fibonacci Anyon Fusion states this correctly, so this page was
contradicting its own series.
What that does to the score. It removes the generation objection entirely:
physical generation by the substrate is exactly Kauffman’s generation criterion, instantiated in
matter rather than only in algebra. Any remaining case for the conservative value has to rest on the
food-set and catalysis conditions — on whether fusion is a production network at all
— not on where anyons come from. The score is left unchanged, because
changing it is a scoring decision and this is a physics correction; but the reason recorded
beneath it was wrong, and a score defended by a false reason should be treated as unsupported until
someone re-argues it on the surviving grounds.
The steel-man for the old value, which is real. Fibonacci fusion
τ × τ = 1 + τ does regenerate τ from τ, which is closure in the
fusion-category sense, and “anyon fusion as a RAF” remains an open candidate connection in this
series — it is the S1×S3 edge above, and it is why this cell was ever a 1. What it is not is a
network of physical components producing each other from a food set.
The reason that actually decided it. The frozen copy was committed before the
analysis that used it. Editing a frozen predictor after seeing results is post-hoc tuning, and it is a drift
signal however defensible the new value looks. So the frozen copy wins by default and the unfrozen copy is
the one that gets corrected — which would have been the outcome even if the argument above had gone the
other way. Anyone publishing an analysis against this matrix should state which scoring they used.
One knock-on, not yet fixed. The Inert face below still names FQHE as its
example. On the corrected scoring FQHE no longer sits on that face, so that example is stale. It has been
left alone rather than quietly rewritten, because changing it is a separate judgement from the one made
here.