Traces of a wheel or similar

[DG97EEB]

1. The ~63% forward/backward asymmetry survives paragraph entry very clearly.

Across the whole sample the d/q/y edges are 318 forward versus 190 reverse, i.e. 62.6% forward.

I reran the count excluding the first transition of every paragraph entirely - so no line 1→line 2 transitions at all. It is then 311 forward versus 178 reverse, or 63.6% forward.

The paragraph-preserving permutation test gives the same answer. On continuation lines only, the directional excess is:

- Currier A: +57.9 transitions, null SD 12.8 = 4.52 SD
- Currier B: +72.2 transitions, null SD 15.2 = 4.77 SD

So the directional asymmetry is not being produced by the special behaviour at paragraph starts.

There is also a held-out model comparison in which direction itself adds about 0.0050 bits/opener, null SD 0.0020 = 2.51 SD after accounting for the paragraph-entry regime.

2. I described the 0.323-bit result slightly misleadingly. It wasn't a general paragraph-position model.

That model only distinguishes:

line 1 versus all continuation lines (2+).

Its held-out gain over treating every line identically is 0.3229 bits/opener.

I've now decomposed that gain:

- 70.3% comes from modelling the paragraph's first line separately;
- 29.7% comes from modelling all continuation lines as a separate pooled population.

In absolute corpus-wide terms that is 0.2270 bits/opener from line 1 and 0.0959 from continuation lines.

So yes, the gallows-heavy/special first line is responsible for most of that very large 0.323-bit effect.

But importantly, removing line 1 does not remove the directional transition behaviour. In fact the raw forward proportion goes from 62.6% to 63.6%.

I therefore think your “directed network” description is closer to what the statistics actually show than my original wheel framing.

I would still separate two claims:

- there is clearly a directed opener-transition network;
- whether q is formally the hub of that network needs its own network-level test rather than choosing q after inspecting the graph.

Your one-line-memory interpretation is also consistent with our existing lag-2 test. A first-order transition matrix predicts the apparent reversal at distance two: the observed lag-2 reversal is only about 0.4 SD away from the first-order prediction. So we currently have no evidence that the line two above contributes extra information once the immediately preceding line is known.

That combination is starting to look like a special paragraph-entry regime, followed by a predominantly first-order directed continuation process, but what it all means, I still haven't figured out...