When the methods agree,
is the agreement information?
A confluence event is a cell where more than one witness fires. Naively, agreement looks powerful: at order 2 and above the corpus passes about ten percentage points more often than the independence prior predicts. Three separate nulls were built to price that surplus, and a fourth test ran the whole machine against markets where nothing is real. The surplus survives none of them.
Eighty-one names, seven voices.
Events by order, against three nulls.
Every event is priced three ways: against the independence prior (what the members' individual chances predict if they were independent), against the best single member in the event (would you have done better just following the strongest rule?), and against the product of marginals (agreement excess). The order-2+ row is the headline: a large lift against independence, and a negative lift against the best member. Agreement adds nothing you could not get from the single best voice in the room.
| order | events | mean members | realised | independence prior | lift vs prior | best member | best member lift | event − best | agreement excess |
|---|
The methods co-target. That is not agreement, it is duplication.
Seventy pairs of rules fire on the same cells at a rate of one half or better across at least two hundred joint cells — the empirical merge criterion. At the top of the list are pairs that co-target perfectly. Two rules that always point at the same bar are one rule wearing two names, and counting them as two witnesses manufactures confluence out of nothing.
| rule A | rule B | channel | joint cells | co-target cells | co-rate |
|---|
And the label shuffle settles it
Assign the rules' identities at random and re-run the confluence machinery. The order-2+ surplus does not disappear — it gets larger. Whatever produces the surplus is a property of how claims are distributed across cells, not of which method said what.
| seed | order-2+ events | lift vs prior | event − best |
|---|
The same surplus appears on markets where nothing is real.
Before trusting a null you must show it can see. A deliberately constructed real confluence edge (the oracle pair) and a deliberately empty one (the null pair) were planted and run through every surrogate universe.
| universe | control | real | surrogate mean | surrogate sd | universes | p | at floor |
|---|
| universe | order | statistic | real | surrogate mean | surrogate sd | p | p floor |
|---|
Five families were declared before the surrogate run, each matched to the surrogate kind that destroys exactly the structure the family claims to use. None separates from its match.
| family | members | n testable | rules scored | rules positive | pooled lift | sign rate |
|---|
Confluence on the century, as reported.
The run's own report, published verbatim — every partition, all seventy empirical merges with their co-rates and joint-cell counts, the events and the three in-ledger nulls by order, the ex-ante families and the label shuffle.
Rendered from CONFLUENCE_MEASUREMENT.md, unedited. The tables above are read from confluence_data.json, which is the same run in structured form.