DD-003
Effective Channels
Exact source-network censuses and a heterogeneous pairwise-moment counterexample.
Completed finite studyChecked independently
The question
Which source-network features predict discovery and action concentration beyond pairwise signal correlation?
What we found
- DD-C-0032: The bounded DD-003 class has exactly 51 nonisomorphic model-valid bipartite source networks with four searchers and one to three nonisolated sources, split as 1, 8, and 42 graphs by source count.
- DD-C-0033: In the complete bounded DD-003 class at source accuracy 2/3, ten exact first-and-pairwise scalar-report moment signatures each match two nonisomorphic graphs, and none of the ten matched pairs differs in private discovery.
- DD-C-0034: Graphs K2N4:00011110 and K2N4:01111111 both have mean pairwise scalar-report agreement 3/4, but their exact private discovery probabilities are 8/9 and 31/36, a difference of 1/36.
- DD-C-0042: The registered DD-003 heterogeneous base class contains exactly 41612 valid labeled colored source objects and 671 color-preserving orbits; the single three-color expansion adds 12966 labeled objects and 168 orbits, for 839 canonical networks total.
- DD-C-0043: Two nonisomorphic colored networks with source accuracies 1/2 and 2/3 have identical complete first and pairwise scalar-report moments but exact private discovery 3/4 and 2/3, differing by 1/12.
- DD-C-0044: Among all 839 registered colored networks, 163 complete first/pairwise-moment signatures match multiple networks, covering 485 networks, and 111 matched groups contain different exact private-discovery values.
What this result covers
Checked independently. The formal evidence wording and registry state remain available below.
Technical details
- Study phase
complete-bounded-study- Registry status
complete-bounded-heterogeneous-census- Evidence status
independently-reproduced-colored-census-and-full-pairwise-counterexample
Reproducible evidence
20260720T232223Z_DD-003_2ea8dad5_ae62f6c1f120260721T032358Z_DD-003_84238b76_2cbc13e66a
Files and data
What comes next
preserve exact colored regressions; require a new bounded question before expanding the source model