PUBLIC MEMBERSHIP COVERAGE — 12 OCTOBER 2026
Duho Kim | KAS 2026 Fall | retained aggregate results, no new analysis

1. MEMBERSHIP: WHAT WAS RETRIEVED AND WHAT A MATCH MEANS
The catalogue service stores double-quote characters in its TAP_SCHEMA table
and column name strings. The earlier unquoted table-name lookup therefore did
not establish that the catalogue was absent. Two new, prospectively reviewed
metadata queries resolved the exact table key and 21 columns. The independent
schema verifier passed seven checks. The route was established before the fixed
01:56:24 KST viability decision deadline. No schema query was repeated by the
member retrieval stage.

The 133 public host IDs were queried in batches of 64,64,5, COUNT before data,
with six single-attempt requests. The member responses used 1,565,130 new wire
bytes. Their 7,025 rows include 1,712 external spectroscopic redshifts and 5,313
missing redshifts. No duplicate host/ObjID rows were found; seven ObjIDs occur
in multiple external hosts. Original rows, exact textual IDs, missing masks,
PMem, Pfree, tLum and tRad were retained separately. No probability products or
weights were formed. The offline retrieval verifier passed all eleven checks.

Local matching retained all edges within 2 arcsec. A primary candidate required
separation <=1 arcsec and either an external redshift consistent at
|z_external-z_local|/(1+z_local)<=0.001 or missing external zspec. Missing-z
candidates were flagged, not described as spectroscopically confirmed. No
nearest-neighbour or maximum-PMem tie-breaking was used. The independent
verifier used a different angular-distance calculation, required identical
threshold flags, and passed all ten checks. No edge fell within 1e-6 arcsec of
the 0.5,1 or2 arcsec thresholds in its boundary audit.

Population | original systems | member occurrences | unique candidates | systems with candidates
Groups     | 1,713            | 22,301             | 158               | 30
Clusters   | 9                | 1,322              | 168               | 2
Total      | 1,722            | 23,623             | 326               | 32

Of the 326 unique positional candidates, 118 have no external spectroscopic
redshift. They are z-consistent only where an external redshift exists. All 326
have finite catalogue PMem, spanning 0 to1. They are candidate counterparts for
candidate external hosts, not confirmed identities of our systems or members.
No ambiguous primary counterpart status occurred under these fixed criteria;
this does not resolve unobserved ambiguity or establish correctness.

The remaining statuses are explicit:
- Groups:20,605 member occurrences have no candidate host;1,538 have a candidate
  host but no primary counterpart;158 have one;0 are multiply matched.
- Clusters:1,047 have no candidate host;107 have a host but no primary
  counterpart;168 have one;0 are multiply matched.

Unknown or uncovered does not mean non-member. Edges/member occurrences are not
independent galaxies. redMaPPer PMem is conditional on that external red-sequence
host model. It is not a native Gfinder posterior and does not automatically
transfer to our velocity-selected systems. No native membership probabilities
were created, no spin estimator was reweighted, and no map was changed. Full
native membership and centre probabilities remain an external/model gap; they
cannot be filled with zeros or invented distributions.