SPIN PARITY: PUBLIC SCIENTIFIC AUDIT — 12 OCTOBER 2026
Duho Kim | KAS 2026 Fall | companion to poster v69

The scientific sections below reproduce the accepted overnight audit. References
to “this overnight phase” describe the closed retrieval/validation phase. The
v69 text correction subsequently completed in a separate checked run. This
public edition omits internal execution records and local paths. It preserves
scientific findings and limitations; retained source hashes are in the public
45-claim register. The private catalogues are not part of the public package.

MAIN FINDINGS
The external membership lookup is now resolved. Six bounded catalogue requests
returned 7,025 rows for all 133 previously identified candidate external hosts.
Independent offline verification checked every saved response and reconstructed
the member table. Local matching and a separate angular-distance verifier found
326 unique positional candidate counterparts across 30 groups and 2 clusters.
All 23,623 original member occurrences in 1,713 groups and 9 clusters remain in
the accounting. This is useful but limited external coverage, not native
membership probabilities for the full group/cluster sample.

The main poster correction is a superseded statement in section 3. Significance
and partial measurement-error propagation HAVE now been evaluated. Conditional
system-sign and spatial-block tests did not detect an excess; their separately
adjusted p-values are all 1. Formal-error propagation remains conditional, and
deterministic centre shifts and selection comparisons show sensitivity. These
are neither proof of exact randomness nor a complete uncertainty model.

The galaxy conclusion remains: measured spin/winding imbalance depends on the
method, including a separate comparison on the same 30,910 galaxies. Neither
method establishes a statistically significant preferred sky direction under
the reported conditional tests. No new classifier, baseline fit, label flip,
random stream or map measurement was introduced in this overnight phase.

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.

2. GALAXY CHAIN: INPUTS, METHODS, MAPS AND INFERENCE
The retained inventory has49,211 attempted targets. SpArcFiRe resolves30,910:
15,479 CW and15,431 ACW, leaving18,301 unresolved. Its observed imbalance is
+0.155%. Fourier assigns49,007 retained compatible tensors, with24,644 CW and
24,363 ACW;204 targets lack a retained tensor. Full-sample maps therefore use
different assigned sets. The separate common-sample comparison uses30,910,
with18,791 method agreements and12,119 disagreements. Agreement is not accuracy.

The documented adapter maps SpArcFiRe S-wise to the displayed positive label
and Fourier display CW to minus its machine sign. Saved map reconstruction and
97-batch source/settings checks found no demonstrated adapter inversion needing
a flip. Relative PNG orientation tests and source conventions do not prove the
opaque historical compiled binaries' internals, their complete build lineage,
or absolute astrometry. Those limitations remain visible.

Galaxy map colour is Delta A=A(toward)-A(opposite), in percentage points, with
A=(CW-ACW)/resolved within each hemisphere. It is not the fitted dipole amplitude.
The two displayed full maps reach about +/-2.1 and +/-2.0 percentage points;
their colour limits are +/-5. The axis coordinate is a possible dividing axis,
not a galaxy position. The antipode is (RA+180 mod360,-Dec); swapping the two
hemispheres reverses contrast. The648 cells are correlated, not648 independent
measurements.

The retained SpArcFiRe fit is2.27%, approximate95% Wald envelope0-7.79%, with
conditional shuffle p=0.684. Fourier full/common amplitudes are1.65%/2.16%, with
approximate Wald envelopes0-6.03%/0-7.68%. Fourier's four full/common dipole-LR and
maximum-map-contrast tests use their stated conditional shuffles and Bonferroni
family of4; all adjusted p-values are1. These tests do not calibrate classification
or selection bias. A Bonferroni value1 is a capped adjusted p-value, not a100%
probability of randomness.

The shared maps are not exact negatives. Existing scalar-field correlations
depend on weighting: uniform-cell r=-0.0456, cos(Dec)-weighted r=-0.2937, and
uniform for candidate-axis |Dec|<30 deg r=-0.4886. These are not RGB/perceptual
correlations. Whole-pair global and within-batch follow-up shuffles yielded
Bonferroni8 p=1 for all comparisons; they did not identify a causal explanation.

On the same5,397 development-exposed human-reference galaxies, SpArcFiRe agrees
with5,001 labels(92.7%) and Fourier with4,356(80.7%); the methods agree on4,216.
This cohort is not the full science sample. Frozen reference-support checks show
substantial magnitude/size coverage gaps; CzSL matched photometry is unavailable.
The reported pooled and cohort-specific calibration ranges are model-conditional
and use different confidence constructions. They are not a demonstrated
full-population accuracy correction. The v68 explanatory calibration wording is
retained.

3. GROUP/CLUSTER CHAIN AND LATER VALIDATION
Both motion estimators use retained member line-of-sight velocities: regression
fits sine/cosine terms against position angle; half-plane estimates the first
harmonic of differences between means across a rotating dividing line. Fitted
directions are not detections of physical rotation. The two methods share data
and are correlated. On1,722 screened systems,1,705 direction pairs are within
45deg,17 are intermediate,0 exceed135deg, and the median difference is10.43deg.

H is an equal-weight, dimensionless pair-handedness statistic of fitted
projected directions. The map displays10^4[H(toward)-H(opposite)], not speed,
CW/ACW percentage, or fraction of rotating systems. Pooled10^4H is+0.674 for
regression and+0.211 for half-plane. Their leave-one-system ranges are
+0.023 to+1.319 and-0.416 to+0.839. These are sensitivity ranges, not confidence
intervals. The primary1722-system result has unchanged maps and denominators.

The earlier arithmetic audit independently checked all map cells and separated
group/group, group/cluster and cluster/cluster pair contributions using the
same full pair denominator. Full fitted groups alone have negativeH, whereas
the screened groups plus clusters have positiveH. That comparison changes both
selection and sample composition; it is not a causal estimate of either one.

Completed later tests replace the old statement that significance was unevaluated:
- 2,048 independent whole-system sign patterns shared by both methods tested
  |H_reg|,|H_halfplane| and the maximum absolute648-axis contrast for each method.
  Raw p-values are approximately.8541,.9536,.9585,.5944;Bonferroni4 values all1.
- Four50/100Mpc Cartesian block partitions with zero/half-cell origins used
  2,048 patterns each and a fixed16-test family. Raw p-values span.570034-.973646;
  Bonferroni16 values all1. Whole-block flips preserve within-block contributions
  and generally have nonzero analytic null means. These arbitrary blocks are a
  sensitivity null, not a calibrated cosmological model.

All saved sign patterns were independently verified without regenerating RNG.
The two families remain separate; no heterogeneous pooled significance or
probability of exact cosmic symmetry is claimed.

All1,322 retained cluster spectra now have identity-matched positive formal
redshift errors. The updated1,024-draw propagation on the1722-system sample gives
10^4H quantiles[.225361,.770468,1.256272] for regression and
[-.244285,.279904,.821382] for half-plane. These are conditional Gaussian
formal-error perturbation quantiles, with fixed members/centres/reference z,
not a full confidence interval. Redshift-error calibration, membership and
centre probability models are not supplied by this calculation.

Four deterministic100kpc centre shifts were evaluated on the same1,690 systems
(1,681 groups plus9 fixed clusters), not all1,722. Matched baseline10^4H is
.53/.09; east2.83/4.31,west-2.50/-3.65,north-4.89/-4.03,south.39/1.53.
This demonstrates sensitivity to those specified shifts, not their probability
or the presence of a real centre error.

Saved P15/S075/V15C selection comparisons use the same1,040 groups plus9 clusters.
Their regression/half-plane10^4H pairs are[-4.367723,-3.951468],
[-3.955682,-3.654016] and[-4.316008,-3.911802]. The673 excluded groups are664 below
the member-count threshold and9 with an azimuth gap. V15C retains identical
members for1,039 of1,040 groups, so its apparent stability is limited evidence.
These selection tests do not create membership posteriors or justify comparing
the1049-subset sign directly to the primary1722 sign as one controlled change.


CURRENT POSTER AND INTERPRETATION
v69 updates only the significance/uncertainty note, third takeaway and footer.
Its measurements and maps are unchanged. A separate print copy embeds Helvetica
and Helvetica-Bold while preserving text placement, images and annotations.
Retained illustrative cutouts remain 58–125 ppi at A0. No PDF/X certification or
physical printer proof is claimed.

Source/method/claim review is distinct from observations. Root performed the
actual full-page and crop inspection; the author and visual checker are the
same workflow. No external model inspected final v69 pixels. Model review is
not journal peer review. Public evidence hashes identify retained local source
records but do not supply the private data needed to independently reproduce
all analyses.

Open limits include historical compiled-code provenance and absolute image
orientation, calibration transfer, native membership and centre probability
models, and systematic effects beyond the specified conditional tests. No
physical-spin or cosmic-parity detection, exact-randomness conclusion or native
membership posterior is asserted.
