Re-scoped 2026-09-12 — one analysis, not another probe portfolio
The previous W1–W5 brief is superseded by merged #702, notes/exact-foundations-correction-20260912.md §3. Keep the valid location-without-shape constructions and the repaired source data. Do NOT rerun their proofs, repeat tiny censuses, test the invalid raw-p C3 of #666, or claim the two Aff(1) actions fail to intertwine.
Decision this task must change
Do the existing square-site, same-observable productions show a resolved departure from reflection-symmetric normalized shape, and does that departure decrease along an actual size lineage? Separately, how much non-affine shape displacement remains between adjacent sizes? This decides whether a further observation is needed and what it must separate; it does not name an exponent or field.
Inputs and resource envelope
Use one ordinary CPU machine with a complete repository checkout; no GPU and no new Monte Carlo. First profile one existing batch to measure runtime. Cap this first delivery at 4 CPU-hours; if the full delete-one path cannot fit, return the measured bottleneck and completed source audit, not a substituted estimator. Machine assignment by the team; do not power on a fleet.
Base: current main including #702; use #703's support policy after it is integrated, or record its exact reviewed head. Read #633/#655 for corrected cos(4theta), per-orientation inversion order and pooled/delete-one semantics. Reuse scripts/threshold_quantile_lineage.py from the #655 lineage if needed, with its source revision recorded.
Primary size lineage: N=145,290,725 from the P50/#612 assets. N725 raw: results/server-20260907/P612-n725-fullcurve/raw/; N145/N290: results/server-20260829/P50-n145-n290-fullcurve/. Resolve actual filenames from the checkout, do not invent missing paths. If one raw block is unavailable, return which and perform only identifiable comparisons. Additional already-committed lineages are sensitivity, not required for this first delivery.
Fixed objects, before examining new scores
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Reconstruct each orientation's pooled inverse CDF Q first, then form the declared spin-0 weighted Q. Check weights sum to one and sum(w*cos4)=0. Do not mix CDFs before inversion. Report equal weighting separately, from the SAME block.
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Primary grid: nine deciles 0.1,...,0.9. Anchors a=0.2,b=0.8. W_N=Q_N(b)-Q_N(a)>0; Z_N(u)=[Q_N(u)-Q_N(a)]/W_N.
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Shape reflection residual:
A_N(u) = Z_N(u)+Z_N(1-u)-1
= [Q_N(u)+Q_N(1-u)-Q_N(a)-Q_N(b)]/W_N.
Do not replace this by M_N(p)+M_N(1-p). The latter is a reflection about raw p=1/2 and conflicts with a location limit centred elsewhere.
-
Keep pooled estimates primary. For each aligned delete-one batch, repeat the entire Q -> weighting -> W -> Z -> A transformation. Retain the joint covariance. Cross-size independence/coupling follows recorded random-stream provenance, not matching batch IDs.
-
Symmetry/anchor identities cause deterministic redundancies. Use independent coordinates, e.g. A at u=0.1,0.3,0.4,0.5 (u=.2 is zero; reflected pairs repeat). Do not interpret a noisy covariance rank as a dimension of the mean law, or discard exact contradictory residuals with a pseudoinverse.
Deliverable
A source-resolved JSON plus one short note and the reusable analysis script. Report:
- N and geometry/lineage, site count versus shortest period, spin0 weights;
- pooled Q,W,Z,A and full delete-one covariance;
- at each size, the covariance-aware A=0 diagnostic on nonredundant coordinates;
- adjacent-size Delta Z and Delta A with correctly propagated covariance; test zero displacement, not a fitted asymptotic exponent;
- measured changes in an explicitly declared norm, with uncertainty. Three sizes cannot establish convergence; distinguish observed finite movement from a limit statement;
- equal-weighting sensitivity without counting it as another experiment.
Nominal Gaussian-reference tests with estimated covariance must be labelled as such. All comparisons are C2 reanalysis: these target blocks have already been seen. No fresh g/PCA basis selected to make residuals smaller, no second exponent, no optional extra sizes, no site/bond/tiny/large pseudo-ladder, no resuscitation of the retired 1.55 factor.
Outcome and stop
Return exactly the conclusions supported by this block: reflection residual resolved/unresolved; adjacent shape change resolved/unresolved; decreasing/increasing/nonmonotone on this finite lineage with uncertainty. If weighting or covariance changes the qualitative reading, say so and stop before a physical claim. A larger-N purchase needs a separate decision identifying which surviving alternatives it distinguishes; this task authorizes no purchase.
This is the continuation channel for #622. Do not open another issue for the same analysis. References #633,#655,#663,#702,#703; #275's original-U candidate-map problem is separate.
Re-scoped 2026-09-12 — one analysis, not another probe portfolio
The previous W1–W5 brief is superseded by merged #702,
notes/exact-foundations-correction-20260912.md§3. Keep the valid location-without-shape constructions and the repaired source data. Do NOT rerun their proofs, repeat tiny censuses, test the invalid raw-p C3 of #666, or claim the two Aff(1) actions fail to intertwine.Decision this task must change
Do the existing square-site, same-observable productions show a resolved departure from reflection-symmetric normalized shape, and does that departure decrease along an actual size lineage? Separately, how much non-affine shape displacement remains between adjacent sizes? This decides whether a further observation is needed and what it must separate; it does not name an exponent or field.
Inputs and resource envelope
Use one ordinary CPU machine with a complete repository checkout; no GPU and no new Monte Carlo. First profile one existing batch to measure runtime. Cap this first delivery at 4 CPU-hours; if the full delete-one path cannot fit, return the measured bottleneck and completed source audit, not a substituted estimator. Machine assignment by the team; do not power on a fleet.
Base: current main including #702; use #703's support policy after it is integrated, or record its exact reviewed head. Read #633/#655 for corrected cos(4theta), per-orientation inversion order and pooled/delete-one semantics. Reuse
scripts/threshold_quantile_lineage.pyfrom the #655 lineage if needed, with its source revision recorded.Primary size lineage: N=145,290,725 from the P50/#612 assets. N725 raw:
results/server-20260907/P612-n725-fullcurve/raw/; N145/N290:results/server-20260829/P50-n145-n290-fullcurve/. Resolve actual filenames from the checkout, do not invent missing paths. If one raw block is unavailable, return which and perform only identifiable comparisons. Additional already-committed lineages are sensitivity, not required for this first delivery.Fixed objects, before examining new scores
Reconstruct each orientation's pooled inverse CDF Q first, then form the declared spin-0 weighted Q. Check weights sum to one and sum(w*cos4)=0. Do not mix CDFs before inversion. Report equal weighting separately, from the SAME block.
Primary grid: nine deciles 0.1,...,0.9. Anchors a=0.2,b=0.8. W_N=Q_N(b)-Q_N(a)>0; Z_N(u)=[Q_N(u)-Q_N(a)]/W_N.
Shape reflection residual:
A_N(u) = Z_N(u)+Z_N(1-u)-1
= [Q_N(u)+Q_N(1-u)-Q_N(a)-Q_N(b)]/W_N.
Do not replace this by M_N(p)+M_N(1-p). The latter is a reflection about raw p=1/2 and conflicts with a location limit centred elsewhere.
Keep pooled estimates primary. For each aligned delete-one batch, repeat the entire Q -> weighting -> W -> Z -> A transformation. Retain the joint covariance. Cross-size independence/coupling follows recorded random-stream provenance, not matching batch IDs.
Symmetry/anchor identities cause deterministic redundancies. Use independent coordinates, e.g. A at u=0.1,0.3,0.4,0.5 (u=.2 is zero; reflected pairs repeat). Do not interpret a noisy covariance rank as a dimension of the mean law, or discard exact contradictory residuals with a pseudoinverse.
Deliverable
A source-resolved JSON plus one short note and the reusable analysis script. Report:
Nominal Gaussian-reference tests with estimated covariance must be labelled as such. All comparisons are C2 reanalysis: these target blocks have already been seen. No fresh g/PCA basis selected to make residuals smaller, no second exponent, no optional extra sizes, no site/bond/tiny/large pseudo-ladder, no resuscitation of the retired 1.55 factor.
Outcome and stop
Return exactly the conclusions supported by this block: reflection residual resolved/unresolved; adjacent shape change resolved/unresolved; decreasing/increasing/nonmonotone on this finite lineage with uncertainty. If weighting or covariance changes the qualitative reading, say so and stop before a physical claim. A larger-N purchase needs a separate decision identifying which surviving alternatives it distinguishes; this task authorizes no purchase.
This is the continuation channel for #622. Do not open another issue for the same analysis. References #633,#655,#663,#702,#703; #275's original-U candidate-map problem is separate.