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N580: seven exclusions survive rung-specific bounded H8; correct P3 inference claims #704

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63 changes: 63 additions & 0 deletions docs/manuscripts/p3-projective-inference/CORRECTIONS-20260912.md
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# P3 correction addendum — 2026-09-12

The historical manuscript/tables are retained, but are NOT submission-ready.
This addendum supersedes the incompatible claims listed below; it is not a
claim that the entire manuscript has been rewritten or externally reviewed.

1. **Signed line versus ray.** The existing a in R model is a signed line.
A cone or a bounded nuisance image has different inference geometry. A general
one-parameter family of directions need not be a linear subspace.

2. **Singular covariance.** A pseudoinverse alone is not a test. In exact-support
mode enforce U0^T(y-Va)=0, then use df=rank(S)-rank(W V Z), with Z the null
basis of the deterministic amplitude constraints. Empirical low rank does not
establish deterministic constraints. #703 now validates PSD and refuses an
undeclared singular/truncated policy. Saturated df=0 models have exact residual
zero after numerical consistency checking; roundoff is not a rejection.

3. **Fieller equivalence.** On the same two coordinates the GLS line statistic
is Fieller's contrast squared. The three-rung gain is from additional data and
changed nuisance assumptions, not from defeating correct Fieller inference or
recovering information destroyed by the ratio parameterization itself.
A shared random stream is not required for a joint covariance: independent
runs have zero cross-covariance when independence is justified; coupled runs
require the actual covariance. Use source provenance, not matching batch IDs.

4. **Recovered covariance.** #703 recovered cov(r2,r4)=5.5621485097801135e-9
from existing shards. Bare aspect is no longer 'undetermined because covariance
is missing': the retrospective pure-line score is D=10.8644599/2,
p=.00437333, equivalent 2.84990 sigma, NOT rejected at the nominal 3-sigma
cutoff. The original frozen two-rung underpowered verdict is unchanged.
No new replay is needed for this entry.

5. **Curvature and sign.** Raw curvature z=-3.11062 is a one-coordinate contrast,
not the two-df model test. The sign of a convex v is reversed by negative a;
'negative curvature excludes every signed convex-shape model' is invalid.
An annihilator removes an algebraic nuisance; it does not guarantee adequate
power or immunity from covariance uncertainty.

6. **Common bound versus common ratio.** |rho_i|<=B for every rung does not
imply rho_1=rho_2=rho_4. Common-ratio results are labelled sensitivities.
The new rungwise bounded analysis in notes/n580-rungwise-leakage-20260912.md
removes that equality assumption. Even at B=1 seven of eight candidate images
miss a common nominal 99.73% three-dimensional mean ellipsoid. Do not assign
an ordinary chi-square law with guessed residual df to the bounded cones.

7. **Novelty and literature.** The linear algebra is classical. Do not claim
ratio testing is ubiquitous, or that no multivariate Fieller analogue exists,
from an unverified gap. Use #701/#695's retrieved sources only at their actual
PRIMARY_TEXT_READ/ABSTRACT_ONLY level. Frame the contribution around this
worked observation/design failure and its corrected inference, not a newly
invented general statistical theory.

8. **Design.** N650 does not cleanly identify angular H8 because angle and
Smith class move together (#589). Three rows cannot identify four unconstrained
columns (constant, H4, H8, Smith nuisance). Also, two unanchored model cones
both contain zero: their minimum pairwise distance is zero. A maximin sample
allocation needs a justified nonzero signal range, a fixed-SNR criterion, or
a source-anchored design objective. Do not hide this by assuming a strong
amplitude or calling an arbitrary normalization physical.

All recovered and new bounded scores are same-block C2 analyses with estimated
covariance. They do not increase the count of independent experiments, identify
a continuum field, prove a threshold law, or turn this draft into a submission.
126 changes: 50 additions & 76 deletions docs/manuscripts/p3-projective-inference/README.md
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# P3 — Test the ray, not the ratio

Draft manuscript workspace for portfolio track **P3**, arising from
[issue #579](https://github.com/LightChainr/Matching-One/issues/579).

**Target venue:** *Physical Review E*.

| File | Role |
|---|---|
| [`manuscript.md`](manuscript.md) | the draft, sections 1–8 |
| [`tables.md`](tables.md) | **generated** — every numerical table (T1–T5) |
| `results/p3-projective-inference-manuscript/latest.json` | the machine-readable evidence artifact |
| `results/aspect-ladder-n580/latest.json` | the frozen Fieller scoring (§4.1, §4.3) |
| `results/aspect-ladder-n580-projective/latest.json` | the projective rescoring (§4.4–§4.6) |
| `predictions/aspect_ladder_n580_20260905.yaml` | the frozen design, competitor rays, declared systematic |
| `scripts/projective_inference.py` | the statistic: pseudo-inverse, subspace residual, χ² tail |
| `scripts/aspect_ladder_projective_rescore.py` | the N=580 rescoring |
| `scripts/p3_manuscript_evidence_table.py` | assembles the artifact and renders the tables |
| `tests/test_projective_inference.py` | 8 tests, including the Fieller identity anchor |
| `tests/test_aspect_ladder_projective_rescore.py` | 11 tests on the rescoring |
| `tests/test_p3_manuscript_evidence_table.py` | 11 tests locking the assembly and the tables |
| `notes/aspect-ladder-n580-projective-rescore-20260906.md` | the working note the draft is built from |

## Ground rules honoured here

No Monte Carlo was run for this manuscript and no frozen design was reopened. `p3_manuscript_evidence_table.py`
reads three committed artifacts and derives only statements that follow exactly from them; it rescores nothing
that was not already rescored and committed under #579. The one computation it performs that is not a lookup is
the two-entry control of §4.3 — the projective statistic restricted to the pair of rungs the frozen test used —
and that exists to *remove* a possible explanation for the paper's headline, not to supply one.

No number in the draft is hand-typed into a generated table. `tables.md` is rendered from the artifact and
`test_the_rendered_tables_do_not_drift_from_the_artifact` fails if the two separate. The summary tables inside
`manuscript.md` §4.4–§4.6 restate T3–T5 for readability; the generated tables are authoritative.

## Section readiness

| § | Content | Status |
|---|---|---|
| Abstract | claim and scope | draft complete |
| 1 | the problem: proportions, ratios, conditioning, the design pathology | complete |
| 2.1–2.4 | ray, subspace, residual distance, Fieller as the 2×1 case | complete, proposition proved and tested |
| 2.5 | annihilating functionals | complete |
| 3 | why the ratio framework fails invisibly | complete |
| 4.1–4.2 | the measurement and the eight rays | complete, generated |
| 4.3 | two-entry control | complete, generated, `1.5e-15` |
| 4.4 | verdict table | complete, generated |
| 4.5 | curvature | complete, generated |
| 4.6 | the priced assumption | complete, generated |
| 5 | established / undetermined / not established | complete |
| 6 | the N=650 design consequence | complete; see [#583](https://github.com/LightChainr/Matching-One/issues/583) |
| 7 | reproducibility and preconditions | complete |
| 8 | related work | **one open item**: reference [6] is marked **[LIT]** and needs a primary reading |

## One correction already applied to this draft

The `|A₈/A₄|` column of §4.6 first shipped as the raw gap divided by the leakage coefficient, which is the
leading-order form and drops the `(u + 1)` the exact solution carries. It overstated the requirement by 2.4× for
the bare aspect ratio and by 45× for the weight-12 rays, where it read 783 instead of 17.5. The frozen design
records the leakage *per rung with its sign*, which is what makes the exact solve available at all; the fix is in
`required_spin8_ratio`, and `test_every_survivor_of_the_clean_pair_needs_a_large_spin8` now pins the top of the
column below 20 so the leading-order form cannot come back silently. The dichotomy is unchanged.

## Open items before submission

1. **Reference [6].** The claim that ratio-testing of aspect-ratio amplitudes is standard practice in the
conformal-invariance finite-size literature is stated from familiarity, not from a primary reading. Either
read and cite specific instances, or weaken §8 to a statement about this repository's own practice. This is
the only unresolved item in the draft and it is deliberately marked rather than quietly asserted.
2. **§5.2's undetermined verdict.** One deterministic replay of the N=580 ladder under the current scorer
recovers `cov(r2, r4)` and settles `bare_aspect_ratio`. The draft is publishable without it — an undetermined
verdict, reported as undetermined, is a legitimate result — but the replay is cheap and would remove the one
soft spot.
3. **Figure.** The draft is currently table-only. One figure would carry §4.4–§4.5 well: the three-rung response
with its jackknife errors, the eight competitor rays normalised through the `r=1` point, and the measured
concavity as a shaded band. Not required for the argument.
# P3 — Covariance-aware comparison of finite-size amplitude laws

**Current status (2026-09-12): numerical corrections available; manuscript NOT
submission-ready.** Read [CORRECTIONS-20260912.md](CORRECTIONS-20260912.md)
before using the historical manuscript. Target venue remains a proposal, not
an acceptance/readiness claim. Track: #579.

## Current result

#703 recovered the complete N580 covariance from the existing delete-one shards,
without simulation. The retrospective three-rung pure-line score for bare aspect
is 10.8644599 on 2 df, nominal p=.00437333: not rejected at the declared nominal
3-sigma threshold. Seven other pure lines are rejected under that contract.
The original frozen two-rung underpowered result remains unchanged.

A second completed analysis allows independently varying rung-specific H8/H4
ratios. At a uniform bound B=1, the same seven candidate images remain outside
one nominal 99.73% three-dimensional mean ellipsoid; bare aspect intersects.
This is not a fitted-cone chi-square calibration, a measurement of H8, or a new
independent evidence block.

## Files to use

- `notes/n580-complete-covariance-20260912.md` and
`results/research-control-20260912/n580-complete-covariance-summary.json`:
executed covariance recovery and pure-line results.
- `notes/n580-rungwise-leakage-20260912.md` and
`results/research-control-20260912/n580-rungwise-leakage-summary.json`:
independently bounded leakage, projection proof, results and limits.
- `scripts/projective_inference.py`: explicit covariance-support policy;
`scripts/recover_n580_covariance.py`: existing-shard reader;
`scripts/n580_rungwise_leakage.py`: bounded-image calculation.
- `manuscript.md`, `tables.md`, and the original manuscript-evidence JSON:
HISTORICAL draft/evidence assembly, retained rather than silently overwritten.
Their readiness, missing-covariance, common-ratio and sign claims require the
corrections in the addendum. The old assembler does not generate the new tables.
- `predictions/aspect_ladder_n580_20260905.yaml` and
`results/aspect-ladder-n580/`: original freeze/results; do not rewrite history.

## Remaining writing work, not more N580 production

Integrate the addendum into the manuscript and a new versioned table assembly.
Separate the frozen two-rung analysis, retrospective pure-line comparison and
rungwise bounded sensitivity. Replace unsupported literature-practice/novelty
claims with the narrow sourced account. The existing #695/#701 retrieval is
input, not proof that all citations were read in full. N650 remains subject to
#589's angular/Smith identifiability question.

No replay is needed for cov(r2,r4). No new size, free exponent or optional
sample top-up follows from this draft.
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# N580: seven exclusions survive independently varying bounded H8 leakage

2026-09-12. Direct analysis following #703; same-block retrospective C2, not
new sampling, not a revised freeze, and not a continuum identification.

## Question and answer

A uniform bound on |A8/A4| does not imply the SAME ratio on different moduli.
The common-ratio sensitivity in #703 and the older point-reconciliation column
therefore leave a genuine question: do the exclusions survive rung-specific
ratios? Yes, for B=0.2 and even B=1, against the explicit simultaneous mean
region below. Bare aspect remains compatible, already at B=0.

The input is #703's recovered mean and full covariance, as committed at
b924b2af94ebb99a058e252df6884594c51da381. Local computation used the published
vector/matrix/rays, not a new local shard replay. All eight B=0 distances
reproduce that artifact. The script reads the committed input directly in a
complete checkout. Historical production data, scores and freezes are unchanged.

## Model: weaken the unnecessary assumption, not the observation definition

For each existing positive shape v, let

mu_i = a v_i (1 + lambda_i rho_i), |rho_i| <= B,
lambda = (1148/21025) * (-1,+1,-1), a in R.

The three rho_i may differ. A4 still obeys the nominated shape a*v; the only
allowed additional angular contribution here is the declared H8 leakage.
For 0 <= B < 21025/1148, the amplitude sign is preserved at every rung.
For a>=0, the model image is the cone over the eight vertices
v_i*(1+lambda_i*B*t_i), t_i in {-1,+1}; a<=0 gives its negative. An arbitrary
convex combination of vertices gives exactly all independently bounded rho_i.
Thus both amplitude signs are covered, without treating a signed line as a
positive ray. Opposite leakage signs do not reduce this larger set: independent
symmetric bounds absorb each sign. Equality of the ratios would be extra physics.

The nearest point on either cone can be represented with at most three
linearly independent generating rays in R^3: a conic representation with more
than three can be reduced along a linear dependence until a coefficient is
zero. At the optimum, the positive coefficients satisfy the least-squares
normal equations on their active span. Enumerating supports of sizes 1,2,3
and the origin therefore includes the global optimum. Both sign cones are
solved, not just whichever sign looks favourable in the observed data.

The independent numerical optimality check re-solves each selected support at
60 dps and verifies q=S^-1(y-mu), g_j^T q<=0 on ALL eight rays, and mu^T q=0,
for both signs. These are sufficient convex projection conditions. This is a
high-precision numerical check, not an exact rational certificate.

## A reference region, not an invented cone chi-square law

Use one three-dimensional Gaussian mean ellipsoid

E(y) = {mu: (y-mu)^T S^-1 (y-mu) <= 14.156413609126687}.

Its nominal tail alpha is erfc(3/sqrt(2))=0.002699796063260189. The cutoff is
chi-square with 3 df because this is the full MEAN confidence region, not the
residual df of a fitted cone. With known Gaussian covariance it has the stated
coverage. With this estimated jackknife covariance it is nominal/asymptotic;
no exact finite-sample coverage is asserted.

The simultaneous statement needs no guessed cone reference distribution:
on the event that E contains the true mean, every model image containing that
mean intersects E. Hence declaring any image disjoint from this SAME region
cannot falsely exclude a true image on that event. This applies simultaneously
to all eight models and nested bounds. It is conservative relative to an
individual 2-df line test, and is not its replacement or a change to the freeze.

## Executed result

| Shape | min D at B=0 | min D at B=1 | first B intersecting E |
|---|---:|---:|---:|
| bare aspect | 10.86446 | 5.72524 | 0 |
| no modulus dependence | 89.85851 | 73.37075 | 6.55584 |
| area scaling | 57.51249 | 50.29088 | 5.71612 |
| Q4 weight-4 shape | 55.58771 | 48.31480 | 5.49417 |
| weight-12 E12 | 132.26732 | 131.64755 | 17.33571 |
| weight-12 E4 cubed | 132.22612 | 131.60161 | 17.30638 |
| weight-12 delta | 513.65922 | 511.91617 | 18.31398 |
| weight-8 E8 | 115.80438 | 113.36508 | 14.29176 |

The artifact also reports B=0.2. Seven images remain disjoint even at B=1.
In particular, under the stated shape-plus-H8 model a Q4 explanation needs
at least one |rho_i| of about 5.49 before it can reach this nominal region;
area scaling needs about 5.72. This is not a measurement of H8, does not
exclude other angular terms or observer errors, and does not refute the Q4
module as a possible contributor to a different observable.

Do not confuse these uncertainty-aware intersection bounds with fitting the
observed point exactly. For positive z_i=y_i/v_i and common |lambda_i|=lambda,
point interpolation first occurs at

B_point = (max z - min z)/(lambda*(max z + min z)).

This follows by choosing a=(max z+min z)/2 and equalizing the two extreme
relative residuals. Bare aspect has B_point=4.30327, yet B=0 already intersects
E: the point estimate's mismatch is not a rejection at this coverage level.
The earlier common-ratio point requirement must not be promoted into a lower
confidence bound on contamination.

## Validation and reproduction

Three inexpensive mathematical controls passed: an identity-covariance toy
with exact projection (42/11,14/11,14/11) and D=2/11; B=0 versus GLS; sign
reversal and nesting. All 24 fixed-bound fits and both endpoints of each
positive B threshold were checked at 60 dps on both cones. Fixed-bound maximum
relative KKT/complementarity residuals were 1.76e-61 and 5.10e-61. Threshold
brackets are numerical 38-step bisections, not exact intervals.

python scripts/n580_rungwise_leakage.py --summary --source-revision b924b2af94ebb99a058e252df6884594c51da381
python -m unittest discover -s tests -p 'test_n580_rungwise_leakage.py'

Omit --summary for fitted means, nuisance witnesses and branch distances.
--output refuses to overwrite an existing file. NumPy/mpmath are sufficient.
The compact generated result is
results/research-control-20260912/n580-rungwise-leakage-summary.json.

## Decision

No new N580 sampling or covariance replay is justified by this question.
The seven exclusions are not merely a common-ratio artefact. Bare aspect is
not established; it remains a surviving finite model at the declared evidence
resolution. Further angular acquisition belongs to #589's identifiability
question, not an attempt to push this same block across a preferred cutoff.
The independent next analyses remain #622's within-model shape motion and
#681's restricted finite-torus/cylinder dictionary. Neither needs a GPU.
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