[P1][ANALYSIS/COMPUTE] Dyadic norm-4 closure for q=2 versus Jordan S-prime structure

[LightChainr]

当前决定：独立传递实验完成，按冻结规则停该源主解释优先级

0820b8d2冻结后，固定N85=5M、N340=160M新排列已全部完成；旧发现数据没有进入新得分。净U导数为0.04347±0.04363 / 0.06068±0.08266。六坐标共同95%渐近区间为[-0.07164,0.15858] / [-0.15739,0.27875]，两者都在预定±0.50内；四个entry/completion区间也都在±0.30内。

按合同停止把这个lag=1条件簇源列为当前主要H4解释继续优先投入；强entry与强completion两数值预测均排除。双通道弱限制整体相容，不代表物理理论身份、精确零或所有滞后源皆无效。读出分解共用完整源的根/斜率导数，不能改称源的独立因果通道归因。不追加样本、不扫lag、不换source、不加第四个救场模板。

完整结果、独立复核与复算入口。一般norm4/场身份问题仍开放，优先级改P1，已完成实验移出生产队列。下一项P0必须先给出一个具名机制对global U的区分预测；当前只维护STATUS为科学入口。全部历史正文保留如下；Draft交付不合并。

Question

Can a prospectively frozen microscopic source -> ingress/egress -> J_grad -> original global U mapping distinguish the surviving norm-4 mechanism family on an independent target block, instead of generating another retrospective source coordinate from the historical archive?

The target remains the original pooled-root, slope-normalized U; local/source amplitudes are not substitutes for that observable.

Current evidence (SHA + path)

• Frozen norm-4 q2/Jordan production: PR Reveal frozen norm-4 q=2 versus Jordan production score #273 head 8b26a30a785bc142a9d17bfed99a8d0e98ddc4dc. The declared scalar q2 completion is rejected; Jordan survives only as a model family, not a unique identification.
• Generation-4 target: PR Fit minimal Jordan plus one even-mode transfer after norm-4 reveal #277 head 3e855ced4fd98d8979c0b712636b45c2fa54f969, results/server-20260829/P154-norm4-generation4-pilot. Lambda 0, 1/2 and 1 remain similarly compatible; the secondary eigenvalue is not identified.
• Ordinary integrated bulk-energy reconstruction is an exact alias of the existing topology-even coordinate: 54b3e80822fa4c407470cd669912c959b9ea4591. It is not a second independent field direction.
• Fixed-p source response is strong but does not identify global H4 transport: 56a6267d6a6826a165f93ed3a64a670ca7088180, results/p40-even-given-odd/REPORT.md.
• Latest lagged-source discovery: dd48177340f169c18cd1fc9217101b54090e1e3a, results/norm4-lagged-source/REPORT.md. Reused historical permutations show strong prior-step effects on later entry/exit and moving-root rank-one population, while the original global U H4 source response remains unresolved. This is discovery/training, not an independent validation block.
• Historical handoff pointers are frozen in notes/issue-154-handoff-archive.md on cleanup PR maintenance: converge status and archive research entrypoints #528. The current claim boundary is docs/STATUS.md in maintenance: converge status and archive research entrypoints #528; do not prepend more handoff prose here.

Next discriminator

Before producing or reading any fresh target, freeze one machine-readable prediction for the same global U target:

M0 = lifecycle/current-only transmission
M1 = contact-regulated current transmission
M2 = extra transfer coordinate only if frozen before target reveal

The freeze must specify the source/readout semantics, numerical M0/M1(/predeclared M2) U predictions, full covariance/model uncertainty, an equivalence/separation band showing that the chosen budget can distinguish the models, and the failure action. Historical source archives may train the mapping and estimate variance but may not enter the independent target score.

If the candidate mechanisms cannot make distinguishable prospective U predictions before new data, do not launch a fresh block.

Stop rule

If a frozen validation fails, eliminate or demote the failed model. Do not use the same target block to add a source feature, fit a new exponent, redefine the readout or introduce an M2 rescue. A failed transmission test leaves the established C3 finite-size H4 phenomenology intact and ends the current operator-identification attempt for this observable until a genuinely independent design is proposed. Future comments should be delivery pointers (freeze/result SHA/path/status), not new Scientific cards or conjecture sections.

[LightChainr]

One zero-extra-compute secondary score seems worth freezing if the N260/N340 full curves are promoted for the q2/Jordan purpose. The same norm-4 children give a direct root-character closure for the leading thermal H4 mechanism.

Because (1+i)^2=2i, the net microscopic rotation is pi/2, so the H4 angular factor returns to +1. If the root-moving field is the level-4 thermal Q4 / master-g2 sector, the root contrast scales as N^-2, hence

DeltaRoot(4N)/DeltaRoot(N) = 4^-2 = +1/16.

Equivalently this is the exact two-step composition (-1/4)^2=+1/16 of the norm-2 root character. It contains no fitted amplitude or pc, and the N260/N340 children are noncyclic, so it is also a useful arithmetic/topology-class check of the Gaussian character picture.

I would keep it strictly secondary and jointly covariance-scored from the same histograms (not independent evidence from the q2/Jordan rows), and not let it delay #57. But if the norm-4 run happens, omitting this root readout would discard a very high-specificity free check.

[LightChainr]

Post-P57/N290 priority update: reinterpret norm 4 as the even-generator phase-node test

Issue #200 / PR #202 sharpens the role of this experiment after the norm-5 and N145->290 reveals.

The key new fact is not merely that N260/N340 give equal log-scale spacing. The net multiplier is

(1+i)^2 = 2i,
chi4(2i)=+1,
sin(4 arg(2i))=0.

The P57 higher-jet diagnostic leaves a coherent Gaussian-conjugation-odd tendency, while the pre-reveal N290 phase-node artifact predicts that a simple sine-H4 quadrature vanishes on 1±i. Therefore norm 4 should be treated as the first prospective isolation of the conjugation-even radial generator:

1. execute/score the already-frozen N290 phase node first;
2. run only a small N260/N340 variance pilot;
3. freeze complete source+target covariance;
4. score the existing q=2 completion before Jordan;
5. score one source-frozen full-jet even-generator vector, not separate rank corrections;
6. use DeltaRoot(4N)/DeltaRoot(N)=+1/16 only as a correlated secondary character check.

The completion means remain exactly those already recorded here and are now also machine-frozen in predictions/norm4_two_generator_transfer_20260829.yaml on PR #202.

If both one-even-generator closures fail prospectively, do not add q=3/q=4/etc. scalars here; promote the smallest source-stable matrix transfer under #180. If one survives, norm 10 becomes scientifically interesting as a nonzero phase/quadrature closure rather than just a larger child.

[LightChainr]

Variance/power gate is now published in PR #204: #204

Key result: target-only scaling was misleading. With the existing 100M common-random-number source block, even 2B per target is capped at expected sqrt noncentralities 2.019 (q2 null if Jordan true) and 1.567 (Jordan null if q2 true). Propagating the full 4x4 source covariance shows that the lowest-CPU tested approximately three-sigma allocation is 2B total per source size and 1B per target: projected 3.155 and 3.025, respectively, at 260111 incremental CPU-seconds.

The 1M/10M N260/N340 pilot histograms, metadata, checksums, dedicated stable-center variance analyzer, and frozen execution manifest are committed. Pilot target means were not used to choose the allocation.

Production is now running on Huawei DevEnv f415a4bcbd9a438b85f5f29e4a507ea4 at commit bfab033: first wave N260/N340 1B (8+8 cores), followed by the aligned 1.9B source extensions. This also retains the independent noncyclic T4=T2^2 / conjugation-even phase-node objective frozen in PR #202.

[LightChainr]

Pre-reveal scoring is now frozen on PR #204 before either 1B target completed.

• scripts/score_norm4_production.py: primary two-lineage scalar score in fixed order q2 then Jordan, with full 4x4 source CRN covariance plus independent target covariance; central-D and +1/16 root character are explicitly correlated secondary views.
• scripts/score_norm4_thermal_jet.py: one common cocycle multiplier acts jointly on the width-corrected finite-N Hermite-Krawtchouk vector r=2..6 (c=3/2 q2 before c=2 Jordan). There are no rank-specific fitted amplitudes; numerical covariance null modes are removed by the already-used generalized covariance score.

CI is green on Python 3.9/3.11/3.13 and C++17. Huawei production remains on the frozen generation commit bfab033; later scorer commits do not alter the running RNG block.