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d6g8k5htny-coder merged 2 commits into from
Oct 8, 2026
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Actual finite Gaussian H0 elder-bar lifetime intensity #326

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c69cc72
Prove actual finite Gaussian H0 elder-bar lifetime intensity
d6g8k5htny-coder Oct 8, 2026
bf9793a
Reconcile H0 proof source with current required graph evidence base
d6g8k5htny-coder Oct 8, 2026
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32 changes: 28 additions & 4 deletions experiments/universality/README.md
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Expand Up @@ -57,10 +57,34 @@ or gap, and do not support an unrestricted covariance floor. Its
[review](finite_contact_genericity/REVIEW.md) records the exact argument and
classical Sard import. Finite-r additional conditioning is a separate contract.

Actual bar selection, counting with that selection, global once-counting and
complement control, further conditional ranks, critical formal alignment and
numerical coupling remain admission obligations. The sampler and catalogue
admissibility labels retain their original meaning.
The [elder-transfer proof](finite_elder_transfer/PROOF.md) now supplies the
local-to-global topological step for the actual pinned field. Under its isolated
cubic contact limit, the nearby maximum component is enclosed above the saddle
and the saddle connects it to an older component. Compactness and the global
critical-point gaps exclude a bypass. Canonical Gaussian coupling and polynomial
domination make this the actual elder pair with determinant-weighted probability
tending to one, uniformly over compact birth/gap marks for the fixed law. Its
[review](finite_elder_transfer/REVIEW.md) records the bounded classical imports,
exact source chain and review exposure.

The [finite H0 lifetime theorem](finite_h0_lifetime/PROOF.md) constructs a Borel
selector and counts every actual finite superlevel H0 bar exactly once. For each
fixed positive full-square ideal Gaussian law at cutoff at least 2, it proves a
finite nonnegative Borel density with leading law `C_loc * ell^(-1/3)` for its
specified canonical representative, and the intrinsic cumulative law
`(3/2) * C_loc * t^(2/3)`. The coefficient equals the candidate local jet
functional. The essential global-maximum class is excluded. The selected density
is not asserted continuous; missed near pairs contribute only `o(ell^(-1/3))`,
while the far contribution is bounded. Its
[review](finite_h0_lifetime/REVIEW.md) binds the measurable once-counting argument,
all-mark limit and precise finite Gaussian scope.

These conventional analytic results discharge selected-bar counting and the
leading near/far intensity composition for those ideal Gaussian laws. Further
conditional ranks, literal critical formal alignment, certified sampler and
numerical/count coupling, genuinely blind law-by-law admission, higher homology
and marked point-process convergence remain separate obligations. The sampler
and catalogue admissibility labels retain their original meaning.

`models.py` defines the implemented finite-cutoff normalized sampler. Only
cutoffs 2 and 3 are supported: at cutoff 1, Gaussian and separable spectra
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