A slot left free absorbs the data, and the relation cannot fail

[sotashimozono]

Five relations pass for any input, because a value the physics fixes is written as a caller-supplied slot with nothing pinning it. Measured before the fix:

relation	free slot	should be	passed with
WiedemannFranz	L0	π²/3 = 3.2899	3289.87, and −3.29 (negative κ)
RighiLeduc	L0	π²/3	3.29e6
KMSGreaterLesser	ζ	+1 or −1 only	7.3
KeldyshFDT	h	coth(βω/2) in equilibrium	0.017, fully non-equilibrium
SelfEnergyKeldyshFDT	h	the same	the same

WiedemannFranz's docstring claimed the ratio was "checked against the Sommerfeld constant". The kernel is κ - L0*σ*T; π²/3 appears nowhere in it.

The Lorenz number is a constant

L0 now defaults to π²/3, so omitting it tests the law. Supplying it is still allowed (a non-Fermi liquid does have its own Lorenz number), and the docstring now says what a self-derived L0 is worth instead of claiming a check it never made. solve-for-L0 is untouched: extracting that ratio from a measurement is the honest use. MottFormula, which hardcodes π²/3, was the exemplar already in the file.

The statistics sign takes two values

ζ = G^</(e^{−βω} G^>) zeroes the residual for every pair, so the KMS condition could never fail. Refused outside {+1,−1}. The condition still bites at a legal ζ, which is what says the guard did not swap one tautology for another.

The FDT was missing its other half

GK - h*(GR-GA) is not wrong: it is the definition of h and holds out of equilibrium by construction. What was absent is the claim that makes it a theorem. The package already had keldysh_distribution, whose own docstring says it is "the function multiplying the spectral weight in the FDT" — and no relation used it.

	KeldyshFDT	KeldyshDistributionEquilibrium (new)
equilibrium	true	true
non-equilibrium	true	false
wrong statistics declared	n/a	false

SelfEnergyKeldyshFDT shares the same h, so one relation covers both.

Mutation

Against test/relations/test_free_slots.jl (27 assertions):

mutation	assertions failed
remove WiedemannFranz's default (the bug above)	3
RighiLeduc's constant set to 1.0	1
the statistics guard never fires	2
KeldyshDistributionEquilibrium made vacuous	5

Breaking, and what it costs

0.7.17 -> 0.8.0: variables() changes for two relations, and a previously accepted ζ is refused. The three in-tree dependents pin 0.6.x/0.7 and none of them call any of the five.

What I could not establish

Four mechanical sweeps for other instances all failed. The broad one returned 37 with mostly false positives; the tightened one returned 18 of which 14 were false positives and it missed the two confirmed L₀ cases, because the docstrings write the subscript L₀ while the slot is L0. All five were found by reading. There is no basis here for claiming the registry holds no others.

🤖 Generated with Claude Code

[github-actions]

📚 Docs preview: https://qatlashub.github.io/AbstractQAtlas.jl/previews/PR164/

(updates on each push to this PR)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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