Run every route to a target, not the first one the registry reaches

[sotashimozono]

Stacked on #162, which is stacked on #161. Merge order: #161, #162, then this.

derive forward-chains and takes the first relation that produces the target. Measured on the current registry:

door	outputs	with MORE THAN ONE producing relation	worst
symbol	219	66	19 routes (:β)
typed	84	38	15 routes (InverseTemperature)

Which one runs is iteration order. If two disagree the caller is handed a number and told nothing.

derivation_routes returns them all; derive_crosschecked refuses when they disagree.

The hazard is the vacuous agreement, and it has two levels

Both are guarded, and each guard is pinned by a mutation that removes it.

1. A supplied target lets the closure manufacture its own inputs. With only c and ncuts supplied, the closure builds dS_dlogℓ, dS_dlogchord and ΔS from c, and three routes hand the supplied number back:

CFTEntanglementChordSlope:    {dS_dlogchord, ncuts} → 0.9
CFTEntanglementSlope:         {dS_dlogℓ, ncuts}     → 0.9
HalvedChainEntropyDifference: {ΔS, ncuts}           → 0.9

So the target is held out before the closure runs, as a given, and (β and T being one quantity under two names) so is its alias.

2. A derived target does the same thing one level down. Given a real dS_dlogℓ, the chain derives c, rebuilds the chord slope from it, and reads c back off that:

derivation_routes(:c; dS_dlogℓ, ncuts)	rows	values
as written	1	0.5
without avoid	3	0.5, 0.5, 0.5

Three rows, one measurement, perfect agreement. The chains therefore take avoid and never produce the target at all.

min_routes is how to ask that a cross-check actually happened. The default accepts data affording no independent route, which returns a number this verb's name would otherwise claim it had checked.

What it catches

Typed door, F reachable both through Z and through the Legendre transform, entropy broken by 0.5:

	result
derive(FreeEnergy, bad)	-1.3733, the right number off the other route
derive_crosschecked(FreeEnergy, bad)	refused, spread 0.3128, both routes named

derive returning the correct value from good data while silently ignoring an input that contradicts it is the case this exists for.

Mutation

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

mutation	assertions failed
drop the symbol-door holdout	2
drop the typed-door holdout	2
drop the β/T alias holdout	1
symbol chain ignores avoid	3
never refuse a disagreement	4
min_routes never fires	1

The first pass of this test file let two of these through. The typed assertions passed for reasons unrelated to what they claimed, and were rewritten against fixtures that can fail: FreeEnergyLegendre produces both F and S, and KelvinRelation produces T from a Peltier coefficient that β can build.

The two deleted lines in src/ are the signatures of _forward_chain and _typed_chain!, both private, widened with a defaulted keyword. No public API removed or changed, so 0.7.16 -> 0.7.17.

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[github-actions]

📚 Docs preview: https://qatlashub.github.io/AbstractQAtlas.jl/previews/PR163/

(updates on each push to this PR)

[codecov]

Codecov Report

❌ Patch coverage is 99.33333% with 1 line in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/derivative_routes.jl	97.29%	1 Missing ⚠️

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