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HODGE TRANSPORT CLOSURE · 2026-08-19

The previously open canonicalization obligation now has a corrected finite witness in REVISED E47 MULTI-BRANCH FORMALISM: the originally pasted simplicial data failed $\partial_1\partial_2=0$ because edge (0,2) was absent; after repairing the edge set, $\partial_1\partial_2=0$, $\beta_1=1$, and $T_\epsilon=P_{47}W_\epsilon\Psi_H$ lands in $E_{47}$ at machine precision. The E47 projector dependency follows the current generator 10667959 and controlled release da5501b. This closes the finite repaired bridge only; it does not retroactively validate the malformed original complex or imply a physical transport realization.

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TRANSIT CREDENTIAL · H-03 · FOUNDING COHORT

Route: Foundations → Harmonic Construction → Python Subway → Verification Hall

Current evidence: named executable identity; certification scoped to the explicit generator and transport law in source

Standing: Enrolled with open canonicalization obligation.

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Canonical designation

$\boxed{\mathcal T_{\mathrm{harm}}:\Sigma\longrightarrow E_{47}}$

A transport operation carrying states or observables from the full carrier into the protected spectral sector under a specified harmonic generator.

Origin family

• Canonical Harmonic Transport
• Master validation-engine documents
• E47 spectral-kernel formalism

Required exact record

Citizenship preserves the identity while leaving these fields visibly open until extracted from the source:

• generator;
• domain and codomain;
• boundary conditions;
• conservation or dissipation law;
• intertwining relation with $P_{47}$;
• numerical tolerance and reconstruction residual.

Non-collapse rule

$\mathcal T_{\mathrm{harm}}$ is not another name for $P_{47}$. A projector selects; a transport operator moves according to a law.