LedgerToGeometryBridgeStatus
plain-language theorem explainer
A two-flag status record for the ledger-to-geometry bridge: whether the deficit map is assumed rather than derived, and whether the conformal edge ansatz fails for gravitational waves. Gravity and continuum-limit workers cite it to keep those honesty constraints machine-visible. It is a plain structure definition with no proof content.
Claim. A status record consisting of two Boolean flags: (i) the ledger-to-hinge bridge condition is an explicit assumption, not a consequence of the recognition-ledger axioms; (ii) the conformal edge ansatz cannot realize the transverse-traceless gravitational-wave sector.
background
The module states the honest link between the discrete recognition ledger and the effective geometric (hinge) description. Ledger deficits are the discrete cost imbalances on the recognition substrate; hinge deficits are their continuum geometric counterparts. The bridge packages a map $x_\sigma$ and a deficit-matching condition as assumed fields, not theorems from the ledger axioms.
Separately, the conformal edge ansatz tries to realize continuum modes by a vertex-conformal potential. Upstream work in the tensor shear sector shows a rectangle/shear obstruction: a nontrivial rectangle shear mode ($h \neq v$) has no such realization. Gravitational waves need transverse-traceless shear degrees of freedom, so that conformal route cannot recover them.
The structure only records those two facts as named Boolean fields for downstream status objects.
proof idea
No proof: this is a structure definition. It declares two Boolean fields with doc-comments fixing their meaning (bridge assumed not derived; conformal route insufficient for GW). Inhabitation and the concrete true/true assignment live in the sibling canonical status definition.
why it matters
In Recognition Science the continuum geometric layer must not silently pretend to follow from the discrete ledger. This status type is the typed carrier for that honesty: the bridge remains an explicit assumption, and the conformal route is flagged as blocked for the TT sector by the shear obstruction.
The sole immediate consumer is the canonical status value, which sets both flags true and feeds the status-flags theorem asserting that assignment. Anyone auditing gravity emergence, hinge geometry, or wave-sector recovery should read these flags before treating ledger-to-metric maps as derived. The record does not close the open derivation of the bridge; it makes the gap and the conformal failure unmissable in the dependency graph.
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