IndisputableMonolith.Gravity.LedgerToGeometryBridge
Bridge package from a recognition ledger on substrate Λ to geometric hinge deficits on a hinge type H. The comparison map x_σ sends each substrate cell to a hinge; bridge_assumed equates ledger and geometric deficits by explicit hypothesis, not from ledger axioms. Gravity workers on the discrete-to-geometry step cite this interface. The module defines the assumption and status flags rather than deriving the equality.
claimA ledger-to-geometry bridge is a substrate-to-hinge map $x_\sigma:\Lambda\to H$ together with the explicit assumption that the recognition-ledger deficit at each cell equals the geometric hinge deficit at the image hinge. Ledger axioms alone (symmetry, diagonal zero, non-negativity, RCL subadditivity) do not force that identification.
background
The recognition ledger is the central bookkeeping object of recognition gravity. Its continuum limit is used as gravitational action; the ledger axioms encode symmetry, vanishing on the diagonal, non-negativity, and RCL subadditivity of the cost.
Upstream, the tensor/shear sector records that the Track 1.B conformal ansatz assigns one scalar potential per vertex and induces edge lengths by averaging endpoints. That scalar slice cannot represent pure shear, so it cannot cover transverse-traceless gravitational-wave modes by itself.
This module sits between those layers. It names the discrete-to-geometry comparison needed if ledger deficits are to be read as geometric hinge deficits, and it tags the equality as assumed because the ledger axioms do not determine any particular geometric identification.
proof idea
Definition and status module, not a derivation. It introduces the bridge structure with the substrate-to-hinge comparison map and the explicit bridge-equality hypothesis; records that the conformal ansatz cannot recover gravitational-wave modes; and exposes status flags summarizing assumed versus derived content. No proof that ledger axioms force the geometric identification is attempted.
why it matters in Recognition Science
Downstream, SevenGaps.LedgerBridgeNoGo imports this module and proves obstruction theorems against the assumed substrate-to-triangulation bridge that equates ledger deficit at each cell with raw geometric hinge deficit. The present interface is exactly what that no-go attacks.
In the Recognition gravity stack this is the load-bearing discrete-to-geometry step: until the bridge is settled, ledger costs cannot be identified with curvature-like hinge deficits. It also borders the tensor/shear gap (Track 1.D) on incomplete weak-field coverage. The module therefore pins the hypothesis that Lane 1a of the Seven Gaps program either discharges or rules out.
scope and limits
- Does not derive the bridge equality from recognition-ledger axioms.
- Does not construct a continuum metric or Einstein equation from the ledger.
- Does not claim the conformal ansatz covers transverse-traceless GW modes.
- Does not discharge the Seven Gaps Lane 1a obstruction theorems.