IndisputableMonolith.Gravity.LedgerToGeometryBridge
Packages the ledger-to-geometry bridge: a recognition ledger on substrate Λ, a hinge type, a cell-to-hinge comparison map, and an explicit assumption equating ledger deficits with geometric hinge deficits. Gravity workers on the discrete-to-continuum step cite it as the named load-bearing assumption. Also records that a pure conformal ansatz cannot recover TT gravitational-wave modes, and exposes status flags. Definitional packaging, not a derivation from ledger axioms.
claimA ledger-to-geometry bridge pairs a recognition ledger on substrate $\Lambda$ with geometric hinge deficits on a hinge type $H$ via a comparison map $x_\sigma$ from substrate cells to hinges, together with an explicit assumption that the ledger deficit at each cell equals the geometric deficit of the matched hinge. Separately, a pure conformal (scalar-potential) ansatz cannot recover transverse-traceless gravitational-wave modes.
background
The recognition ledger is the central bookkeeping object of recognition gravity. Upstream it is used for the gravitational action (continuum limit of total ledger cost) and related structural roles. Its native axioms include symmetry, diagonal zero, non-negativity, and RCL subadditivity; those axioms alone do not force any particular identification with geometric hinge deficits.
The tensor/shear sector scaffold records a complementary gap: the Track 1.B conformal ansatz assigns one scalar potential per vertex and induces edge-length changes by averaging endpoint potentials. That scalar slice cannot represent pure shear, so it cannot cover transverse-traceless gravitational-wave modes by itself.
This module sits between those ingredients. It names the substrate-to-hinge comparison map and packages the ledger-equals-geometry equality as an explicit assumption field, rather than a theorem, so later obstruction and continuum arguments can target a precise interface.
proof idea
Definition and status module, not a deep proof chain. It introduces the bridge structure with the comparison map and the named bridge_assumed equality (ledger deficit equals matched hinge deficit), states the conformal-ansatz limitation against gravitational-wave recovery, and exposes status flags summarizing what is assumed versus derived. Load-bearing obstruction theorems live downstream; here the work is interface packaging and gap bookkeeping.
why it matters in Recognition Science
Feeds the Seven Gaps Lane 1a module on the ledger-to-hinge bridge no-go, which proves obstruction theorems against the assumed form of the substrate-to-triangulation bridge (equating recognition-ledger deficit at each cell with a raw geometric hinge deficit). Making bridge_assumed an explicit field, not a silent identification, is what lets that no-go be stated cleanly.
The conformal/shear flag ties the bridge story to the incomplete weak-field sector: scalar potentials alone miss pure shear and TT modes, so any continuum geometry recovered from the ledger must eventually outgrow the conformal ansatz. In the broader Recognition gravity program this is the discrete-to-geometry interface sitting under the continuum limit of ledger cost as gravitational action.
scope and limits
- Does not derive the ledger-equals-hinge equality from ledger axioms.
- Does not prove existence of any comparison map satisfying the bridge assumption.
- Does not construct a full weak-field metric with shear or TT modes.
- Does not discharge the Seven Gaps bridge obstruction theorems.
- Does not compute continuum Einstein or wave equations from the ledger.