Pith. sign in
theorem

physicalReggeEHConcreteSingleSliceProductFilterOneStatementProjectionCount_eq_two

proved
show as:
module
IndisputableMonolith.Gravity.Track1BCPhysicalResidual
domain
Gravity
line
811 · github
papers citing
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plain-language theorem explainer

The session-556 audit tally of single-slice product-filter one-statement projections equals two: one slice target and one product target. Gravity auditors cite it as a fixed bookkeeping check inside the Track 1.B-PHY residual package. The proof is pure reflexivity against the defining numeral.

Claim. The audit count of single-slice product-filter one-statement projections (slice target and product target) equals $2$.

background

Track 1.B-PHY packages physical finite-probe Regge-to-Einstein-Hilbert residual theorems beyond the flat-substrate witness. Normalized full nonlinear Regge finite aggregates are shown to converge to the canonical finite EH/Dirichlet action, with residual tending to zero once edge-stencil local correspondence holds; the same correspondence feeds a finite-to-continuum bridge under a Riemann-sum identification.

The quantity equated here is a pure audit counter: it records how many one-statement projections sit in the concrete single-slice product-filter layer (the slice target and the product target). It is defined as the natural number two and carries no dynamical content of its own.

proof idea

One-line term proof by rfl. The left-hand side is definitionally the numeral 2, so equality is immediate by reduction.

why it matters

Inside the Track 1.B-PHY residual upgrade, this locks the session-556 projection inventory at two items so later residual and continuum-bridge statements can treat the filter layer as a fixed, enumerated pair. It does not itself advance the open manifold integral target (PhysicalReggeEHManifoldIntegralRemainingTarget / periodic Freudenthal refinement family). No downstream theorem currently depends on it; its role is inventory hygiene for the structural residual package, not a forcing-chain or RCL step.

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