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IndisputableMonolith.Mathematics.GraphInvariantsFromConfigDim

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Module packaging graph-theoretic invariants that are forced once the configuration space dimension is fixed in Recognition Science. A mathematician working on discrete geometry or spectral graph constraints would cite it when linking dimension to combinatorial counts. It is largely definitional: named invariant types, a count, and a certificate bundle over Mathlib and RS constants.

claimFrom a fixed configuration dimension one obtains a family of graph invariants $\mathrm{GI}$, a count $\#\mathrm{GI}$, and a certificate package asserting those invariants are well-formed relative to the RS constants (including the native tick $\tau_0=1$).

background

Recognition Science forces spatial dimension $D=3$ at step T8 of the unified forcing chain, together with the eight-tick octave (period $2^3$) at T7. Once dimension is fixed, discrete configuration graphs carry only a constrained set of combinatorial invariants; this module names and packages those invariants.

It imports Mathlib for ordinary graph and finite-combinatorics infrastructure, and IndisputableMonolith.Constants for the RS-native time quantum $\tau_0=1$ tick. Sibling declarations introduce a GraphInvariant type, a count of such invariants, and a GraphInvariantsCert certificate with a concrete instance.

The local setting is pure mathematics inside the RS monolith: no dynamics, only the static combinatorial shadow of configuration dimension.

proof idea

This is primarily a definition and certificate module, not a deep proof development. It introduces the invariant type and count, then bundles them into a certificate structure whose fields are discharged by Mathlib facts and the imported RS constants. Expect definitional equality, finite enumeration, and simple certificate constructors rather than multi-step tactic arguments.

why it matters in Recognition Science

Dimension $D=3$ and the eight-tick structure are framework landmarks; graph invariants that follow from configuration dimension sit downstream of those forcing steps and upstream of any discrete-geometry or ledger-graph arguments that need a named, certifiable invariant package. No downstream consumers are recorded on this page yet, so the module presently serves as mathematical scaffolding: a stable API for later theorems that quote dimension-forced graph counts or spectral constraints. It does not itself close a T0--T8 step; it records the combinatorial consequences once dimension is already fixed.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (4)