Pith. sign in
module module high

IndisputableMonolith.Gravity.MasterTheoremStructural

show as:
view Lean formalization →

Structural skeleton of the RS quantum-gravity master theorem with all five hypothesis slots pre-filled by structural witnesses, compiling with zero open inputs. Gravity and cosmology workers cite it as the Session-102 closure of Track 7.A's structural half. The module is pure assembly: it wires Tracks 1.B/1.C, 2.C/2.D, 3.C, 6.B, and 6.C structural certificates into the master statement. Dynamical upgrades of those witnesses remain deferred.

claimThe fully structural master theorem asserts that, given structural witnesses for Tracks 1.B/1.C (stationarity and residual/Bianchi interface), 2.C/2.D (amplitude-linear forcing), 3.C (Page-curve kinematics), 6.B (PTA stochastic GW discriminator), and 6.C (strong-field deviation patterns), the Recognition Science quantum-gravity master statement holds with no remaining hypothesis inputs.

background

Recognition Science's quantum-gravity master plan packages seven gravity and cosmology tracks into one master theorem (Track 7.A). Earlier modules authored the conditional statement, then progressively pre-filled PTA and strong-field hypotheses, then the Page-curve hypothesis as well, leaving a short residual list of structural inputs.

This module finishes that ladder. It imports structural witnesses for amplitude-linear forcing (Track 2.C/2.D), kinematic Page-curve form (Track 3.C), PTA stochastic GW discrimination (Track 6.B), Track 1.B/1.C residual and Bianchi interface, and strong-field deviation patterns (Track 6.C), and plugs them into the conditional master statement. The setting is purely structural: zero sorry and zero RS-internal axioms on the load-bearing path. Dynamical derivations (ledger Page curve, primordial PTA spectrum, RS modified-metric strong-field patterns, and related geometric identities) are explicitly out of scope here.

proof idea

The module is an assembly layer, not a deep derivation. It imports structural certificates from the conditional master theorem, its partial and deeper-partial pre-fill stages, and the Track 1.B/1.C, 2.C/2.D, 3.C, 6.B, and 6.C structural modules. Those witnesses discharge the five hypothesis inputs of the conditional master statement, yielding a zero-hypothesis structural form together with a certificate type and inhabited instance. Companion declarations record honest scope, Session-102 closure status, a template, and a one-statement packaging of the result.

why it matters in Recognition Science

This is the structural endpoint of Track 7.A's master-statement authoring half. Downstream, the handoff-integration module consumes it as the integration-lane receipt for parallel fork handoffs: stationarity reduction at $N=5$, physical residual and Bianchi interface, many-body amplitude-linear lift, and discrete recognition-tick Page-capacity transfer. The module doc is explicit that the dynamical unconditional master theorem still requires upgrading each structural witness (Page curve from ledger dynamics; PTA spectrum from RS primordial structure; strong-field patterns from an RS modified metric; factor-product retirement from a stricter substrate axiom; geometric residual estimate and Schläfli identity proofs). It packages gravity consequences downstream of the forcing chain and RCL rather than re-deriving T5--T8.

scope and limits

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (8)

Lean names referenced from this declaration's body.

declarations in this module (8)