Pith. sign in
module module moderate

IndisputableMonolith.Foundation.UnifiedForcingChain

show as:
view Lean formalization →

Unified home of the Recognition Science forcing spine from the absolute floor (T-1) through T8. It packages the successive forced steps: logic from distinguishability, cost uniqueness to J, self-similar φ, the eight-tick octave, and D = 3. Foundation and gravity audits cite it as the single spine. The module is an assembly of named tier theorems and bridges rather than one monolithic proof.

claimThe Recognition forcing chain is the ordered spine $T_{-1}\to T_0\to\cdots\to T_8$: absolute floor (statability: distinguishable propositions and a non-singleton universe), forced logic, analytic cost refinement, uniqueness of the cost $J(x)=(x+x^{-1})/2-1$, self-similar fixed point $\varphi$, period-$2^3$ eight-tick octave, and forced spatial dimension $D=3$.

background

Recognition Science claims physics is forced from one functional cost equation once a minimal floor of statability is granted. This module is the Foundation assembly point for that claim: it imports absolute-floor closure, cost-from-distinction, logic realization, universal forcing, discreteness and ledger forcing, and $\varphi$-forcing, then exposes the numbered tiers as a single chain.

The doc-comment fixes the bottom rung: $T_{-1}$ is the absolute floor below the Law of Logic, namely meta-language proposition distinguishability and a non-singleton universe of discourse. Sibling names in the module track the early spine explicitly ($T_{-1}$ absolute floor, $T_0$ logic forced, Boolean recognition cost, analytic-cost refinement).

Upstream material also pulls cosmology and constant structure (electroweak VEV framing, $\Lambda$, $\eta_B$ rung work, $g_\star$) so the same spine can be audited against derived physics, but the local theoretical setting remains the Foundation forcing ladder, not a single observational fit.

proof idea

Not a single proof object. The module wires a ladder of tier declarations: floor witnesses and Boolean recognition-cost constraints at $T_{-1}$/$T_0$, then successive forcing modules (logic-from-cost, discreteness, ledger, $\varphi$, and later $T_5$–$T_8$ landmarks) each contributing a named theorem or bridge.

Argument shape is compositional: discharge the absolute-floor preconditions, lift to forced logic and cost uniqueness $J$, then specialize to the self-similar fixed point $\varphi$, the eight-tick period $2^3$, and $D=3$. Downstream audits read the exported tier flags rather than re-proving the chain in place.

why it matters in Recognition Science

This is the canonical citation point for the T-1–T8 forcing spine named in the Recognition primer (T5 $J$-uniqueness, T6 $\varphi$, T7 eight-tick octave, T8 $D=3$). Downstream, DistinctionToT4 starts closure from a supplied distinction witness onto the early spine; LedgerFloorT0Bridge identifies the $T_0$ floor with the Boolean truncation of the extensive recognition ledger; Gravity.MasterTheorem sits on the structural gravity track gated by spine closure; T6T8SpineAudit machine-checks honest tier tags (theorem vs forced-conditional) for $T_6$–$T_8$.

Without this module, foundation and gravity developments would each re-import a fragmented ladder. It is the place a referee checks whether the chain is assembled, not merely advertised.

scope and limits

used by (4)

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

depends on (40)

Lean names referenced from this declaration's body.

… and 10 more

declarations in this module (540)

… and 460 more