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def

horizonCombPreflightStatus

definition
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module
IndisputableMonolith.Gravity.SevenGaps.HorizonLedgerPreflight
domain
Gravity
line
570 · github
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plain-language theorem explainer

Canonical Boolean status record for the φ-horizon absorption-comb preflight: continuous scaling family exists (true), area gap forced (false), discrete horizon state class absent, asymptotic entropy-gap theorem landed (true), exact gap and transition capital missing, mechanism unforced, dead echo route not revived. Downstream flag-equality and the P1 ledger no-uniform-gap verdict cite it. Pure structure literal; documentation, not new mathematics.

Claim. The canonical preflight status for the horizon absorption comb is the record with: continuous admissible scaling family $A(\lambda e)=\lambda^2 A(e)$ exists at the current formalization (true); area gap $\Delta A=4\ln\varphi\,\ell_P^2$ forced (false); discrete horizon state class in RS capital (false); asymptotic entropy-gap theorem $\ln F$ ratio $\to\ln\varphi$ landed (true); exact area gap derived (false); transition capital exists (false); mechanism forced (false); echo-train discriminator revived (false).

background

This module is a falsifier-gated preflight of a model mechanism for Pillar 3 (φ-horizon absorption comb), not a prediction. The candidate claims horizon-area quantization with gap $\Delta A=4\ln\varphi,\ell_P^2$, converting via BH thermodynamics into a repeated absorption comb at $GM\omega_*=\ln\varphi/(8\pi)\approx 0.019147$ for Schwarzschild. Load-bearing hypotheses are not derived from RS capital.

Existing capital (mirrored area $A=4\pi R_s^2$, ledger capacity bound $A/\ell_0^2$, recognition ledgers with real-valued boundaryCost on a bipartition) is continuous and scale-covariant. No discrete horizon state class and no forced spectrum appear. The dead $0.618$ echo-train route stays dead; this preflight concerns absorption/level structure only.

HorizonCombPreflightStatus packages the honest forced fraction: kinematics plus one asymptotic entropy-gap fragment versus zero forced quantization content.

proof idea

Definitional structure literal: each Boolean field of HorizonCombPreflightStatus is assigned a constant true or false matching the capital map. No tactics, no lemmas, no computation. The companion theorem horizonCombPreflightStatus_flags then discharges the equalities by rfl. Documentation record only.

why it matters

Pins the public scoreboard for Seven Gaps Pillar 3 so downstream claims cannot silently upgrade model hypotheses into forced RS theorems. Used by horizonCombPreflightStatus_flags (rfl-forced flag conjunction) and sits beside the P1 verdict ledger_boundary_cost_no_uniform_gap: every positive claimed gap $g$ admits an axiom-preserving ledger scaling whose boundary cost lands inside $(0,g)$, so the discrete-lattice capital does not quantize horizon cost.

Framework role: keeps Pillar 3 open. Only the asymptotic $\ln F\to\ln\varphi$ fragment and kinematic scaling algebra count as landed; $\varphi$-area quantization, transition capital, and mechanism force remain false. Explicitly refuses revival of the killed BlackHoleEchoesSI $\varphi$-rung echo discriminator. Honest forced fraction: kinematics and Fibonacci limit; physical quantization content $0%$.

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