 371
 372/-- **THEOREM**: The Spacetime Emergence Certificate is inhabited.
 373    Zero sorry. -/
 374theorem spacetime_emergence_cert : SpacetimeEmergenceCert where
 375  dim_eq_four          := spacetime_dim_eq_four
 376  temporal_one         := rfl
 377  spatial_three        := rfl
 378  signature_lorentzian := lorentzian_signature
 379  metric_trace         := η_trace
 380  metric_det           := η_det
 381  cone_timelike        := timelike_iff_subluminal
 382  cone_lightlike       := lightlike_iff_speed_c
 383  mass_gap_positive    := massGap_pos
 384  mass_gap_universal   := spectral_gap
 385  octave_period        := rfl
 386  sig_unique           := ⟨rfl, rfl⟩
 387  arrow                := fun _ => Nat.lt_succ_of_le le_rfl
 388
 389/-- The certificate is nonempty. -/
 390theorem spacetime_emergence_cert_nonempty : Nonempty SpacetimeEmergenceCert :=
 391  ⟨spacetime_emergence_cert⟩
 392
 393/-! ## Summary
 394
 395**The Spacetime Emergence Theorem**: η = diag(−1, +1, +1, +1).
 396
 397The question "Why is spacetime 4D Lorentzian?" has the answer:
 398**Because J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y).** -/
 399
 400end  -- noncomputable section
 401
 402end SpacetimeEmergence
 403end Unification
 404end IndisputableMonolith

papers checked against this theorem (showing 4 of 4)

Gravity as a broken gauge symmetry, with no Big Bang singularity
echoes · 2505.02925

"the gauge group of these theories à la Yang–Mills, a metric structure for spacetime emerges and the field equations recover both the Einstein and the Cartan field equations for gravity"
Gauss-Bonnet charge leaves a fingerprint in EMRI waveforms
unclear · 2506.05015

"we investigate ... gravitational waveforms ... finding that variations in α and Q can lead to distinguishable differences in periodic orbit structures and gravitational wave phases"
"Weak null singularity survives a relativistic fluid"
unclear · 2506.16635

"We study the behavior of a self-gravitating perfect relativistic fluid satisfying the Einstein–Euler system in the presence of a weak null terminal spacetime singularity. ... we prove that the fluid variables also extend continuously to the singularity."
A lattice with gain and loss mimics a black hole horizon
unclear · 2507.03826

"The metric for this particular model is ds² = −(1−f²(r))dt² + 2f(r)dr dt + dr², matched order-by-order to Schwarzschild in Painlevé–Gullstrand coordinates by tuning κ₁,κ₂,l,r₁."