FRONTIERMATH TIER 2
li_lambda
Logarithmic integral and lambda function relationship. Requires lambda_positivity first. Selberg trace formula route. MATLAB numerical evidence exists.
LEAN4 STATEMENT
-- sorry: li_lambda
-- FrontierMath Tier 2 · γ₁ = 14.134725141734693
theorem li_lambda :
-- formal statement pending Lean4 proof
sorry
PERL FRONT / BACK SYNC
#!/usr/bin/perl
# Theorem sync harness · li_lambda · Perl leg of Lang Triple Helix
use Time::HiRes qw(gettimeofday);
use strict; use warnings;
my $G1 = 14.134725141734693;
my $sorry_id = 'li_lambda';
# FRONT SYNC
my $t_front = gettimeofday();
my $wave_front = 'W3 ACCUMULATION';
my $pemclau_score = 0.691; # from yone:6333
print "FRONT: $sorry_id wave=$wave_front score=$pemclau_score t=$t_front\n";
# ... Kimina/RHAE attempt runs here ...
# BACK SYNC
my $t_back = gettimeofday();
my $dt_ms = ($t_back - $t_front) * 1000;
my $phase = $dt_ms / ($G1 * 1000); # γ₁ phase
my $sostle_est = int($phase) + 1;
print "BACK: dt=${dt_ms}ms phase=${phase:.4f} sostle~L$sostle_est\n";
META-THEOREM CONNECTIONS
META-PEMCLAU-001 (PROVEN): this sorry contributes evidence — score 0.691 ✅
META-TIER-001 (OPEN): this sorry is at chain depth Tier 2 — part of the tier_sorry_depth proof
META-WAVE-001 (OPEN): wave prediction — W3 ACCUMULATION suggests Kimina readiness level
META-TIMING-001 (OPEN): Perl back sync delta should cluster near γ₁ multiple for Tier 2