# Prop 4 Decision Log
[init] 2026-05-23T16:46:51-07:00 ok prop=4 template=v2 budget=open
[L1.ranker] 2026-05-23T16:53:47-07:00 split positive=hard_F2vsF3_mismatch negative=info_bound_tight
[L1.sentinel] 2026-05-23T16:56:35-07:00 STATUS lemma1=broken implication=angle_A_free_lunch_dead prop4=warn(viable_via_D_only)
[L2.search] 2026-05-23T17:15:45-07:00 ok n_papers=11 positive_path_blocked_by_lemma1_kill negative_path=info_bound_tight
[L2.reader] 2026-05-23T17:20:01-07:00 ok positive_revised=non_indicator negative=info_bound_tight
[L3.advocate] 2026-05-23 verdict=revised_form_value=ok 4channels=spread_encoding+omega_klogk+char23_barrier+meta_C_ge_2
[L3.prover_1] 2026-05-23 sidon_B2plus1 attempted; (∗) only necessary not sufficient; B3[1] dim=Ω((log n)^2) over target; tensor 2nd order = B3[1] equivalent; verdict=non_indicator_constructions_all_fail
[L3.prover_2] 2026-05-23 negative_tightness=tight_constant_factor_1.46x conditional_on_P1star_bidirectional erdos_rado_2^(klogk(1-o(1))) cap-set_2.756^m gives m≥0.687klogk
[L3.lit_1] 2026-05-23 char2_vs_char3_barrier documented sources=Croot-Sisask_2010+Sanders_2011+Bloom-Sisask_2020+GGMT_2023; F3-PFR partial only
[L3.lit_2] 2026-05-23 PFR_2023→sunflower indirect_via_entropy not_direct; pivot=PFR_entropy_optimize_ALWZ_constants; AND_vs_XOR_structural_mismatch fundamental
[L3.numerical] 2026-05-23 cap-set alone gives only Ω(k); missing logk factor from petal-disjointness codimension; need Linial-Meshulam shifted sieve (informal not paper-grade)
[L4.adversary] 2026-05-23 verdict=conditional_bridge_unverified positive=abstain_neg negative=conditional advocate_4channels_entangled actual_independent=1
[L4.algebraic] 2026-05-23 verdict=positive_hold negative_publish_ready prover_2_clean_under_P1star sidon_necessary_only
[L4.analytic] 2026-05-23 verdict=positive_accept_revised_pivot_to_spread negative_tight_conditional kill_prover_1b 1.46x_math_tight_def_fragile
[L4.numerical] 2026-05-23 verdict=positive_reject negative_accept linear_phi_1.46x_tight nonlinear_phi_only_qualitative
[L5.summary] 2026-05-23 status=split_WARN positive=KILL_5constructions_fail+lemma1_broken+B3[1]_dim_blowup negative=weak_PASS_conditional_on_P1star_bridge_unverified next_steps=char_barrier_note+abandon_positive+wait_P1star_bridge
[L5.decision] 2026-05-23 ok html=sunflower-proposition4_f3_embedding.html sections=7 verdict=split_WARN action=barrier_note+open_question_for_positive