Reframe the constraint floor honestly as a conjecture

Section 4 no longer states the floor as a proven Proposition. Now: prove
interior-free disks attain 2^(n-2) (ear-peeling) and the un-stacking
lemma, state |Phi(D)| >= 2^(n-2) as a Conjecture, and give an honest
status remark -- holds for the Apollonian class, reduces to the
irreducible case, empirically strict (5/4), but |Phi| is NOT monotone
(the earlier freedom-positive monotonicity claim was wrong) and both
natural elementary proofs provably fail. Soften the note's observation to
match.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

papers/heawood_restrictions_on_nested_tire_graph_duals/paper.aux

@@ -34,13 +34,14 @@
 \newlabel{rem:why-clusters}{{3.7}{5}}
 \newlabel{conj:heawood-chain-pigeonhole}{{3.8}{5}}
 \newlabel{conj:heawood-route-fct}{{3.9}{5}}
-\bibcite{Heawood1898}{1}
 \@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The constraint floor}}{6}{}\protected@file@percent }
 \newlabel{sec:constraint-floor}{{4}{6}}
 \newlabel{def:achievable-boundary-set}{{4.1}{6}}
-\newlabel{prop:constraint-floor}{{4.2}{6}}
-\newlabel{rem:freedom-positive}{{4.3}{6}}
-\newlabel{rem:floor-consequences}{{4.4}{6}}
+\newlabel{prop:attainment}{{4.2}{6}}
+\newlabel{lem:unstack}{{4.3}{6}}
+\newlabel{conj:constraint-floor}{{4.4}{6}}
+\newlabel{rem:floor-status}{{4.5}{6}}
+\bibcite{Heawood1898}{1}
 \bibcite{bauerfeld-depth}{2}
 \bibcite{bauerfeld-nested-tires}{3}
 \bibcite{bauerfeld-medial-tires}{4}
@@ -50,5 +51,6 @@
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 \newlabel{tocindent3}{0pt}
+\newlabel{rem:floor-consequences}{{4.6}{7}}
 \@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{7}{}\protected@file@percent }
 \gdef \@abspage@last{7}