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Add the freedom-positive counting balance to the constraint floor

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Remark: a disk with k interior vertices has 2k+n-2 faces (Euler) but only
k interior constraints, so each interior vertex adds two degrees of
freedom against one constraint -- depth is freedom-positive and Phi can
only retain or enlarge below the interior-free floor 2^(n-2). Motivates
the lower bound and replaces the prior TODO sketch.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-06-17 02:24:04 -04:00
parent b70ea2c087
commit 1d981b4d01
4 changed files with 56 additions and 43 deletions
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papers/heawood_restrictions_on_nested_tire_graph_duals/paper.aux
+8 -7
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@@ -35,6 +35,12 @@
\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}}
\bibcite{bauerfeld-depth}{2}
\bibcite{bauerfeld-nested-tires}{3}
\bibcite{bauerfeld-medial-tires}{4}
@@ -44,10 +50,5 @@
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\newlabel{sec:constraint-floor}{{4}{6}}
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\newlabel{prop:constraint-floor}{{4.2}{6}}
\newlabel{rem:floor-consequences}{{4.3}{6}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{6}{}\protected@file@percent }
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