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Scaffold the 2^(n-2) constraint-floor proposition

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Add section 4: define the achievable boundary set Phi(D) of a triangulated
disk and state the constraint-floor proposition |Phi(D)| >= 2^(n-2), with
the attainment direction proved (fan injectivity) and the lower bound left
as a marked gap with strategy. Remark records the zonotope structure and
the short-interface concentration of difficulty.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-06-17 02:14:52 -04:00
parent 60c9f1d3a8
commit d2156f06ee
4 changed files with 124 additions and 30 deletions
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papers/heawood_restrictions_on_nested_tire_graph_duals/paper.aux
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@@ -30,10 +30,11 @@
\newlabel{eq:heawood-face-sum-dual}{{3.1}{4}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Why the programme runs between nested clusters}}{4}{}\protected@file@percent }
\newlabel{prop:two-sided-decomposition}{{3.6}{4}}
\bibcite{Heawood1898}{1}
\citation{bauerfeld-nested-tires}
\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}
\bibcite{bauerfeld-depth}{2}
\bibcite{bauerfeld-nested-tires}{3}
\bibcite{bauerfeld-medial-tires}{4}
@@ -43,5 +44,10 @@
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\@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:floor-consequences}{{4.3}{6}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{6}{}\protected@file@percent }
\gdef \@abspage@last{6}