SCVeamer 1.4 prototype — English edition
A Beamer-style HTML slide editor for visualizing several complex variables
2026-10-24

RESEARCH PROJECT
Developing geometric intuition in several complex variables through AI-assisted visualization
Programme: MEXT — Supporting Pioneering Research through AI for 1,000 Discovery challenges (SPReAD)
Funding period: June 2026–January 2027
Principal investigator: Takayuki Koike, Institute of Pure and Applied Sciences, University of Tsukuba
Nickname: Project Holomorphonautica

Created as part of the project's work on visualization and geometric intuition
in complex analytic geometry and several complex variables.

JOINT DEVELOPMENT OF THE WHOLE SCVEAMER SYSTEM
Takayuki Koike, with:
  Kyoka Marui — Tohoku University
  Masakazu Takakura — Tokyo Metropolitan University
  Ryo Uchimoto — Kyushu University
This credit covers the three interactive visualizations, editor, conversion engine and slide player.

SHARED CONCEPTION OF THE GAMES
Discussions among Kyoka Marui, Masakazu Takakura, Ryo Uchimoto and Takayuki Koike
about what to observe and understand through 3D VR visualizations of complex
analytic geometry led to games for practicing visual observation.
Subharmonic?, Plurisubharmonic? and Ryokuinzu — Pseudoconvex? arose from that shared conception.
Existing in-game credits are retained.

IMPLEMENTATION ASSISTANCE
ChatGPT assisted with coding and documentation.

SOFTWARE
Python and Tkinter: https://www.python.org/ / https://docs.python.org/3/library/tkinter.html
pypdf 6.10.0: https://pypdf.readthedocs.io/
pypdfium2 5.14.0 / PDFium: https://pypdfium2.readthedocs.io/
Pillow 12.3.0: https://pillow.readthedocs.io/
The user's TeX installation supplies LuaLaTeX, Beamer, fontspec and fonts.
https://tug.org/texlive/ / https://ctan.org/pkg/beamer / https://ctan.org/pkg/fontspec
The Japanese edition also uses LuaTeX-ja: https://ctan.org/pkg/luatexja
Optional executable packaging: PyInstaller, https://pyinstaller.org/
Python, pypdf, pypdfium2/PDFium, Pillow, PyInstaller and TeX itself are not bundled in this source ZIP.
Pinned dependencies are installed separately; their collected notices are in the kit root's THIRD_PARTY_NOTICES.txt and licenses/ directory.
Their authorship and license terms are those of the respective official distributions.

COLORS
blue: white background, blue headings and green accents.
red: based on the tkoike.com heading color #9F166A.
yellow: original Beamer/Metropolis-inspired #EB811B, #23373B and #FAFAFA.

EDITING AND GENERATION
The workflow follows Takayuki Koike's requirements for lectures and talks:
write mathematics in Beamer, typeset as PDF, render pages as PNG and combine
them with interactive visualizations in a single HTML presentation.

INCLUDED ASSETS
resources/games/: interactive visualizations and fixed-example catalogs.
resources/player/: navigation, overlays, interaction focus, planned times and optional notes.
bundled/day1/: English sample lecture source, HTML and PDFs, without speaker notes.
bundled/template-v2/: English presentation template source and outputs.
starter/: six-slide English Beamer starter and its HTML/PDF outputs.
There are 194 registered examples: SH106, PSH34 and Ryokuinzu54.
Each project's CREDITS.html / CREDITS.txt records its specific references.

Project website: https://tkoike.com/proj_holomorphonautica/?lang=en


THIS ENGLISH SAMPLE LECTURE

Intensive Lecture -- Day 1: Complex Analysis in Several Variables.
English version of the Japanese version 1.3 lecture aligned with the R135 notes,
including the boundary Levi form and holomorphic extension. There are 46 logical
slides, 76 display states and 135 planned minutes (14:55-17:10).
The title remains the lecture title inside the deck; the website presents it
as sample slides. The final question compares strong 1-completeness / strong
1-convexity with weak 1-completeness.

The mathematical source, timing and printed explanations are in talk.tex.
The kit includes two theme files, eight static PDF figures, the supplied
analytic-disc illustration, supplementary slide metadata and these credits.
The finished HTML embeds all three English interactive interfaces. The English
source uses LuaLaTeX and Latin Modern fonts, without Japanese font packages.

LECTURE AUTHOR AND SOURCE NOTES

Takayuki Koike, University of Tsukuba.
Complex Analytic Geometry and Dynamics on Analytic Neighborhood Spaces.
Supplied R135 file: ANNS_R135_FULL (1).pdf, 916 pages.
Version shown on its title page: Version v0.4, September 26, 2026.

Reference map:
  Chapter I, Section 9: one-variable review and subharmonic functions.
  Chapter I, Section 8.7: complex derivatives and the Laplacian convention.
  Chapter I, Sections 6.4-6.5: distributions and function-space topologies.
  Chapter III, Sections 1.1-1.2, 2.1, 2.7 and 2.10: holomorphic functions,
  complex geometry, plurisubharmonicity and pseudoconvexity.
  Observation III.2.148, printed p. 492 / PDF p. 510: boundary Levi form
  and holomorphic functions. Lemma III.1.14 supplies the background for the
  normal form, which is used without proof in this lecture.
  Figure III.4, printed p. 493 / PDF p. 511: analytic-disc configuration.

The content continues to reflect the 24 annotations on previously supplied
lecture slides. The original notes and annotated PDFs are not redistributed
in the kit; the lecture reorganizes their material for this presentation.

HISTORICAL REFERENCE: RYOKUINZU AND OKA

Toshio Nishino, "Oka Kiyoshi sensei no sugaku" [The Mathematics of Professor
Kiyoshi Oka], Sugaku 33(2) (1981), 171-178 (in Japanese).
The discussion of Ryokuinzu is on pp. 174-175; the short quotation is on p. 175.
The English quotation in the slide is identified as a translation.
https://doi.org/10.11429/sugaku1947.33.171

SUPPLEMENT FOR OKA'S LEMMA

Jean-Pierre Demailly, Complex Analytic and Differential Geometry (2012),
Chapter I, Theorem (7.2)(e), p. 54.
https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/agbook.pdf

SUPPLEMENT FOR LOCAL HOLOMORPHIC EXTENSION

Jiri Lebl, Tasty Bits of Several Complex Variables, version 4.4,
Theorem 2.3.11, printed pp. 75-76.
https://jirka.org/scv/scv.pdf
Observation III.2.148 directly gives a uniform bound at the disc centers and
the resulting failure of holomorphic convexity. The local extension argument
is a separate supplement using a Cauchy integral and parameter variation.
The positive-Levi function 1/w is local, not asserted to exist globally.

INTERACTIVE EXAMPLES AND NOTATION

The interfaces originate in the Project Holomorphonautica materials supplied
on 22 October 2026. Their version 1.2 behavior is retained, with English text
and English language defaults in this edition. The kit embeds resources/games/
in each generated HTML file; no external game download is needed for viewing.

Lecture mode selects a registered example by ID. It offers a formula display,
question/answer-and-explanation switch, interactive controls and reset. It does
not use scoring, random next questions or saved progress. Existing credits
inside the three interfaces are retained.

Examples used:
  Subharmonic?: std-b03, std-b02, std-i02.
  Ryokuinzu: lecture-ball, lecture-polydisc, n18.
  Plurisubharmonic?: N01, A03.
The lecture-ball and lecture-polydisc IDs are existing fixed lecture examples.
The three Ryokuinzu questions and observation instructions are stored in
lecture-plan.json. The kit manual lists all 194 registered examples.

Notation follows R135: the negative-sign Delta, H(phi), Psh(Omega), sqrt(-1),
roman Re and Im, and Lebesgue measure d lambda. The SH interface's Laplacian
corresponds to -Delta; the PSH interface's Levi matrix is H(u), the complex
Hessian of the function. The boundary Levi form is its restriction to the
complex tangent space when the function defines a boundary.

FIGURES

The eight existing static PDF figures in assets/ show surfaces, complex-line
restrictions and domain fibers. They already use English or mathematical
labels and are preserved. The source includes editable TikZ sketches of
circles, overlapping domains, tangent vectors, sublevel sets, compact fibers
and a locally supporting hypersurface. These are ordinary lines, circles,
arrows and labels; no image-generation application is needed to rebuild them.

assets/levi-analytic-discs.png is the supplied illustration, preserved unchanged.
It corresponds to R135 Figure III.4 and illustrates the relationship between
discs, their centers and their boundary circles in Observation III.2.148.
Its labels are mathematical and need no translation. Matplotlib is unnecessary
for normal rebuilding because the figure assets are included.

OUTPUTS AND PRESENTATION SETTINGS

SCVeamer renders the typeset PDF pages as PNG using pypdfium2/PDFium and Pillow, reads PDF structure with pypdf, and packages
them with interactive examples and a player in a self-contained index.html.
talk.pdf contains every display state; handout.pdf contains the final state
of each logical slide. This sample disables speaker notes and does not
generate a speaker guide. Its blue theme and lack of footer branding are
unchanged. Planned finish times follow the start time and per-slide minutes
written in talk.tex. They are a schedule, not an elapsed-time timer.
