NEXT_PASS_CHECKLIST.md

Mathematics Database — Next Pass Checklist

A prioritized checklist for the next major revision: Cite links, Frontier sections, and uniform color scheme.

---

Phase 0: Database Table Page (Intro & Start Here) — DONE ✓

• Concise introduction at top (conceptual-framing)
• Move search box into "Start Here" section
• Remove "Named Collections" (avoids who-is-named complaints)
• Start Here: search field + link to Whole of Mathematics
• Describe Whole of Mathematics as "Interactive UI" in link text

---

Reference: 5/6-Color Scheme (GLMP)

Use this palette across all charts for consistency:

Role	Hex	Semantic
Red	#ff6b6b	Triggers, inputs, postulates
Yellow	#ffd43b	Structures, objects
Green	#51cf66	Processing, operations, propositions
Light blue	#74c0fc	Intermediates, states
Violet	#b197fc	Products, outputs
Lavender	#e6e6fa	Decision diamonds (algorithms only)

Axiomatic/dependency chart mapping:

Node type	Hex	Role
Axiom	#ff6b6b	Red — inputs, postulates
Postulate	#ff6b6b	Red — same as axiom
CommonNotion	#ffd43b	Yellow — structures
Definition	#b197fc	Violet — products
Lemma	#74c0fc	Light blue — intermediates
Theorem	#51cf66	Green — propositions
Corollary	#1abc9c	Teal
Proposition	#51cf66	Green — same as theorem
Reference	#bdc3c7	Gray

---

Phase 1: Cite Links

Add attribution (Cite badge + popover) to charts with identifiable primary sources.

Already have Cite (7)

• Gödel First Incompleteness
• Schemes & Sheaves (Grothendieck)
• Group Representations
• Riemannian Geometry
• ZFC Axioms
• Shannon Entropy
• C*-Algebras

High priority (add Cite)

• Euclid's Elements charts
• Peano Arithmetic (Landau, Kirby–Paris)
• Szemerédi Theorem
• Green–Tao Theorem
• Galois Theory (Field Theory charts)
• Cauchy / Complex Analysis charts
• Sullivan collection charts
• Hubbard–Douady collection
• Devaney collection
• Kolmogorov axioms, Bayes, CLT (Statistics)
• NIST DADS algorithms (Binary Search, etc.)

Medium priority

• PDE charts (Laplace, Heat, Wave)
• Functional analysis (Banach, Hilbert)
• Spectral theory charts
• Representation theory (remaining)
• Commutative algebra charts

Schema

See ATTRIBUTION_SCHEMA.md. Fields: primary, contributors, publication, year, doi, url.

---

Phase 2: Frontier of Research Links

Add or expand "Recent & Frontier" sections on index pages. Each section: proved results, open conjectures, links to charts, links to arXiv/external.

Already have Recent & Frontier (3)

• Number Theory
• Algebraic Geometry
• Representation Theory

Add Frontier section

• Differential Geometry
• Complex Analysis
• Statistics & Probability
• Partial Differential Equations
• Foundations (set theory, logic)
• Calculus / Real Analysis
• Functional Analysis
• Topology (geometry_topology index)
• Operator Algebras
• K-Theory

Template

Use the pattern from algebraic_geometry.html: .frontier-item.proved (green border), .frontier-item.conjecture (orange border), with .name, .meta, and chart/external links.

---

Phase 3: Uniform Color Scheme

Apply the 5/6-color palette to all charts. Replace per-subcategory accent colors with the standard palette.

Algorithm flowcharts (already mostly correct)

• Sieve, Extended Euclidean, Dijkstra, Prim, Kruskal, BFS
• Binary Search, RSA, AES, Merge Sort, Quicksort, BST
• Bisection, Simpson's Rule
• Bioinformatics (BLAST, sequence alignment)
• Verify any outliers use standard colors

Axiomatic / dependency charts

• Gödel / Peano charts — map Def/Lem/Thm/Cor to palette
• Euclid's Elements — align postulate/common notion/proposition colors
• ZFC / Foundations
• Abstract algebra, algebraic geometry, representation theory, differential geometry, spectral theory, symplectic, metric geometry

P3 charts (operator algebras, K-theory, quantum algebra, optimization, information theory, mathematical physics)

• Replace subcategory-specific header/node colors with 5-color palette
• Header: database orange #e67e22
• Mermaid nodes: Def → Violet, Thm → Green

Header / nav consistency

• Standardize header to database orange #e67e22
• Nav link colors: #e67e22

---

Phase 4: Optional Enhancements (if time)

Content

• Landmark theorem charts: FLT, Riemann Hypothesis (high-level)
• Modular arithmetic: CRT (Chinese Remainder Theorem)
• Primality tests (future)
• namedCollections metadata for cross-linking (Euclid, Gödel, Galois, etc.)

Infrastructure

• Formal verification links (Lean, Coq)
• AI mathematics (AlphaProof, AlphaGeometry)
• math.HO (History & Overview) — added to Number Theory, Foundations

---

Execution Order

1. Phase 3 (Color) — Do first; it's a bulk replace across many files. Establishes visual consistency before adding content.
2. Phase 1 (Cite) — Add attribution to charts that have clear sources. Can be done incrementally.
3. Phase 2 (Frontier) — Add Recent & Frontier sections to remaining index pages. Lower effort, high value.
4. Phase 4 — As capacity allows.

---

Files to Modify

Color scheme

• All processes/**/*.html with Mermaid classDef blocks
• Generator templates: generate_p3_charts.py (P3 charts)
• Possibly: shared CSS or build step for future automation

Cite

• Add attribution HTML + CSS to each chart; or extend generator/template for batch charts
• Update ATTRIBUTION_SCHEMA.md if schema changes

Frontier

• Index pages: processes/<subcategory>/<subcategory>.html (e.g. processes/differential_geometry/differential_geometry.html)

---

Completion Criteria

• All charts with identifiable sources have Cite badge
• All major index pages have Recent & Frontier section
• All charts use the 5/6-color palette (no stray per-chart accent colors in node fills)
• Header/nav colors are consistent (or explicitly documented as domain accents)