Fractional Hex Indexing (FHI)

What is FHI?

Fractional Hex Indexing (FHI) is a system for assigning unique, flat, lexically sortable IDs to notes, cards, or objects. Its key feature: you can always insert a new item between any two existing items without renumbering anything else.

Unlike decimal-based or hierarchical IDs, FHI uses hexadecimal fractions to create infinitely flexible, insertion-friendly IDs.

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🌟 Core Principles

✅ Fractional Hex IDs

• IDs are written as n.x, where:
  • n is the base number (1, 2, 3, …)
  • .x is a hexadecimal fractional part (base 16: 0 to F).
  • example: 1.8, 30.C, 4.18

✅ Lexical Sortability

• IDs are purely alphanumeric and naturally sortable in filenames, text files, and databases.
• Sorting by filename = correct logical order.

✅ Midpoint Insertion (Core Mechanic)

• You can always calculate a midpoint between any two IDs in hexadecimal.
• No renumbering or restructuring needed.
• Example:
  • Between 1 and 2: insert 1.8
  • Between 1 and 1.8: insert 1.4
  • Between 1.8 and 2: insert 1.C
  • Between 1.7 and 1.8: insert 1.78

✅ Suffixes for Follow-ups

• You can add suffixes like -1, -2, -z if notes have a limited character space. base 36 is ideal (1 to 9, 0 and a to z)
• Example: 1.3-1, 1.3-2.

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📊 Example Use Case: Zettelkasten

You’re writing notes in sequence but want the freedom to insert related ideas between existing notes without breaking the ID system.

• Original: 3, 4
• Insert between: 3.8
• Insert another: 3.4, 3.C, etc.
• Never need to change 3 or 4.

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🟡 Why Not other methods?

• Harder to insert in dense sequences.
• IDs get longer quickly.
• Some IDs are "impossible" to create without renumbering or referencing.

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🚀 Advantages of FHI

• Infinite insertions between any two IDs.
• Works beautifully with filenames & filesystem sorting.
• Simple mental model: just find the hex midpoint.
• Keeps IDs flat yet expandable — no tree depth explosion.
• IDs are stable — no renumbering ever.
• IDs tends to be shorter with dense sequences than other methods

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🔥 Comparison Table

Feature	FHI (Fractional Hex Indexing)	Folgezettel with Base-36 IDs
ID Format	n.xxx, where .xxx is a hex fraction (0-9, A-F per digit)	Hierarchical numbers like 1, 1a, 1a1, 1a1b, etc.
Sorting Mechanism	Lexical sort by alphanumeric order (natural for filenames)	Lexical sort works, but hierarchy gets messy at deep levels
Insertions Between IDs	Always possible by calculating hexadecimal midpoint	Requires planning; inserting between 1a and 1b forces 1a1
Scalability	Infinite insertions, logarithmic growth with hex fractions	Limited by depth of hierarchy, base-36 mitigates but still rigid
Visual Complexity	Controlled growth (1.A3F2) stays compact longer	Can explode in depth (1a1b2c3d)
Mental Model	Binary tree, always midpoint between two IDs	Tree-like hierarchy, requires structure planning
Over-insertion Behavior	Fractions get longer but sorted order is always correct	IDs become nested and hard to manage in deep hierarchies
Practical in Filenames	Yes, perfect for file explorers & systems	Works, but deeply nested IDs become unwieldy
Human Readability	Needs hex familiarity, but stays logical	Familiar at first, but deeply nested IDs become cryptic
Core Philosophy	Immutability of existing IDs, never forces renumbering	IDs are mutable, renumbering happens as tree grows

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⚠️ Known Trade-offs

While FHI is robust, consider:

• Over-inserting may lead to visually long IDs (1.ABCDEF), but they're still functional.
• Users must stay mindful to insert logically, not compulsively.
• Requires basic comfort with hexadecimal (0-9, A-F).

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📊 Formulas for Nerds:

1. Number of Possible IDs Between Two Cards

For d hexadecimal fractional digits:

Total IDs = 16^d

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2️. Total IDs Including Suffixes (-s)

Total IDs with suffixes = 16^d × 36

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3️. Total IDs in a Range of N Cards

Total IDs in range = (N - 1) × 16^d × 36 + N

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4️. Midpoint Calculation

midpoint = (a + b) / 2

Where a and b are hexadecimal fractional values.

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5️. Relationship Between Digits and Resolution

Resolution per digit = 1 / 16^d

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6️. Logarithmic Growth of ID Length

d = ⌈ log₁₆(n) ⌉
or
d = ⌈ log₂(n) / 4 ⌉

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🔎 Why FHI is Different

FHI's core mechanic is built on the principle of immutability. IDs are permanent once assigned. Inserting a new note never forces you to change existing IDs.

This is the opposite of systems where "renumbering" or "shuffling IDs" is necessary.

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📂 Ideal For:

• Zettelkasten systems.
• File & folder ordering.
• Game object IDs.
• Any system where order matters but renumbering is a headache.

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License

MIT License — Free to use, modify, and share.

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Edited by a large language model, Reviewed and developed by me.