Research-Stack/6-Documentation/docs/specs/SYMBOLOGY_DERIVED_LOGOGRAM_DESIGN.md

Symbology-Derived Logogram Design

Status: Draft v0.1 Date: 2026-05-08 Scope: lawful extraction of symbol-density principles into original Omindirection atoms Claim state: design and compiler contract; not a copyright opinion, cultural claim, compression benchmark claim, or endorsement of copying glyph systems

1. Purpose

This document defines the safe quarry rule for dense symbolic systems.

The goal is not to copy scripts, glyphs, alphabets, or fictional symbol sets. The goal is to extract compression principles and visual grammars, then reissue them as original, receipted Omindirection atoms.

Canonical rule:

borrow the compression principle
not the protected symbol identity

Lawful path:

source symbology
  -> extracted design grammar
  -> original Omindirection atom
  -> payload hash
  -> explicit direction/chirality/phase/placement
  -> residual policy
  -> receipt
  -> byte-savings witness

Formal anchor:

0-Core-Formalism/lean/Semantics/Semantics/SymbologyBorrowing.lean

2. Source Classes

Source Class	Targets	Borrowed Principle
Array languages	APL, J, K/Q, BQN, Uiua	dense one-symbol transforms, rank, tacit composition
Code-golf languages	05AB1E, Jelly, GolfScript, Pyth	custom code pages, implicit arguments, opcode density
Math notation	logic, set theory, tensors, category notation	relation families, proof/status operators, binding glyphs
Shorthand systems	Pitman, Gregg, Teeline, Tironian notes	omission plus residual recovery, phrase collapse
Logographic systems	Hanzi, Kanji, hieroglyphic systems, Blissymbolics	radicals, determinatives, concept composition
Syllabaries and featural scripts	Hangul, Cherokee, Canadian Aboriginal Syllabics, Yi, Vai	compact syllable packets, feature-bearing shape
Ancient scripts	Cuneiform, Linear B, Ogham, Runes, Mayan glyph clusters	block atoms, positional clusters, class marks
Constructed or fictional scripts	mode-based or fictional alphabets	mode remapping, phase, chirality, stroke grammar
Specialist symbol systems	alchemy, astrology, music, chess, IPA	domain-specific compact vocabularies

These classes are inspiration surfaces only. They do not grant the resulting atom semantic authority, legal clearance, cultural authority, or compression competitiveness.

3. Borrowable Principles

Allowed principles:

Principle	Use
denseOperator	one atom invokes a high-dimensional transform
modifierFamily	base atom plus modifier changes arity, mode, or route
customCodePage	compact byte identity separate from display glyph
residualOmission	omitted material is recovered by a sidecar
radicalComposition	smaller atoms compose into a concept family
syllablePacket	multiple low-level units become one packet atom
semanticDeterminative	class mark narrows interpretation without replacing payload
phaseChiralityGrammar	orientation carries structural metadata
domainNotation	specialist compact marks become domain atoms

Forbidden shortcut:

literal glyph copy -> payload identity

The glyph is always an optional view. The payload is the recoverable canonical object.

4. Omindirection Atomization

Every borrowed principle must become an internal atom:

symbol_id:
semantic_key:
canonical_payload:
payload_hash:
glyph:
direction:
chirality:
phase:
placement:
residual_sidecar:
receipt_hash:
decision:

The source system may explain why the atom exists. It does not define what the atom means. Meaning and recovery come from the internal payload and receipt.

5. Extraction Ladder

1. Mine symbol family
2. Identify compression principle
3. Reject literal glyph identity as payload
4. Convert to original Omindirection atom
5. Assign byte-code or compact route ID
6. Attach expert behavior or transform semantics
7. Add residual repair path
8. Emit receipt
9. Promote only if byte accounting wins

6. Byte Law

The byte law is:

B(atom)
+ B(dictionary/reference state)
+ B(thresholds or mode parameters)
+ B(residual)
+ B(receipt)
< B(baseline)

If the inequality fails, the symbol may still be useful for display or inspection, but it is not a compression promotion.

Lean-facing predicate:

byteLawHolds atomBytes dictionaryBytes thresholdBytes residualBytes receiptBytes baselineBytes

7. Initial Quarry

Start with these because they expose dense structure without forcing literal glyph reuse:

APL
BQN
Uiua
J
K/Q
05AB1E
Jelly
Mathematical Operators
Supplemental Mathematical Operators
IPA
Pitman shorthand
Gregg shorthand
Blissymbolics
Egyptian hieroglyphic sign organization
Alchemical-symbol organization
Tengwar-like shape grammar
Canadian Aboriginal Syllabics
Nushu
Ogham
Runes
Cuneiform

For fictional and culturally specific systems, the default is stricter:

extract mode/chirality/feature grammar only
do not copy literal glyphs
do not imply cultural ownership or equivalence

8. Compiler Gate

The compiler must reject or hold any borrowed-symbol candidate unless:

1. The atom is original to the internal registry.
2. Protected glyph identity is not copied into payload identity.
3. Payload hash is declared.
4. Direction is declared.
5. Chirality and phase are declared.
6. Placement is declared.
7. Residual policy is declared.
8. Receipt hash is declared.
9. Compression promotion has a byte-savings witness.

Lean gates:

borrowedSymbologyLawful
borrowedSymbologyPromotable
copiedGlyphBlocksLawfulBorrow
promotableBorrowIsLawful

9. Relation To Candidate Dictionaries

Symbology-derived atoms should feed the vectorless candidate dictionary as internal payloads, not as external glyph borrowings.

borrowed principle
  -> original atom payload
  -> candidate dictionary entry
  -> selectCandidate range reference
  -> replay receipt

This lets dense symbol design improve the sidecar stream without introducing embedding vectors or unreceipted visual identity.

10. Claim Boundary

This design borrows symbology as compression physics:

symbol density
+ orientation
+ phase
+ composition
+ domain shorthand
+ residual repair

It does not copy protected glyphs, prove compression wins, define cultural meaning, or replace legal review for a public glyph set. Public-facing glyph design should use original marks or cleared open resources.