Mazecoin: An Energy-Efficient Cryptographic
Framework for Digital Currency
Introduction
Across the developed world, the way people pay for goods
and services is changing fundamentally. Cash, once the universal medium of
exchange, is in steady decline. In Australia, for example, cash accounted for
approximately 70% of consumer payments in 2007; by 2022, that share had fallen
to just 13%.[^1] Cheques, already a marginal payment method, are scheduled for
complete elimination by September 2029.[^2] ATMs and bank branches are
disappearing. Yet this march toward cashless societies is not without friction.
An estimated 1.5 million Australians rely on cash for over 80% of their
in-person payments, including many elderly, disabled, and remote community
members.[^3] Governments are therefore seeking digital alternatives that are
efficient, secure, and inclusive.
At the same time, many nations are actively exploring
Central Bank Digital Currencies (CBDCs). Australia's Project Acacia, a joint
initiative of the Reserve Bank of Australia and the Digital Finance Cooperative
Research Centre, is currently piloting a wholesale CBDC across multiple
distributed ledger platforms, with findings expected in early 2026.[^4] Similar
projects are underway globally: the digital euro, China's e-CNY, Sweden's
e-krona, and others. These initiatives share a common challenge: how to design
a digital currency that is not energy-intensive, that can be controlled by
monetary authorities, and that offers genuine scarcity without relying on
proof-of-work mining.
Bitcoin demonstrated that digital scarcity is possible, but
at a tremendous environmental cost. Its proof-of-work mechanism consumes
electricity comparable to that of medium-sized nations, and its value basis —
essentially, a certificate of energy destruction — has been described as
putting gold into a volcano and being rewarded for the effort. Whether or not
one accepts this critique, the energy intensity of Bitcoin remains a barrier to
government adoption.
This paper poses two main questions. First, what is
Mazecoin? Second, how could it be used in a digital economy?
Mazecoin is not proposed as a Bitcoin killer; Bitcoin is entrenched. Rather,
Mazecoin offers a candidate model for government-issued digital currency —
energy-efficient, mathematically scarce, and controllable by monetary
authorities. It is designed to be understood by policymakers while providing
sufficient technical detail for implementation.
[^1]: Reserve Bank of Australia, Consumer Payments Survey,
2022.
[^2]: Australian Government, Cheque Elimination
Announcement, 2023.
[^3]: Australian Banking Association, Cash Inclusion
Report, 2024.
[^4]: RBA/DFCRC, Project Acacia Pilot Framework, 2025.
Question One: What is Mazecoin?
1.1 Mazes as Topological Structures
A Mazecoin is fundamentally a number — a string of
hexadecimal digits — derived from a special kind of maze. Not all mazes
qualify. The mazes used in this system are hermetic (fully enclosed by
an unbroken border) and unicursal (containing a single continuous path
with no branches, dead ends, or choices). Every reachable cell of the maze lies
on this single path.
The structure resembles a walnut. The outer shell
corresponds to the maze border. Internal compartments correspond to primary
partitions attached to the border. The kernel at the centre corresponds to
secondary partitions. The single path winds through all compartments, visiting
every part of the maze exactly once. (See Annex A for a complete topological
treatment.)
Mazes are represented as rectangular grids of icons,
each icon being a hexadecimal digit from 0 to F. An m × n grid of icons
corresponds to a maze of 2m × 2n sub-cells. The path must visit every
sub-cell that is not designated as a void.
Each icon type determines how many times the path passes
through its 2×2 block of sub-cells — from zero times (void, icon F) up to four
times (icon 0). Icons 1, 2, 4, and 8 force the path to visit three times; icons
3, 6, 9, and C force two visits; icons 5 and A force one visit; icons 7, B, E,
and D also force one visit but with a different internal topology. (See Annex B
for the complete icon mapping and visit count table.)
1.2 Path Strings as Cryptographic Numbers
Tracing the unicursal path from beginning to end, and
recording the hex value of each icon encountered, produces a path string
— a sequence of hexadecimal digits. This string is the fundamental
cryptographic object underlying Mazecoin.
The rarity of a path string is determined solely by its
length, L. Among all possible hex strings of length L, any specific string
appears with frequency 16^−L. This mathematical rarity, not the expenditure of
energy through proof-of-work, constitutes the value basis of Mazecoin. A simple
spiral path and a highly complex, apparently random path of the same length
have identical rarity and therefore identical value — but simple patterns are
exponentially less likely to occur.
It should be noted that the linear construction of the path
string described here does not necessarily conform to the linear construction
rules for maze strings used in other contexts (such as Maze Scrabble). This has
no bearing on the path string's integrity as a unique cryptographic number.[^5]
[^5]: The hex digit F (void) never occurs in a valid path
string and may therefore serve as a delimiter for optional metadata, such as
denomination or other transaction data.
1.3 Toroidal Derivatives
A single path string can be transformed into a family of
related objects through a toroidal construction. The path string is wrapped
around a cylinder L times, producing L rings. Each ring may be independently
rotated using a "bike lock" mechanism — a set of turn settings that
act like the dials of a combination lock. The ends of the cylinder are then
joined to form a torus. The longitudinal strings extracted from this
torus become public derivatives: they can be published without revealing the
original path string.
In the stronger model adopted here, each of the L rings is
generated from a different, independent maze. This dramatically reduces the
risk that combining two tori will produce degenerate derivatives (strings full
of zeros). The rings are arranged radially around the torus, and their order
can be permuted: a given set of L mazes yields (L-1)! distinct tori from
different radial orders alone. (See Annex C for the complete toroidal
construction and ring permutation rules.)
Each torus has a seam — the join where the cylinder
ends meet — which serves as a reference point analogous to the 12 o'clock
position on a clock face. This seam defines a coordinate system for the torus,
with positions numbered 0 to L-1.
1.4 Negation and Conjunction of Tori
Every torus has a negative twin obtained by applying
bitwise complement (logical NOT) to each hex icon in its representation. For
example, N3 = C and N5 = A, following the standard 4-bit complement.
Tori may be combined using an operation denoted J A r B
s = C. Here A and B are input tori, r and s are rotation counters (0 to
L-1) that rotate the tori relative to each other before combination, and C is a
new torus resulting from the conjunction. The operation is applied ring-wise
using a symmetrical Polish XOR operator. In practice, it suffices to fix r = 0
and vary only s, as rotating both tori by the same amount produces equivalent
results.
The resulting torus C always has its seam at the top
(position 0) regardless of the rotations applied to its parents. This
simplifies subsequent operations. The conjunction operation satisfies two
symmetry properties:
- EJpqJNpNq:
Conjoining two tori yields the same result as conjoining their negations.
- EJnpqJpNq:
Conjoining the negation of p with q yields the same result as conjoining p
with the negation of q.
These properties ensure that the number of distinct
conjunctions is limited and well-defined. (See Annex D for the complete
conjunction algorithm.)
1.5 Transformations: Rotations and Reflections
A maze represented as an icon grid may be rotated (90°,
180°, 270°) or reflected (horizontally, vertically, or diagonally) while
preserving all topological relations — the maze remains hermetic and unicursal.
These transformations act simultaneously on the grid positions and on the
internal orientation of each icon.
For an asymmetrical maze, the eight transformations of the
dihedral group D4 yield up to eight distinct icon matrices, and therefore up to
eight distinct path strings, from a single underlying topological maze. This
multiplies the available cryptographic assets without requiring the generation
of new base mazes.
The canonical transformation tables, derived experimentally
from a magnetic whiteboard, are provided in Annex E. These tables are
sufficient to transform any hex matrix correctly.
1.6 Divisibility and Metadata
A valid path string contains no occurrence of the hex digit
F, since F represents a void and is never traversed. This property allows F to
serve as a delimiter in extended representations. A Mazecoin may therefore be
expressed as:
text
[path_string] F [metadata]
The metadata field can encode any additional information
required for transaction processing, including:
- Denomination
(fractional amounts of the base unit)
- Version
number
- Timestamp
- Cryptographic
signature
- Nonce
- Checksum
- Issuer
identifier
The exact scheme for denomination — whether decimal,
hexadecimal, or some other base — is not fixed by this specification. The only
requirement is that the first occurrence of F separates the cryptographic core
from any metadata. This design is future-proof and parsable without ambiguity.
Question Two: How Could Mazecoin Be Used in a
Digital Economy?
2.1 Three Institutional Models
Mazecoin is not a single instrument but a family of
instruments distinguished by who issues them and how they are backed. Three
models are identified.
|
Model
|
Backing
|
Value Basis
|
Typical Use
|
|
Private/Entrepreneurial
|
Market faith
|
Rarity + speculation
|
Competing with Bitcoin, Ethereum
|
|
Government Fiat
|
State authority
|
Legal tender, tax acceptance
|
CBDC replacement
|
|
Intermediate (Bond)
|
State/local credit
|
Repayment promise
|
Municipal bonds, development finance
|
Each model uses the same mathematical primitives — mazes,
path strings, tori, derivatives, and conjunction — but applies different
institutional rules for issuance, validation, and transfer.
2.2 Private Cryptocurrency
In the private model, Mazecoin would be launched by an
entrepreneur or consortium, with value determined by market supply and demand,
exactly as with Bitcoin. The difference lies in the energy efficiency: no
proof-of-work mining is required. The rarity of path strings is mathematical,
not energetic. Private Mazecoin could be listed on exchanges, traded, held as a
speculative asset, or used for payments where merchants accept it.
The hope of displacing energy-intensive cryptocurrencies
through market competition alone is, however, a faint one. Bitcoin is deeply
entrenched, with network effects, brand recognition, and a committed community.
The private model is therefore not the primary target of this proposal.
2.3 Government CBDC
The most promising application of Mazecoin is as a
candidate model for government-issued Central Bank Digital Currency.
Governments are actively designing CBDCs now — Project Acacia in Australia, the
digital euro, China's e-CNY, Sweden's e-krona, and others. These initiatives
share common requirements:
- Energy
efficiency (to meet climate commitments)
- Mathematical
scarcity (to avoid inflationary arbitrariness)
- Controllability
(monetary authority must manage supply)
- Inclusivity
(must serve cash-dependent populations)
- Verifiability
(transactions must be auditable)
Mazecoin meets these requirements. A central bank would
define the parameters of the system: the number of rings L, the bike lock key
settings, the radial order of mazes, and the rules for conjunction. The bank
would control the money supply by issuing new base mazes, retiring old ones,
and regulating JArBs conjunctions.
Unlike ledger-based CBDC proposals that merely replicate
existing database architectures, Mazecoin offers genuine mathematical scarcity.
Unlike Bitcoin, it consumes negligible energy. And unlike both, it provides
native composability through the conjunction operation, allowing financial
instruments to be combined directly at the cryptographic level.
2.4 Intermediate Instruments: Bonds and Local
Currencies
Between the fully private and fully government-backed
models lies an intermediate space: instruments issued by states, provinces, or
local authorities, backed by their credit rather than by a central bank. A
municipal government, for example, could issue a bond represented as a torus,
with the bond's principal, maturity date, and coupon encoded in the metadata
field. The bond's derivatives could be traded on secondary markets, and
multiple bonds could be pooled using the JArBs conjunction to create synthetic
instruments.
This model has a lower barrier to entry than a full CBDC.
It could be piloted by a single city or region without requiring national
legislation. If successful, it would demonstrate the viability of the Mazecoin
framework in a controlled environment, building confidence for larger-scale
adoption.
2.5 Comparison with Existing CBDC Proposals
Existing CBDC projects vary widely in their technical
architectures. Some are built on conventional databases (e.g., the e-CNY);
others explore distributed ledgers (Project Acacia). Almost none incorporate
mathematical scarcity as a primary design principle. Most are, in essence,
digital representations of fiat currency — convenient but not scarce in
themselves.
Mazecoin differs in three fundamental respects:
- Energy
efficiency: No proof-of-work, no mining arms race.
The cost of validation is trivial.
- Mathematical
scarcity: Value rests on the rarity of path
strings (16^−L), not on trust in an issuer or ledger.
- Native
composability: The JArBs conjunction allows tori to be
combined directly, creating new financial instruments without intermediate
layers.
These properties make Mazecoin suitable not only as a
replacement for physical cash but also as a platform for programmable finance,
bond issuance, and interbank settlement.
Conclusion: A Framework for Cashless Digital
Currency
The march toward cashless societies is well advanced.
Cheques are being eliminated. Cash usage continues to decline. Governments are
actively designing digital currencies to replace or complement physical money.
Yet the dominant model of cryptocurrency — Bitcoin's proof-of-work — remains
too energy-intensive for government adoption.
Mazecoin offers an alternative. It is energy-efficient
because its value basis is mathematical rarity, not energy destruction. It is
mathematically scarce because path strings of a given length have frequency
16^−L. It is controllable because monetary authorities can set parameters,
issue base mazes, and regulate conjunctions. And it is flexible, supporting
private, government, and intermediate institutional models.
Mazecoin is not proposed as a Bitcoin killer. Bitcoin is
entrenched, and the hope of displacing it through market competition is faint.
The target is whatever governments decide to do with CBDCs. Project Acacia and
similar initiatives show that governments are actively seeking digital currency
architectures. Mazecoin offers one such architecture — one that is ready for
technical specification, implementation, and pilot.
Further work is required: formal cryptanalysis of the
inversion hardness of the toroidal derivative construction; optimization of
parameters (L, K, maze dimensions); and the development of reference software.
These are matters for implementation, not for this foundational paper.
The framework is complete. The technical annexes provide
the detail required for implementation. The policy window is open. Mazecoin is
ready for consideration.
Technical Annexes
Annex A: Topological Classification of
Hermetic, Unicursal Mazes
*[Content: Walnut structure, Euler's formula V–E+F=1,
component counts for m×n grids, proof that such mazes are valid topological
figures]*
Annex B: Icon Types and Visit Counts
[Content: Complete table of hex icons 0–F,
visit counts (0–4), internal topology descriptions, mapping of F as void]
Annex C: Toroidal Derivative Construction
*[Content: Cylinder wrapping, independent rings per maze,
bike lock turn settings, radial permutations (L-1)!, seam definition,
longitudinal string extraction]*
Annex D: Negation and Conjunction (JArBs)
[Content: Bitwise complement definition,
ring-wise XOR application, rotation counters r and s, seam inheritance rule,
symmetry properties EJpqJNpNq and EJnpqJpNq]
Annex E: D4 Transformation Tables (Rotations
and Reflections)
[Content: 4×4 tables for original, 90°, 180°,
270° rotations; tables for Top, Right, Bottom, Left reflections; programmer
specifications in Python, JSON, and C]
Annex F: Parameter Enumeration and Divisibility
[Content: Recommended ranges for L, K, maze
dimensions; F separator specification; denomination schemes (optional)]
Annex G: Glossary of Terms
[Content: Definitions of hermetic, unicursal,
icon, sub-cell, path string, torus, seam, derivative, JArBs, etc.]
References
- Reserve
Bank of Australia, Consumer Payments Survey, 2022.
- Australian
Government, Cheque Elimination Announcement, 2023.
- Australian
Banking Association, Cash Inclusion Report, 2024.
- RBA/DFCRC,
Project Acacia Pilot Framework, 2025.
- RBA/DFCRC,
Project Acacia Use Case Selections, 2025.
- ASIC,
Regulatory Relief for CBDC Pilots, 2025.
- Australian
Treasury, Cash Mandate Legislation, effective January 2026.
- European
Central Bank, Digital Euro Progress Report, 2024.
- People's
Bank of China, e-CNY White Paper, 2021.
- Sveriges
Riksbank, E-krona Pilot Phase 2 Report, 2022.
Annex A: Topological Classification of
Hermetic, Unicursal Mazes
A.1 The Walnut Structure
A hermetic, unicursal maze corresponds topologically to a
walnut:
|
Walnut part
|
Maze equivalent
|
|
Outer shell
|
Unbroken border
|
|
Shell compartments
|
Primary partitions (trees attached to border)
|
|
Kernel
|
Secondary partitions (discrete network inside)
|
The general topological form requires:
- An
unbroken border
- A
primary network of trees attached to the border at various points
- A
secondary, discrete network occupying the spaces defined by the
tree/border network
- An
unbroken path running between the tree network and the kernel network
A.2 Euler's Formula for Plane Figures
For a hermetic, unicursal maze considered as a plane
figure:
V – E + F = 1
where:
- V
= total points (vertices)
- E
= total partitions (edges)
- F
= faces (always 1 for this treatment)
A.3 Component Counts for an m × n Icon Grid
Let the maze be represented by an m × n grid of icons (each
icon being a 2×2 block of sub-cells).
|
Component
|
Formula
|
|
Grid points
|
(m+1)(n+1)
|
|
Border points
|
2(m+n)
|
|
Primary points (not touching border)
|
(m-1)(n-1)
|
|
Secondary points
|
mn
|
|
Border partitions
|
2(m+n)
|
|
Primary partitions
|
(m-1)(n-1)
|
|
Secondary partitions
|
mn
|
|
Total points V
|
2(m+n) + (m-1)(n-1) + mn
|
|
Total partitions E
|
2(m+n) + (m-1)(n-1) + mn – 1
|
|
Faces F
|
1
|
A.4 Verification
For any m, n ≥ 2, the identity V – E + F = 1 holds. Thus
hermetic, unicursal mazes are valid topological figures.
Annex B: Icon Types and Visit Counts
B.1 The Icon Grid
Each icon represents a 2×2 block of sub-cells. An m × n
icon grid corresponds to a maze of 2m × 2n sub-cells.
B.2 Visit Counts by Icon Type
|
Icon (hex)
|
Visit count
|
Notes
|
|
0
|
4
|
Path passes through all four sides
|
|
1
|
3
|
Path uses three sides (type 1)
|
|
2
|
3
|
Path uses three sides (type 2)
|
|
3
|
2
|
Path uses two sides (type 3)
|
|
4
|
3
|
Path uses three sides (type 4)
|
|
5
|
1
|
Path transits once (type 5)
|
|
6
|
2
|
Path uses two sides (type 6)
|
|
7
|
1
|
Path transits once (type 7)
|
|
8
|
3
|
Path uses three sides (type 8)
|
|
9
|
2
|
Path uses two sides (type 9)
|
|
A
|
1
|
Path transits once (type A)
|
|
B
|
1
|
Path transits once (type B)
|
|
C
|
2
|
Path uses two sides (type C)
|
|
D
|
1
|
Path transits once (type D)
|
|
E
|
1
|
Path transits once (type E)
|
|
F
|
0
|
Void — no path through this icon's sub-cells
|
B.3 Sub-Cell Visitation
The global path must visit every non-F sub-cell exactly
once. For a maze with no voids (no F icons), this means the path visits all
4mn sub-cells exactly once — a Hamiltonian path on the sub-cell grid.
When F icons are present, the corresponding sub-cells are
omitted from the path.
B.4 Path String Construction
Tracing the unicursal path from start to end, record the
hex value of each icon whose 2×2 block is entered. The resulting sequence of
hexadecimal digits is the path string.
Length of path string = total number of icon visits along
the path.
Annex C: Toroidal Derivative Construction
C.1 Cylinder Wrapping
Take a circular path string (the maze path looped). Wrap it
around a cylinder L times, creating L distinct rings. In the stronger model, each
ring is generated from a different, independent maze rather than from the
same path repeated.
C.2 Independent Mazes per Ring
Let there be L distinct, random, hermetic, unicursal mazes
M₁, M₂, …, Mₗ. Each maze yields a path
string P₁, P₂, …, Pₗ. These L strings form the
rings of the cylinder.
C.3 Bike Lock Turns
Each ring may be rotated by a turn setting, analogous to
the dials of a combination lock. If each ring has K possible turn positions,
then there are Kᴸ possible turn configurations for the cylinder.
The turn settings act as a key: without knowing the
settings, one cannot reconstruct the original torus from its derivatives.
C.4 Radial Permutations
The L rings are arranged radially around the cylinder.
Because the cylinder has rotational symmetry, the number of distinct radial
orders of the rings is (L-1)! (not L!). For L = 10, this is 362,880
distinct tori from the same set of mazes.
C.5 Closing the Cylinder: The Torus
The ends of the cylinder are joined to form a torus. The
join creates a seam — a specific gap that is structurally identical to
the gaps between rings but is designated as the reference point (position 0) on
the torus clock.
C.6 Longitudinal Derivatives
From the completed torus, extract the longitudinal
strings — the strings that run along the length of the torus (orthogonal to
the rings). These longitudinal strings are the public derivatives that
can be published or used as coin identifiers.
C.7 Seam as Clock Reference
The seam defines a coordinate system. Each ring position is
numbered 0 to L-1, with the seam at position 0. Rotations are counted by how
many positions the seam moves relative to an external reference.
Annex D: Negation and Conjunction (JArBs)
D.1 Negation
Negation is bitwise complement on the 4-bit hex
representation of each icon.
|
Icon
|
Binary
|
Negation
|
Result
|
|
0
|
0000
|
1111
|
F
|
|
1
|
0001
|
1110
|
E
|
|
2
|
0010
|
1101
|
D
|
|
3
|
0011
|
1100
|
C
|
|
4
|
0100
|
1011
|
B
|
|
5
|
0101
|
1010
|
A
|
|
6
|
0110
|
1001
|
9
|
|
7
|
0111
|
1000
|
8
|
|
8
|
1000
|
0111
|
7
|
|
9
|
1001
|
0110
|
6
|
|
A
|
1010
|
0101
|
5
|
|
B
|
1011
|
0100
|
4
|
|
C
|
1100
|
0011
|
3
|
|
D
|
1101
|
0010
|
2
|
|
E
|
1110
|
0001
|
1
|
|
F
|
1111
|
0000
|
0
|
Examples: N3 = C, N5 = A.
D.2 Conjunction Notation
J A r B s = C
- A,
B: input tori
- r:
rotation applied to A (0 ≤ r < L)
- s:
rotation applied to B (0 ≤ s < L)
- C:
resulting new torus
D.3 Practical Simplification
Rotating both tori by the same amount produces an
equivalent conjunction. Therefore, it suffices to fix r = 0 and vary only s:
J A 0 B s = C
This yields up to L distinct conjunctions from the same
pair of tori.
D.4 Ring-Wise XOR Operation
For each ring position i (0 to L-1), apply XOR to the hex
icons of the aligned rings:
text
C_ring[i] = A_ring[(i + r) mod L] XOR B_ring[(i + s) mod L]
The XOR is applied bitwise to the 4-bit representation of
each hex icon.
D.5 Seam Rule
The resulting torus C always has its seam at the top
(position 0), regardless of r and s. Parent seams are not inherited; they are
expunged during conjunction.
D.6 Symmetry Properties
The J function satisfies two logical equivalences:
|
Property
|
Expression
|
|
Double negation invariance
|
EJpqJNpNq
|
|
Cross negation symmetry
|
EJnpqJpNq
|
These ensure that certain sign combinations produce
identical results, limiting the number of distinct conjunctions.
Annex E: D4 Transformation Tables (Rotations
and Reflections)
E.1 Original 4×4 Icon Matrix (Natural Order)
text
Row 0: 0 1 2 3
Row 1: 4 5 6 7
Row 2: 8 9 A B
Row 3: C D E F
E.2 90° Clockwise Rotation
text
Row 0: 9 1 8 0
Row 1: B 3 A 2
Row 2: D 5 C 4
Row 3: F 7 E 6
E.3 180° Rotation
text
Row 0: F B 7 3
Row 1: E A 6 2
Row 2: D 9 5 1
Row 3: C 8 4 0
E.4 270° Clockwise Rotation (90°
Counterclockwise)
text
Row 0: 9 D B F
Row 1: 8 C A E
Row 2: 1 5 3 7
Row 3: 0 4 2 6
E.5 Reflection: Top (T)
text
Row 0: 9 8 1 0
Row 1: D C 5 4
Row 2: B A 3 2
Row 3: 6 7 E F
E.6 Reflection: Right (R)
text
Row 0: 0 1 2 3
Row 1: 4 5 6 7
Row 2: 8 9 A B
Row 3: C D E F
(Identity — verified from whiteboard)
E.7 Reflection: Bottom (B)
text
Row 0: 9 D B F
Row 1: 8 C A E
Row 2: 1 5 3 7
Row 3: 0 4 2 6
(Matches 270° rotation)
E.8 Reflection: Left (L)
text
Row 0: 9 8 1 0
Row 1: 4 5 C D
Row 2: 2 3 A B
Row 3: 6 7 E F
E.9 Programmer Specifications
See attached code files for Python, JSON, and C
implementations of these transformations. The transformation function must:
- Permute
grid positions according to the geometric operation
- Apply
the appropriate icon mapping from the tables above
Annex F: Parameter Enumeration and Divisibility
F.1 Core Parameters
|
Parameter
|
Symbol
|
Range
|
Purpose
|
|
Number of rings
|
L
|
≥ 2
|
Determines torus complexity
|
|
Turn positions per ring
|
K
|
≥ 2
|
Bike lock key space
|
|
Icon grid dimensions
|
m, n
|
≥ 2
|
Maze size (icons)
|
|
Sub-cell dimensions
|
2m, 2n
|
≥ 4
|
Actual path resolution
|
F.2 Combinatorial Multipliers
|
Factor
|
Multiplier
|
Notes
|
|
Maze independence
|
(number of possible mazes)^L
|
Effectively infinite
|
|
Radial permutations
|
(L-1)!
|
From ordering of L rings
|
|
Bike lock settings
|
K^L
|
Per-ring turn choices
|
|
Transformations (D4)
|
Up to 8
|
For asymmetrical mazes
|
|
Conjunction rotations
|
L
|
From JA0Bs
|
F.3 Divisibility via F Separator
A valid path string contains no F (void) icons. Therefore,
F can serve as a delimiter:
text
[path_string] F [metadata]
The metadata field may encode:
- Denomination
(e.g., integer number of base units)
- Version
- Timestamp
- Signature
- Nonce
- Checksum
- Issuer
ID
F.4 Denomination Schemes (Optional)
The exact denomination scheme is not fixed. Examples:
- Hexadecimal
scaling: Metadata = integer n, value = n ×
16^(−L)
- Decimal
scaling: Metadata = integer n, value = n ×
10^(−8) (like Bitcoin)
- Direct
length scaling: Shorter path strings represent
fractional values
Any scheme is permissible as long as parsing at the first F
yields a valid path string on the left.
Annex G: Glossary of Terms
|
Term
|
Definition
|
|
Hermetic maze
|
A maze with an unbroken border; fully enclosed
|
|
Unicursal maze
|
A maze containing a single continuous path with no
branches or dead ends
|
|
Icon
|
A hexadecimal digit (0–F) representing a 2×2 block of
sub-cells
|
|
Sub-cell
|
The smallest unit of maze area; path visits each sub-cell
exactly once
|
|
Void
|
An F icon; indicates sub-cells not visited by the path
|
|
Path string
|
Sequence of hex icons recorded along the unicursal path
|
|
Rarity
|
Frequency 16^−L for a path string of length L; the basis
of value
|
|
Torus
|
A donut-shaped surface formed by joining the ends of a
cylinder
|
|
Ring
|
One of the L circular paths around the cylinder/torus
|
|
Seam
|
The join where cylinder ends meet; defines position 0 on
the torus clock
|
|
Derivative
|
A longitudinal string extracted from a torus; can be a
public coin identifier
|
|
Bike lock key
|
Turn settings applied to each ring; acts as a private key
|
|
Radial permutation
|
The order of rings around the torus; (L-1)! possibilities
|
|
JArBs
|
Conjunction operation: J A r B s = C
|
|
Negation
|
Bitwise complement of each hex icon
|
|
D4 group
|
The eight symmetries of the square (4 rotations, 4
reflections)
|
Author: © E A Thomas 2025
