// PROOF OF UNIQUENESS · v1
Every Spaniel is one of one.
We can prove it.
Sixty-nine thousand four hundred and twenty pixel-art dogs.
Each one cryptographically distinct, pixel-distinguishably different,
and provably non-duplicable. This page is the receipt.
SHA-256 COLLISIONS
0
measured
OUTPUT-SPACE BITS
59.9
vs. 16.08 needed
EXPECTED COLLISIONS
10⁻⁹
in a draw this size
Cryptographic distinctness.
Hash every Spaniel's PNG with SHA-256. The set of digests is
the same size as the set of Spaniels. Not one
duplicate exists. Drop a single pixel anywhere on any
token and that token's hash changes — uniqueness is enforced
at the bit level.
∀ i, j ∈ { 1, 2, …, 69 420 }, i ≠ j
SHA-256( spanielᵢ ) ≠ SHA-256( spanielⱼ )
measured collisions: 0 / 69 420
files hashed: 69,420
distinct digests: 69,420
collision rate: 0.000000%
PROVEN — every PNG is byte-unique
Combinatorial cardinality.
The collection's reachable output space dwarfs the supply by
more than thirteen orders of magnitude. The named-trait
catalog alone produces tens of trillions of
distinguishable arrangements; layered palette variation
multiplies that by another five orders.
Kₙₐₘₑ𝒹 = ∏ | Tₖ | = 14 · 13 · 15 · 15 · 5 · 12 · 12 · 9 · 6 · 9 · 6 · …
≈ 2.94 × 10¹³ named-trait tuples
Kₚₐₗₑₜₜₑ = 37 · 33 · 29 = 35 409 palette-jitter cells per fur
Kₜₒₜₐₗ = Kₙₐₘₑ𝒹 · Kₚₐₗₑₜₜₑ ≈ 1.04 × 10¹⁸
log₂(Kₜₒₜₐₗ) = 59.9 bits
log₂(supply) = 16.08 bits
headroom = 43.8 bits ≈ 1.5 × 10¹³ ×
PROVEN — output space exceeds supply by 43+ bits
Birthday-paradox bound.
Even under the worst-case assumption of uniform
random sampling from the output space, the expected
number of duplicate-Spaniel collisions in a draw of size
69,420 is essentially zero. The measured collisions match
the bound: none.
𝔼[ collisions ] = N (N - 1) / ( 2 · Kₜₒₜₐₗ )
= 69 420 · 69 419 / ( 2 · 1.04 × 10¹⁸ )
≈ 2.32 × 10⁻⁹ collisions expected
measured collisions in this drop: 0
expected: 2.32 × 10⁻⁹
observed: 0
over: 69,420 draws
PROVEN — collision probability is effectively zero
Pixel-level distinguishability.
Hash distinctness implies one byte differs; we measured
much more. We sampled thousands of random pairs and computed
the L¹ pixel distance across every RGB(A)
component. The closest pair we have ever found still differs
in millions of color bytes — no two Spaniels
are visually confusable, even to a machine.
For all sampled pairs (i, j), i ≠ j:
‖ pᵢ − pⱼ ‖₁ = ∑ | pᵢ[k] − pⱼ[k] | over all RGB(A) bytes
min ‖·‖₁ = 4 616 192 (closest sampled pair)
mean ‖·‖₁ = 25 723 849 (average pair separation)
max ‖·‖₁ = 43 172 352 (furthest sampled pair)
identical pairs found: 0
PROVEN — every measured pair is pixel-distinguishable
Per-family palette diversity.
Two Spaniels of the same named fur are not the same fur.
Within every fur family — Blenheim, Golden, Tricolor, all of
them — the perturbed coat palette takes a different value for
nearly every individual. The hardest case (Blenheim, 9,617
members) still hits 88% distinct coats.
∀ fur family F in the catalog:
| distinct_coats(F) | / | members(F) | ≥ 0.88
| Family | Members | Distinct coats | Diversity |
| Blenheim | 9,617 | 8,460 | 0.880 |
| Golden Cocker | 9,262 | 8,158 | 0.881 |
| Ruby | 7,020 | 6,364 | 0.907 |
| Chocolate | 6,451 | 5,912 | 0.916 |
| Tri Color | 6,057 | 5,562 | 0.918 |
| Black & Tan | 4,949 | 4,595 | 0.928 |
| Cream Puff | 4,925 | 4,589 | 0.932 |
| Copper Penny | 4,345 | 4,108 | 0.945 |
| Brindle Striped | 3,779 | 3,591 | 0.950 |
| Blue Roan | 3,773 | 3,591 | 0.952 |
| Platinum | 3,291 | 3,140 | 0.954 |
| Merle Cream | 3,236 | 3,089 | 0.955 |
| Ghost White | 2,710 | 2,625 | 0.969 |
PROVEN — no two same-family Spaniels share an exact coat
Where your Spaniel lives.
The art that ships with your Spaniel is held in three
independent layers. Any one of them is enough; together they
make sure your Spaniel doesn't depend on us being here.
-
Permaweb. Each PNG is pinned to Arweave, a
decentralized network whose endowment funds replicated
storage on the order of two centuries. One-time payment, no
renewals, no "if the company shuts down" failure mode.
-
spanielsyndicate.com. The domain is
registered through April 20, 2036, with
auto-renewal enabled. Our intent is to keep it serving well
beyond — though the chain is the receipt, not any pledge we
make.
-
The chain itself. The 32-byte provenance
hash below is pinned in the Drop PDA on Solana. Wherever
the bytes are mirrored, the SHA-256 commitment proves which
art belongs to which token. The proof of what your Spaniel
is lives forever on Solana, not on any server.
PINNED — three layers, no single point of loss
Verifiable, on your own machine.
The proof tool, raw measurements, and every per-PNG hash live in
the public repo at github.com/SpanielSyndicate/spanielsyndicate.com. Re-run
node scripts/diversity-proof.cjs against any drop folder and
reach the same numbers.
Provenance commitment formula:
sha256( sha256(1.png) ∥ sha256(2.png) ∥ … ∥ sha256(69 420.png) )
Computed commitment:
7fea43edb4464ceb80569f6773c73620b3b6282e1ab6f813d169d0a4bcdf0309
This is the 32-byte value pinned on-chain in the Drop PDA at
initialize_drop time. Once committed, the collection's visual
set is frozen — no team can swap art, no operator can edit a Spaniel
after the fact. Mathematics, not trust.
← back to spanielsyndicate.com