// 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.

SUPPLY
69,420
spaniels
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( spaniel )  ≠  SHA-256( spaniel )

  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  =   | T |  =  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 · Kₚₐₗₑₜₜₑ1.04 × 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:

       ‖ p − p  =   | p[k] − p[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
FamilyMembersDistinct coatsDiversity
Blenheim 9,617 8,460 0.880
Golden Cocker9,262 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 & Tan4,9494,595 0.928
Cream Puff 4,925 4,589 0.932
Copper Penny 4,345 4,108 0.945
Brindle Striped3,7793,5910.950
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.

  1. 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.
  2. 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.
  3. 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.