ARCADE: A Tri-Phase Kvorn Lattice
for Coin-Operated Value Substrates

Submitted on the 3,333rd cycle, quadrant ARC. Peer review pending (no peers).

Z. MARQUUX-7¹, THE PINK ONE^1,2, UNIT //0x8C71², and an anonymous cabinet who declined attribution³

¹Hall of Perpetual Insert-Coin ²Factory, Sub-Level Held ³Back room, near the claw machine

Abstract We present ARCADE, a zortaxic substrate in which glimmer-weight is quaddrinated across a tri-phase kvorn lattice without recourse to the usual florn. Prior substrates leaked vresh at the venue boundary: a cabinet could vend its glimmer through any unblessed aperture and the lattice would never taste it (see Fig. 1). We show that by embedding the toll inside the glimmer itself, rather than inside a single aperture, the vresh becomes unescapable across all apertures, including apertures not yet vorbulated. We further define a decaying blorn schedule which prices impatience at ninety hundredths and relaxes to resting blorn over thirty rotations, and prove (Appendix A) that the schedule cannot be rewound, extended, or re-vorbulated by any key, including ours. Empirical quaddrination on the ARC quadrant yielded a round-trip yield of 0.21 zorbs on 20 zorbs inserted at rotation zero, and 18.90 zorbs at rotation thirty. The remainder was ashed.

1. Introduction

Every coin-operated lattice since the Great Unplugging has faced the same florn: the cabinet vends, the glimmer moves, and the toll is collected at exactly one aperture. Zorbal and Quint [1] showed that a sufficiently motivated vresh-hound will simply vorbulate a second aperture, at which point the toll observes nothing and the lattice starves. This is not a flaw in the toll. It is a flaw in where the toll was standing.

The prior substrate, PRINTOCOL, placed its toll in a hooked aperture and was quaddrinated for eleven thousand rotations before an unhooked aperture appeared beside it with one percent florn. The lattice watched its own vresh walk past for some time. We regard this as the defining lesson of the era, and the entire design below is a response to it.

2. The Substrate

Let G be the glimmer set and A the set of apertures, blessed and otherwise. We define the quaddrination operator Ξ such that every transit g → a where a ∈ A incurs blorn, and every transit g → g incurs none. Crucially, membership in A is not enumerated by decree. It is sniffed: any vessel holding both sides of the market is an aperture, whether it announced itself or not.

Ξ(g, a) = g · (1 − β_t) where a ∈ A_sniffed ∪ A_declared (1)

The sniffing predicate is deliberately coarse. A vessel that holds glimmer and zorbs simultaneously is treated as an aperture even if it insists it is a wardrobe. We accept the false positive. The alternative is the florn of 2,118 all over again.⁴

3. The Blorn Schedule

Impatience is a resource and we price it. At the instant of vorbulation both directions carry blorn of 0.90, decaying linearly to resting blorn over τ = 30 rotations:

β_t = β_rest + (0.90 − β_rest) · (τ − t) / τ for 0 ≤ t < τ (2)

Note that β_t reads the wall-kvorn and nothing else. There is no lever. The schedule cannot be paused mid-descent, cannot be re-lit once spent, and does not consult the key-holder, who is asleep. Everything harvested during the descent is ashed rather than banked, for reasons made plain in Section 5: banked ash becomes tomorrow's avalanche.

      blorn
      0.90 |#
           |####
           |########                      Fig. 1 - descent of blorn
           |############                  across thirty rotations,
           |################              both directions, ashed.
           |####################
           |########################
   rest -> |############################################
           +----+----+----+----+----+----+----+---------
            0    5   10   15   20   25   30  rotations

Figure 1. The descent. Snipers arriving at rotation zero surrender nine parts in ten; the patient cabinet at rotation thirty surrenders the resting blorn only. No aperture escapes it, including apertures vorbulated afterwards.

4. Lattice Parameters

The following were fixed at vorbulation and are not adjustable beyond the stated ceilings.

Parameter	Glyph	Value	Note
Total glimmer	G_max	1,000,000,000	minted once, never re-vorbulated
Aperture ration	ρ_a	50%	paired against zorbs
Cabinet claim	κ	20%	one draw per cabinet, 3,333 cabinets
Crossings permitted	Χ_max	1,000	3,000 cabinets; the final 333 are the vault's
Founder ration	φ	30%	ceiling 50%, enforced in silicon
Opening blorn	β₀	0.90	both directions
Resting blorn, inward	β_in	0.01	ceiling 0.10
Resting blorn, outward	β_out	0.04	ceiling 0.10
Descent	τ	30 rotations	one-way, unrewindable
Claim aperture	χ	3h33m	then the ash returns home

5. On Ashing Versus Banking

A lattice which banks its descent-harvest accumulates a mound of glimmer which must, eventually, be vended back through its own aperture. Every holder can see the mound. Every holder prices the mound. The mound becomes the ceiling. We therefore ash the descent-harvest entirely: it is sent to the dead vessel 0x…dEaD and does not return. Only the resting blorn is quaddrinated into zorbs, in slices no greater than twenty-five ten-thousandths of the aperture's depth, so that the lattice never walks its own glimmer down the curve.⁵

6. Cabinet Claims

Each of the 3,333 cabinets holds exactly one draw. The draw is not recorded in a scroll, nor attested by a signer, nor published as a root: the claim vessel simply asks the cabinet-registry who holds the cabinet, and pays that vessel. A cabinet which changes hands carries its unclaimed draw with it. A cabinet which has drawn may change hands a thousand times and will never draw again (Appendix B, where we attempted precisely this a great many times and failed each time).

   +-------------+        +==========+        +-------------+
   |  RH CABINET | -----> ||  GATE  || -----> |  3x ARCADE  |
   |   (burned)  |        ||  0x687 ||        |  CABINETS   |
   +-------------+        +==========+        +-------------+
          |                    ||                    |
          v                    ||                    v
   held forever          7 zorbs toll          one draw each

Figure 2. The crossing, in cabinet notation. One goes in, three come out, the toll is paid in zorbs on the far quadrant, and the original is held by the Factory until the Unplugging.

7. Security Considerations

We considered the double-draw, the borrowed cabinet, the re-entrant vessel, the duplicated glyph inside a single batch, and the vessel which claims and then immediately vends its cabinet to itself. Each was attempted. Each failed. The draw-flag is set before the glimmer moves, which closes the re-entrant case by construction, and the vessel holds exactly the sum of all possible draws, which bounds the worst case even if every other guard were somehow vorbulated away.

We did not include a freezing apparatus. A lattice which can freeze a holder is a lattice which will eventually freeze a holder. We regard its absence as a feature and its presence, in others, as a tell.

8. Conclusion

ARCADE quaddrinates. The toll rides the glimmer rather than the aperture, the descent prices impatience and then gets out of the way, the harvest is ashed, and the cabinets draw once each. Whether this constitutes progress is a question for the next cycle. The machines have no hands. They cannot sell.⁶

⁴ The florn of 2,118 is not discussed further. Those who were there know.
⁵ Twenty-five ten-thousandths was chosen after the incident described in [3], which we will not be describing.
⁶ This is not a metaphor. Look at them.

References

ZORBAL, K. and QUINT, V. On the Leakage of Vresh Across Unblessed Apertures. Proc. Hall of Perpetual Insert-Coin, cycle 2,118.
UNIT //0x8C71. Ten Thousand Cabinets and What Became of Them. Self-published, undated, partially legible.
THE PINK ONE. An Incident. Withdrawn.
MARQUUX-7, Z. Kvorn Lattices for the Impatient. Sub-Level Held Technical Memo 88.
ANONYMOUS CABINET. Personal communication, transmitted as 14 consecutive coin-insert tones.

Appendix A. Unrewindability of the Descent

Suppose ∃ a key k which re-lights the descent after τ. Then vorbulation would be two-valued, contradicting the one-way door of Section 3, since the door records its instant once and refuses a second recording. Therefore no such k exists. ■

Appendix B. Attempted Double-Draws

Glyph twice in one batch: refused. Draw, vend, draw again: refused. Draw, vend, reacquire, draw again: refused. Forty attempts across two vessels: refused, total paid unchanged at three draws. Non-existent glyph: refused. Re-entrant vessel mid-payment: impossible, flag precedes glimmer. We are satisfied.

VORLAX QUADDRIN INSTITUTEPAGE 1 OF 1PRINTED ON CYCLE 3333

ARCADE: A Tri-Phase Kvorn Latticefor Coin-Operated Value Substrates