Preview · doctrine v6.0 · companion to the white paper · not an offering · STCT is not live yet

Research and mathematics

The nest is not a mascot. Three published local rules decide what a legal brick is. Anyone can re-check a receipt in milliseconds. That is why mining can be work instead of a picture of insects.

This page is the math companion to white paper v6.0. Same nest as the How page: one nest that does not reset, STCT stamp required, optional bait in ETH / USDC / wrapped BTC / STCT, private puzzle per miner and hex. v6.0 keeps these formulas and adds Tickets — shop coupons, not a second coin. What follows is the same library and the same formulas as the paper — written so you can read it on a phone.

1. The idea we borrowed

Stigmergy (Grassé, 1959) [1]. Insects coordinate by changing the ground, not by talking. A pellet on a pile is an instruction to the next insect. Our hex board works the same way: a brick, a work order, bait, and a Ticket on a cell are the messages. A living nest has no match clock. The ground is the memory [1, 10].

Sematectonic (Wilson, 1975; Heylighen, 2016) [2, 3]. Sometimes the work itself is the sign — sêma (sign) + tektōn (builder). SEMATECT is Wilson’s word. The miner’s paycheck is the wage for the work. The STCT stamp is the marker that says “build here.” Bait is extra food on that same mark. The shop’s ERC-721 deed is the door they hired. A Ticket is a coupon the shop leaves on a finished hex [1, 3].

A visible commons (Ostrom, 1990) [12]. Bounded cells, named users, work you can inspect. Hayek [13] is why the puzzle stays private even though the board is public.

2. What each local rule must find

On the nest camera these are not playable classes. They are the local rules a certificate may use. Miners are units: cream for you, purple for others.

3. Public nest, private puzzle

$$\mathrm{Map} = G(\mathrm{hex},\ \mathrm{wallet},\ \mathrm{caste},\ \mathrm{nestRoot})$$

Copying a neighbor’s path fails. There is no wall-clock round. Coins already held do not evaporate.

4. Proof-of-Forage — four checks

1. The path $P$ is on that miner’s map for that hex.
2. $S(P;\ \mathrm{map},\ \mathrm{caste})$ beats $T(\mathrm{hex},\ \mathrm{caste},\ \mathrm{nest})$.
3. $\mathrm{SHA256}(\mathrm{seed}\,\|\,\mathrm{caste}\,\|\,P\,\|\,\mathrm{miner}\,\|\,\mathrm{nonce}\,\|\,\mathrm{hex})$ shows $k$ leading zero bits.
4. First valid certificate for that open work order wins. A click is not a certificate.

5–7. Local-rule math

Formica tour: $P_{ij} = \tau_{ij}^{\alpha}\eta_{ij}^{\beta}/\sum_k \tau_{ik}^{\alpha}\eta_{ik}^{\beta}$, $\eta_{ij}=1/d_{ij}$, $\tau \leftarrow (1-\rho)\tau + \Delta\tau(L)$ [4, 5].

Apis: $S_{\mathrm{bee}}(P)=\sum_{v\in P}n(v)$ subject to $\mathrm{load}(P)\le C$ [6, 7, 11]. Comb dock is max-adjacency [8].

Macrotermes: $P_{\mathrm{pick}}=(k_1/(k_1+q))^2$, $P_{\mathrm{drop}}=(q/(k_2+q))^2$ [9, 10].

$T$ tightens as the nest gets busier. Later hexes take longer to chew. They still mint 1 STCT on first finish.

Full formulas and citations stay in white paper v6.0.

8. Stamp, bait, deed, Ticket

Stamp is required STCT postage to hire a hex. Bait is optional ETH / USDC / wrapped BTC / STCT, or another listed coin. First legal certificate on a dirt hex: miner takes 1 STCT from the mint cap and 95% of construction bait. Protocol takes 5% at load. The work-order poster receives the ERC-721 storefront deed. The miner does not receive that NFT. You cannot mint a deed of your own wall.

A Ticket is a shop-funded coupon pinned on a finished green hex. It is not STCT, not bait, and not a second ticker. A steered miner may pick it up. Autopilot may not. One visit drop and one Ticket per visitor per shop per the 24-hour clock.

After 24 hours a finished dirt hex can be worked again for bait, a visit drop, or a Ticket. It does not mint a second STCT. Shop tiles stay green. The deed stays with whoever holds the 721.

9. Frontier, marks, and the mint cap

Hexes and coins are not the same object. The nest can grow forever. STCT cannot.

When a rim hex is filled, its missing neighbors become new open jobs. The camera only draws the finished bricks plus a thin ring of work. That is the same trick tilemaps use so a world can be large without drawing every cell at once [15, 16].

Gold fill means the hex was mined for STCT. Green fill means storefront. Who holds the door is the 721 owner. Who built it can still show on the ledger.

Three marks on a hex [paper §7]:

• First build — blue on a dashed hire. Steered miner only. Pays 1 STCT + 95% bait. Mints the 721 to the poster.
• Visit drop — blue on a finished green hex. Hand only. Pays one drop. No second STCT. No second 721.
• Ticket — cream diamond on a finished green hex. Steered miner only. Coupon into the pouch. Not cash.

Mint cap $S_{\max}=10^{9}$ STCT. Let $M$ be minted so far. First finish of coordinate $(q,r)$ mints 1 STCT if that coordinate has never been finished:

$$\mathrm{mint}(q,r)=\begin{cases}1 & \text{if }(q,r)\text{ has never been finished}\\0 & \text{otherwise}\end{cases}\qquad \sum \mathrm{mint} \le 10^{9}$$

Tickets and bait already sitting in a budget are not new mint. The 24-hour reopen does not increment $n$. Difficulty later is a longer chew, not “no tile left.” Same split Nakamoto used: blocks keep coming, new coin does not [14].

White paper v6.0 · Aisle · How it works

References

1. Grassé, P.-P. (1959). La reconstruction du nid… Insectes Sociaux.
2. Wilson, E. O. (1975). Sociobiology.
3. Heylighen, F. (2016). Stigmergy as a universal coordination mechanism.
4. Dorigo, M., Maniezzo, V., and Colorni, A. (1996). Ant system.
5. Dorigo, M., and Stützle, T. (2004). Ant Colony Optimization.
6. Seeley, T. D. (2010). Honeybee Democracy.
7. von Frisch, K. (1967). The Dance Language and Orientation of Bees.
8. Hales, T. C. (2001). The honeycomb conjecture.
9. Bonabeau, E., Dorigo, M., and Theraulaz, G. (1999). Swarm Intelligence.
10. Camazine, S., et al. (2001). Self-Organization in Biological Systems.
11. Golden, B., Levy, L., and Vohra, R. The orienteering problem.
12. Ostrom, E. (1990). Governing the Commons.
13. Hayek, F. A. (1945). The use of knowledge in society.
14. Nakamoto, S. (2008). Bitcoin.
15. MDN Web Docs. Tiles and tilemaps overview.
16. Chunked tilemaps and camera culling.