Working paper · Beta v5.1 · 16 September 2026 · Not an offering

SEMATECT

Proof-of-Forage: sematectonic stigmergy as postage for a public nest

Abstract. SEMATECT is a protocol in which miners search for legal forages on a personal map and, when the search checks, receive a unique brick (an ERC-721 plate). Anyone may spend the native token STCT as postage to pin a work order on an empty hex. The miner who fills that order keeps the plate and the purse; the payer becomes patron of the stall and later collects rent from neighboring builds. The three miner castes implement three published local rules — Dorigo ant-colony optimization, Seeley/Hales comb packing, and Bonabeau termite deposition — not three skins of one tour. A thin SHA-256 lock and a personal map keep a solver from skipping the shift. This paper states the objects, the mathematics, the token rules, and the library they come from. It does not claim that insect mathematics beats an ASIC at SHA-256, and it is not a securities offering.

Problem and one-sentence product
Research library and prior work
Objects of the protocol
Proof-of-Forage
Formica — trail mathematics
Apis — nectar and comb
Macrotermes — deposit mathematics
Work orders, postage, and rent
Tokens and emission
What this is not
References

1. Problem and one-sentence product

Most new tokens either copy a hash grind (SHA-256 and cousins) or copy a smart-contract standard (ERC-20) and then look for a story. SEMATECT starts from a different question: can a visible nest be the ledger, so that work leaves a mark other people can click, hire, and collect rent from?

Miners keep the NFT brick. People who hire the hive keep stall rent. STCT is the stamp.

That sentence is the product. Mining produces a signed plate. Postage directs where the next plate may land. Patronage is title on a stall, not title on the brick. Idle balances do not melt.

2. Research library and prior work

The name SEMATECT is Heylighen’s word sematectonic: coordination by the work-product itself, as distinct from a scent mark [3, 2]. Grassé named the broader fact stigmergy — insects coordinate by changing the nest, not by talking [1]. Wilson split marker stigmergy from sematectonic stigmergy [2]. Ostrom’s design principles for a commons — bounded cells, named users, monitoring — are why a hex you can inspect is part of the protocol and not decoration [12].

The three caste solvers come from three separate literatures, which is why they are not one coin painted three colors:

Caste	Biological / algorithmic source	What the miner must find
Formica	Dorigo Ant System / ACO [4, 5]	A short legal tour on a personal pantry map
Apis	Seeley forage; von Frisch dance; Hales honeycomb [6, 7, 8]	A capacity-limited nectar path plus max-adjacency comb
Macrotermes	Bonabeau–Theraulaz–Deneubourg deposit [9, 10]	A legal drop where local height already invites soil

Camazine et al. collect the construction models [10]. Golden, Levy and Vohra state the orienteering family that the bee path belongs to [11]. The public Research page restates these formulas for a shorter visit.

3. Objects of the protocol

Object	What it is	Who holds it
Hex	One cell of the public 2D nest	Commons; inspectable
Work order	Paid job pinned to one empty hex	Posted by a patron
Postage (STCT)	The stamp that posts that job	Burned / locked at post
Plate (ERC-721)	Signed brick of one legal forage	The miner who laid it
Patron right	Title on the stall, not the brick	Whoever paid postage
Rent	Grain paid when neighbors build	The patron
Epoch	Twelve accepted bricks	Protocol clock

If your own insect fills an order you posted, you spent postage and you still receive that plate, because you did the work.

4. Proof-of-Forage

A certificate that mints must pass four checks.

4.1 Personal map. The map is grown from

$$\mathrm{Map} = G(\mathrm{epoch},\ \mathrm{wallet},\ \mathrm{caste}).$$

Copying a neighbor’s path fails because it is not a path on your map.

4.2 Legal forage. The path $P$ must beat a caste threshold $T$ under the official score $S$:

$$S(P;\ \mathrm{map},\ \mathrm{caste}) \;\text{beats}\; T(\mathrm{epoch},\ \mathrm{caste}).$$

Beating $T$ is the search. Rechecking $S$ is addition. That is the only mining property that matters: search is costly, verification is cheap.

4.3 Thin lock. After the trail is legal,

$$\mathrm{SHA256}(\mathrm{seed}\,\|\,\mathrm{caste}\,\|\,P\,\|\,\mathrm{miner}\,\|\,\mathrm{nonce})$$

must show $k$ leading zero bits. $k$ is not “we are Bitcoin.” It is a well-studied grind so a program that finds a pretty path still pays time. $k$ rises if valid certificates arrive too fast.

4.4 One spend. The wallet has not already spent this epoch. Empty epochs print nothing.

Difficulty also comes from the nest filling. Stages run Foundation → Pillars → Arches → Chambers → Cathedral. More structure means thicker trails and fewer empty docks. That is biological, not a copied Bitcoin target schedule.

5. Formica — trail mathematics

5.1 Source

Dorigo, Maniezzo and Colorni, Ant System (1996); Dorigo and Stützle, Ant Colony Optimization (2004) [4, 5]. Biology: trail laying in Formica / Lasius.

5.2 Local rule

An ant at node $i$ picks the next node $j$ with

$$P_{ij} = \frac{\tau_{ij}^{\alpha}\,\eta_{ij}^{\beta}}{\sum_{k \in A_i} \tau_{ik}^{\alpha}\,\eta_{ik}^{\beta}}, \qquad \eta_{ij} = \frac{1}{d_{ij}}.$$

$\tau$ is scent on the edge. $\eta$ is closeness. After a tour of length $L$, scent evaporates and good tours write more:

$$\tau \leftarrow (1-\rho)\,\tau + \Delta\tau(L).$$

$\rho$ is Grassé’s forgetfulness: old piles fade unless they keep being used [1].

5.3 How this becomes a coin

Score $S$ is integer Euclidean tour length, start and end at the nest, required pantries visited. Target $T$ begins near $\lceil \alpha \cdot \mathrm{MST}\rceil$ of the same points. Anyone re-adds the official distances in milliseconds. Finding the short tour is the work. An amber plate is that signed tour, not a drawing of an ant. A copied bee certificate fails pathLegal for Formica.

6. Apis — nectar and comb

6.1 Source

Seeley, Honeybee Democracy (2010) and the waggle-dance line from von Frisch [6, 7]. Comb geometry: Hales, the honeycomb conjecture — equal hexes are the tightest packing of equal cells on the plane [8].

6.2 Local rule

Forage is prize-collecting / orienteering [11]: start at the nest, collect nectar, stay under crop capacity $C$, return.

$$S_{\mathrm{bee}}(P) = \sum_{v \in P} n(v) \quad \text{subject to} \quad \mathrm{load}(P) \le C.$$

On the public board the next empty gold hex is the cell with the most already-built neighbors (max-adjacency packing). That is why comb grows as a sheet instead of a scattered field.

6.3 How this becomes a coin

A gold plate is a nectar path plus a legal comb dock. It is a different legal object than an ant tour. Copying an amber receipt onto a bee map fails.

7. Macrotermes — deposit mathematics

7.1 Source

Bonabeau, Theraulaz and Deneubourg; construction chapters in Camazine et al., Self-Organization in Biological Systems [9, 10].

7.2 Local rule

Pickup and drop are sigmoids of local density $q$:

$$P_{\mathrm{pick}} = \left(\frac{k_1}{k_1+q}\right)^2, \qquad P_{\mathrm{drop}} = \left(\frac{q}{k_2+q}\right)^2.$$

Insects pick from thin spots and drop on thick spots. A mound grows with no blueprint.

7.3 How this becomes a coin

A sage plate is legal only if the brick lands on an allowed dock and the local height rule is satisfied. It is not an ant tour painted green.

8. Work orders, postage, and rent

A work order is how a stranger directs the nest without owning the mason.

Patron locks postage $n$ STCT on an empty hex. The hex shows a dashed order.
First legal dock on that hex fills it. Miner takes $n$ and the plate.
Poster becomes patron of that stall.
Later legal bricks on adjacent hexes pay rent to that patron.

Why pay: you are buying a stall on a street that may get busier, not a picture. Quiet corners pay nothing. Colony treasury should post the first year of orders so miners have customers before strangers arrive.

Mainnet is not justified until work orders are the only way to direct growth, and until some people post more than once.

9. Tokens and emission

9.1 STCT (ERC-20)

Postage. Cap $1\,000\,000\,000$. Planned network: Base.

Slice	Share	Rule
Mined	80%	Epoch budgets. Empty epoch prints 0. No admin mint.
Colony treasury	12%	Locked. Posts work orders. Runway.
Founder	8%	Cliff + vest.

9.2 Plates (ERC-721)

One unique brick per legal placement. Oldest epochs are finite. Secondary sale split, beta:

Share	Goes to
90%	Seller
5%	Protocol / founder
2.5%	Filling miner, if different
2.5%	Older neighboring plates

A small buyer tithe feeds the colony work-order budget. Optional ERC-1155 epoch sash: “I foraged in epoch $N$.” Fungible per epoch. Not the brick.

9.3 Foreign money

Year one lives on Base. Visitors may later fund a purse in ETH or USDC. Rent and membership stay in STCT, so foreign money walks in without turning STCT into a sticker.

10. What this is not

We claim	We do not claim
Search is real; the check is public	This pays like Bitcoin
Three published local rules, not three skins	Nature beats ASICs
A plate is a signed brick you can point at	Citations create a market
Postage + rent is a reason to use STCT	This is a live ticker today

There is no mainnet STCT until the contract address is published on this site. Do not buy a ticker that claims to be this project without that address.

11. References

Grassé, P.-P. (1959). La reconstruction du nid et les coordinations interindividuelles chez Bellicositermes. Insectes Sociaux.
Wilson, E. O. (1975). Sociobiology. (sematectonic vs marker stigmergy)
Heylighen, F. (2016). Stigmergy as a universal coordination mechanism. Cognitive Systems Research and related essays.
Dorigo, M., Maniezzo, V., & Colorni, A. (1996). Ant system. IEEE Trans. Systems, Man, and Cybernetics.
Dorigo, M., & Stützle, T. (2004). Ant Colony Optimization. MIT Press.
Seeley, T. D. (2010). Honeybee Democracy. Princeton.
von Frisch, K. (1967). The Dance Language and Orientation of Bees.
Hales, T. C. (2001). The honeycomb conjecture. Discrete & Computational Geometry.
Bonabeau, E., Dorigo, M., & Theraulaz, G. (1999). Swarm Intelligence. Oxford.
Camazine, S., et al. (2001). Self-Organization in Biological Systems. Princeton.
Golden, B., Levy, L., & Vohra, R. The orienteering problem.
Ostrom, E. (1990). Governing the Commons. Cambridge.

This draft describes a protocol. It is not investment advice and not an invitation to buy a token.