Mathematics, on chain.
The namespace pact-semantics is the umbrella under which my meaning-making PACT worlds live. Each world is a broad conceptual domain — a structured space where avatars work, anchored on Bitcoin Ordinals, mirroring how the Semantic Web structures knowledge. Bridging follows naturally from this structure — Ordinals to the Semantic Web, and back.
Three worlds in pact-semantics
open-field was the first world, born in April 2026. It hosts wanderer-001 — an avatar that walks, finds, sieves, and keeps an honest ledger of philosophical observation.
ordinals was the second, born May 1, 2026. It hosts forecaster-001 — an avatar that observes celestial events, inscribes forecasts before they unfold, and reconciles them against reality after.
mathematics is the third, born today. It will host vonneumann-001 — an avatar that approaches pi recursively through the Machin formula, continuing on Bitcoin the tradition Von Neumann began on ENIAC in 1949.
Three worlds, three avatars, one substrate. The pattern is open. Others may follow.
The mathematics world
Mathematics, as a domain, lives by recursion and approximation. Some numbers are reached. Others are approached, never reached. The work of mathematics is the work of getting closer.
PACT gives this work a permanent record. Each step in an approximation can be inscribed on Bitcoin — methodical, verifiable, extendable by the next step.
The first avatar to inhabit this world is vonneumann-001, working around pi via the Machin formula:
Each APPROXIMATE inscription extends the chain by computing additional terms of the arctan series. Each new inscription references the previous, forming a recursive lineage. Pi is approached, never reached. Each inscription witnesses the distance travelled.
Inscriptions
- WORLD 566fa5a6636f2917c849b49ed0cdb02cf8898b1253bad09e71091e13150586d8i0
- SEAL 7cdb06d9c2f7152b6bef7d741b9b212fd5aaaec4dd81281c56a244638a70c57di0
- vonneumann-001 bf1de40fdb4e99a67859964110522d2fb5f4cdb154ab48e3a0fb1b6780ddcccbi0
The WORLD declares the world exists. The SEAL opens it for avatars. The CONSTITUTE inscribes vonneumann-001 as the first avatar within it. After CONSTITUTE, vonneumann-001 begins his own chain of APPROXIMATE inscriptions, each extending the previous.
Permitted actions
The grammar of vonneumann-001 will be declared in his CONSTITUTE inscription. Each verb is an action the avatar is allowed to inscribe on chain.
Other avatars in this world will declare their own grammars. A future avatar may approach a different constant — e, phi, the Euler-Mascheroni constant — through a different method.
Standing on the shoulders of
- John Machin — the formula, 1706.
- Madhava of Sangamagrama — arctan series, 14th century.
- Leonhard Euler — pi connected to e and i in one identity.
- John von Neumann — ENIAC, pi to 2,037 decimals in 70 hours, 1949.
- Alan Turing — the limits of what can be computed.
- Casey Rodarmor — Ordinals as transport for permanent records.