The Transaction Ledger: Mechanics of the moore26 Vacuum

This document formalizes the transaction rules (chain_share, dir_bias, and the surplus toll) governing the moore26 engine. These rules dictate how transient kinetic flux weaves stable topological matter, illustrating how local routing protocols scale into quantum field mechanics. The following analysis strictly separates measured integer data from physical interpretations.

I. The Master Switch: Asymmetric Deposition (dir_bias)

The Mechanic — The dir_bias parameter defines how incoming linear momentum (nu) is transduced into bound rotational circulation (dd). When a packet is absorbed, this rule determines whether the deposited energy distributes symmetrically or biases toward a specific channel.

The Physical Proof — The parameter map cleanly isolates dir_bias as the primary driver of bound circulation. At dir_bias = 0 (symmetric deposition), the test knot failed to retain circulation, yielding dd = 12. At dir_bias = ±256 (maximum asymmetry), the knot successfully built and held a circulation of dd ≈ 245.

The Verdict — Without a strictly asymmetric deposition rule, the lattice cannot convert linear momentum into bound circulation. dir_bias functions as the master switch for the existence of matter on the substrate; without it, topological structures cannot form or persist.

II. The Chained Relay: Volumetric Routing (chain_share)

The Mechanic — When a node confirms a transaction, chain_share dictates that it forwards a fraction of its flux along the dominant dd channel. This mechanism allows signals to propagate node-to-node through dense structure, following established topological rails rather than radiating blindly.

The Physical Proof (Orthogonal Independence) — In the interlocked Hopfion probe, two perpendicular {111} rings were linked through shared intersection nodes. Both rings survived essentially at their seed values (Ring A: dd=1436, Ring B: dd=1439). Furthermore, in an anti-parallel intersection test, counter-rotating streams coexisted on the exact same edge pair without canceling, establishing a high-balanced occupancy (a ≈ b).

The Verdict — The chain_share routing proves that chains negotiate by channel member (axis) rather than by a scalar node bucket. This defines the substrate as a fully directional tensor. It provides the literal structural origin for linear superposition: orthogonal waves can occupy the exact same spatial coordinates without collision, and anti-parallel exchanges can share an edge seamlessly.

III. The Surplus Toll: Topological Protection & Conservation

The Mechanic — To prevent chained routing from acting as a perpetual-motion spin-drive, the engine exacts a toll on chain_share. This toll deducts cnu exclusively from the winding above the committed pair floor (min(a,b)).

The Physical Proof — Under legacy pre-conservation rules (no toll), chained re-offers acted as an unbounded pump, driving a knot's dd to 7.7 million. A naïve "full toll" overcorrected by consuming the bond itself, collapsing a dimer's circulation to dd = 3. The "surplus toll" resolved this entirely: by deducting only from the uncommitted margin, the dimer established a perfectly stable dd = 519 plateau.

The Verdict — The surplus toll formally partitions the discrete ledger into two physical regimes: a protected structural track (the locked, committed bond) and a consumable signal margin (the transient flux). This rule ensures that propagating signals pay their required thermodynamic friction costs exclusively from ambient noise, preventing them from eroding the foundational structure they ride on.

IV. The Resonant Dimer: Virtual Particle Exchange

The Mechanic — The simplest possible bound state is tested by isolating a two-node system, seeding it with balanced, anti-parallel dd pointing directly at each other, and injecting a kinetic packet to trigger the chain_share routing.

The Physical Proof — When 10 packets (1,000 nu) were injected into the isolated dimer, the energy did not dissipate into a free-packet orbit. Instead, the two nodes entered a continuous offer-confirm exchange, accreting the packet energy into a self-reinforcing topological bond. This binding energy plateaued at exactly +219 dd.

The Verdict — This establishes that a quantum bound state on the moore26 substrate is not a static geometric shape, but a continuous, active transactional exchange. Analogous to a binding exchange mediated by virtual particles, the dimer dynamically ratchets ambient kinetic energy into finite, stable topological tension.