space accounting

a short whitepaper on exclusive ownership of three-dimensional space.

what. a protocol invariant: in a named frame, two exclusive claims do not occupy the same volume at the same time. claims are TSP-2 Cards whose identity includes a solid; ownership of the Card is who may transfer and lease it; exclusive occupation of the solid is what makes the Card a title in space, not a sticker on an id.

why. graph edges and owner_count(id) = 1 stop double token ownership. they do not stop double place ownership. without a geometry invariant, two Cards can name overlapping ground — the failure mode of every paper and most digital land registries. markets, cities, and off-world settlement all need the second invariant before the first is worth much.

built on TSP-2, marketplace (time), location proof and space doctrine (frames), services (land verbs). presentation lives in cyb / mir / Bevy and is never authority. intellectual debt to Galt Project's double-ownership analysis (polygon exclusivity + deposit challenge); this note generalizes it to 3D frames and the soft3 stack.

→ related: marketplace-spec calendars · land rights agreement · century index

1 · the problem

1.1 three contracts of a place

any durable society over land rests on roughly three contracts (Galt):

1. rules — who may do what
2. property accounting — who has exclusive claim on which region of space
3. budgets — how protection and commons are funded

cyberia already designs (1) as workflows and (3) as community / marketplace cashflows. (2) is incomplete: services models land.buy as moving a TITLE edge; TSP-2 guarantees one owner per Card id. neither says this volume is not already titled.

1.2 double ownership

double ownership of space = two exclusive claims whose solids intersect in the same frame (and, if timed, in the same interval).

state registries fail here not for lack of maps but for lack of code: a human can insert a conflicting record; the conflict is a court case. blockchain registries that only store "token #42 owned by A" import the same hole — uniqueness of id is not uniqueness of place.

land and built volume are special among assets: they physically exclude. two parcels cannot share the same coordinates. that is a mathematical property. algorithms can enforce absolute consistency of a spatial registry if solids are explicit and intersection is checked.

1.3 what soft3 already solves (and does not)

bevy in cyb is the shell (window, input, world switch). mir paints the knowledge graph in spectral R³. neither is a cadastre. space accounting is a state layer; engines are views.

2 · principles

1. geometry is identity, not metadata. a title without a solid is a social label; a solid without exclusive check is a drawing.
2. frames before coordinates. every solid lives in a named frame (Earth WGS84, body-local, virtual map). no cross-frame ownership without explicit transform + policy (space doctrine).
3. two conservations. id: owner_count(id) = 1. space: exclusive solids in a frame are pairwise disjoint (over overlapping validity intervals).
4. pair challenges beat global scans. full "new solid vs all" is off-chain or side; on-chain (or proven) kernel checks pairs — deposit-backed (Galt option 2).
5. hierarchy is containment. children ⊆ parent; siblings exclusive. split/merge are pure geometry ops inside parent bounds.
6. time is orthogonal. exclusive when is the marketplace calendar on a fixed SpaceClaim id; exclusive where is this protocol.
7. presentation is not authority. Bevy entities, mir particles, map JSON are snapshots of committed claims — never the registry.

3 · model

3.1 frame

Frame {
  id:     FrameId
  kind:   EarthWGS84 | BodyLocal(body) | Virtual(map_id) | GraphSpectral  // last = viz only, no titles
  basis:  geodetic | metric-local | abstract
  parent: Option<FrameId>
}

property and settlement live in local frames. inter-frame maps use ephemeris-style public transforms where needed; speculative claims on world X vest when location proof grounds that frame (space doctrine).

3.2 solid (geometry ladder)

ledger primitives stay simple enough to check deterministically:

Prism (canonical Earth and city case):

Prism {
  ring:  [(x, y); n]   // closed, simple; WGS84 lon/lat or local meters
  z0, z1: Real         // height band; z1 ≥ z0
}

intersection of two exclusive claims:

1. project rings to a plane (Mercator for lon/lat, identity for local meters)
2. 2D polygon intersection (Weiler–Atherton / Martinez–Rueda class)
3. height intervals overlap

land-only titles may set z-band to "full column" policy; rooms use tight bands (Galt). free-form 3D (caves, orbital hulls) upgrade to L2 convex pieces under the same challenge rules.

3.3 SpaceClaim (TSP-2 Card)

SpaceClaim {
  id:           CardId
  frame:        FrameId
  solid:        Solid              // L1 or L2
  content_hash: Hash               // optional L3 topology / BIM / media (IPLD)
  rights:       Title | Lease | Easement | Air | Subsurface | …
  valid:        Option<[t0, t1]>   // None = perpetual until burn
  parent:       Option<CardId>     // nesting
  deposit:      Coin               // challenge bond
}

rights types modulate exclusivity:

• Title — full exclusive solid
• Lease — exclusive for valid (or calendar windows via marketplace)
• Easement / Air / Subsurface — typed non-title layers; may share XY with different z or different right class under explicit rules

default product for cyber valley plots: Title prism + optional lease windows on the same id.

3.4 invariants

for all committed exclusive claims C, D in frame F:

(I1)  owner_count(C.id) = 1                         // TSP-2
(I2)  if exclusive(C) ∧ exclusive(D) ∧ C ≠ D
        ∧ time_overlap(C.valid, D.valid)
        then  solid(C) ∩ solid(D) = ∅
(I3)  if C.parent = P  then  solid(C) ⊆ solid(P)
(I4)  split(P → A, B):  A ∪ B ⊆ P  ∧  A ∩ B = ∅
(I5)  challenge(A, B) is pure, deterministic on solids

(I2) is the space-accounting invariant. everything else is plumbing.

4 · enforcement

4.1 why not full on-chain "vs all"

checking one prism against one prism is bounded. checking one against unbounded N does not fit L1 gas or light clients. design for:

• index off-chain / heavy node — R-tree / BVH over L0 AABBs; query_overlap(solid) → [ids]
• pair check on consensus path — pure function intersects(a, b) → bool (Rust now; nox jet later)
• economic completeness — anyone can submit a colliding pair and claim deposits

4.2 mint path

propose(solid, rights, parent?, deposit)
  → local/oracle index: no known overlap
  → mint SpaceClaim Card, lock deposit
  → open challenge window (continuous if deposit remains)

oracles (cadastral / multi-party) may co-sign mint for UX; they do not replace deposits. dishonest mint still loses bond when a pair challenge lands.

4.3 challenge path (primary)

challenge(id_a, id_b)
  → load solids, verify intersects(a, b)
  → if true: burn claim with later commitment time (or lower priority rule);
             pay challenger from that claim's deposit;
             slash mint co-signers if any
  → if false: slash challenger's bond

this is Galt's deposit hybrid, stated as the default. oracles-at-mint and sidechain-vs-all remain optional accelerators, not the sole root of trust.

4.4 multi-registry

private registries, oracle registries, and curated registries may coexist. shared challenge contract (or shared proof object in the graph) is how the plane stays one exclusive map: claims that opt in post deposit and become challengeable across registries. registries that spam fake space can be voted offline without erasing honest deposits — squatting defense (Galt).

4.5 time

marketplace slot calendar: on a fixed SpaceClaim id, bookings are intervals; allocate fails on time overlap. that is exclusive use along t. space accounting is exclusive extent along x,y,z. compose:

full exclusive occupation = solid exclusive ∧ time exclusive

sublease of parcel-time (hak sewa style) is marketplace on the Title Card, not a second overlapping Title.

5 · hierarchy and operations

survey error and crustal motion are update workflows (oracles / arbitration), not silent solid mutation — same spirit as Galt token data change.

6 · presentation (soft3)

authority     graph + TSP-2 + SpaceIndex + challenge
capability    ward gates mint / challenge / transfer
present       optional Bevy WorldState::SpaceMap
              prysm / sugarloaf for title UI
              mir remains spectral graph only

SpaceMap (if built in cyb):

• loads committed claims for a frame
• ECS holds a visible set of solids (frustum), not the registry
• pick → Card id → rights UI
• edit → propose solid → mint flow

mirrors mir's VisibleParticle pattern: engines show snapshots; epochs of truth are graph commits.

7 · relation to cyber valley and space doctrine

on-chain land registry remains gated by legal wrappers where states exist; the geometry invariant is still worth running as private registry + challenge so digital claims stay consistent among participants who opt in.

8 · non-goals

• replacing state BPN / cadastre by force
• GPS as sole oracle of title (location proof is for agents, not for parcel topology)
• storing full BIM meshes as the exclusive-check primitive
• putting titles inside Bevy Transform or mir spectral positions
• perfect global vs-all on every L1 block

9 · implementation order

1. spec — this document; Prism + intersects + invariants (I1–I5)
2. kernel — pure Rust prism_intersect, R-tree index (seed from cyberia-my geometry if useful)
3. ledger v0 — mint + deposit + pair challenge (log or CosmWasm / PLUMB)
4. CV maps — import Phase-0 plot rings as proposed claims; run offline overlap audit
5. marketplace hook — calendar on SpaceClaim id for sublease
6. SpaceMap view — Bevy world, read-only then propose
7. nox jet — proven intersects for challenge path
8. multi-registry — shared challenge object

10 · one sentence

space accounting is the invariant that exclusive volume Cards in a frame are pairwise disjoint (over time windows), enforced by deterministic pair geometry plus deposit challenges — id ownership stays TSP-2, time exclusivity stays marketplace, engines only render what the graph already committed.

see also

• Galt Project whitepaper — galtproject-docs/whitepaper/en/Whitepaper.md (double ownership, WGS84, deposit challenge)
• TSP-2 · marketplace · marketplace-spec · services · location proof · space doctrine · mir · cyb