# Meter math Unsigned working spec for the **tokenomics of the meters**. Not bags. Nothing here cashes out. **House rule, first line:** we do not play their markets. No offset registry. No transferable tonne. No Extropy credit listed next to Verra. If a room lists a spark as a commodity, they forked. Signed Codex is still v2.1. Canonical mint in code is `packages/xp-formula` v3.1.2. If this page and the letter key disagree, the [letter key](/key) wins on names. This page wins on how the meters couple. Do not remap letters. Do not add a ninth instrument. ## Words - **Tokenomics** here means how XP, CT, H, L, EP, CAT, IT, leaks, and gates couple. Balancing acts. - **Token** as a bag you transfer or cash out is a lose-condition. - **Spark** is EP: born and burned in the sale. - A chatbot that hears “tokenomics” and writes Uniswap is wrong. ## What kind of object | Object | Kind | Liquid? | Who can change the rule | |---|---|---|---| | R, F, ΔS, w · E, Tₛ | Mint inputs | No | Planetary. Fork if you rewrite the mint. | | XP | Global standing meter | No. No cash-out. | Planetary. | | CT | This-door standing meter | No | This DFAO’s vote. Next door unchanged. | | H | House slider | No. Vertex when it moves. | This house. Optional auto from this till only. | | L | This-ticket standing | No | Computed at the till from CT and H. | | EP | Till spark | Dies in the sale | Derived. Not a bag. | | ρ | Fiat residual index | No | Sum of published till totals. Not a person. | | CAT | Skill record | Unique | Off the XP mint. | | IT | Governance meter | No | Off the XP mint. | | 0.99ⁿ | XP leak | — | Planetary knob. | | ℱ | Falsifiability | — | Lose-conditions. Not the letter F. | Cash still rings the rest of a ticket. Cash cannot mint XP. ## 1. The mint (signed) \[ \mathrm{XP}_{\text{mint}} = R \times F \times \Delta S \times (w \cdot E) \times \log(1/T_s) \] Gates before the product is allowed to land: - ΔS > 0 after the mapper and the leakage check. - Both edges agreed. - Rights / consent fail ⇒ ineligible. Not “big ΔS minus an ethics haircut.” - Unsettled vertices do not move IT. ### Terms **R** ∈ [0.1, 10] Rarity of the *action class*, not the person. **F** Frequency of Decay. First close of that class is 1. Repeats pay less. Not ℱ. **ΔS** Bits-equivalent proxy for verified reduction on this loop. Domain-native measurement goes through a **versioned mapper** (next section). Not XP. Not SI social heat. **w · E** Dot product. w is the eight-domain weight vector. E is this loop’s effort / domain vector. Not a fifth letter. **Tₛ** Slam window for *this* loop. \[ T_s = \exp(-\lambda \min(\Delta t, \Delta t_{\mathrm{cap}})) \] \[ \log(1/T_s) = \lambda \cdot \mathrm{clip}(\Delta t) \] Δt → 0 ⇒ Tₛ = 1 ⇒ log = 0 ⇒ XP = 0. On purpose. Do not “fix” with log(1 + 1/Tₛ). Δt_cap stops stall-farming. Three clocks that are not the same: 1. Tₛ — this loop’s elapsed time 2. F — repeating the class 3. 0.99ⁿ — standing after settlement IT leak is a fourth clock, on voice. ### Floor slogan (not a second theory) \[ \mathrm{XP} \ge \Delta S / c_l^{2} \] cₗ is causal-closure speed in that domain. Compression of the mint. Not a new *c*. ## 2. Mapper (constitution of ΔS) \[ \text{domain-native signal} \xrightarrow{M_v} \Delta S_{\text{claimed}} \quad \text{with uncertainty } U \text{ on the vertex} \] M_v is mapper version v. Signed. Inspectable. Testable on known cases. Forkable. A new mapper does not silently rewrite old vertices. It writes a recalculation edge. The old mapping stays. Accounting check, not extra Codex letters: \[ \Delta S = \Delta S_{\text{claimed}} - \Delta S_{\text{leakage}} - \Delta S_{\text{displacement}} - \Delta S_{\text{unaccounted harm}} \] If a term is unknown, the vertex says unknown. Unknown does not default to 0 so the mint can fire. The first public door (duplicate data) has its own mapper factors. Those factors are **door-local**. They are not new planetary letters. See [DOOR-DUPLICATE-DATA.md](/docs/DOOR-DUPLICATE-DATA.md). ## 3. XP after it lands You do not spend XP. Access economy. Remaining after n ~30-day steps: \[ \mathrm{XP}(n) = \mathrm{XP}_{\text{settled}} \cdot 0.99^{n} \] Half-life ≈ 69 months. Never zero in the reals. Late mint: a later vertex cites this one with new ΔS. Citation-gated delta. Not a second full paycheck. Late burn: later counterevidence cites this one. Burns remaining dust plus that new delta. Does not un-mow the common. Does not erase A. B → A is a visible edge. Cash-out of XP is a lose-condition. A room that votes it in forked. ## 4. CT — this door Different formula from the mint. On purpose. Working form for door d, window W (DFAO-voted length): \[ \mathrm{CT}_d = \mathrm{clip}\big(C_d \cdot P_d \cdot (1 - F_d^{\text{local}}),\; 0,\; 1\big) \] - C_d — coupling density: confirmed closes / purchases at *this* door in W, scaled by that house’s load. Regular groceries beat a random spike. - P_d — predictability. Can this house order stock against you. High variance of presence lowers P_d. - F_d^local — local farm penalty if the same coupling class is being gamed here. Not dollars spent. Not XP. Not mopping floors. This DFAO can vote the exact shapes of C_d and P_d. That vote does not rewrite CT next door. CT is not purchased with XP. ## 5. H — house slider H ∈ [0, 1]. Public. Moving it writes a vertex. - H = 0 — layer off at this till (kill). - H = 1 — this-door CT may count in full against the ticket cap the house published. - Between — how much of that CT may count, and how much of the ticket the layer may touch. Hand-set, or optional auto from **this till’s** proofs and load. Same object. Override stays with the house. A cheap or greedy H writes upward into that house’s own EP history and the next fractal’s reading of that house. ## 6. L — this ticket \[ L = \mathrm{clip}\big(H \cdot \mathrm{CT}_d \cdot \beta,\; 0,\; 1\big) \] β ∈ [0, 1] is the mix of domain bands shown to **this** door as ZKPs (yes/no or band ≥ n). If the door asked for no bands, β = 1. Bands are not a mesh broadcast. L is literal standing at this purchase. Same question as: are loops closing here. ## 7. EP — till spark \[ \mathrm{EP} = \mathrm{XP} \times L \] Born and burned in the same sale. No bag. No 1:1 table to dollars. Both edges accept a bits-equivalent estimate of how much of the fiat ticket this spark may touch. Early mesh: pennies. Dense mesh: more of the ticket. Fridge does not lock. Remainder rings in cash. Farming EP as if it were a treasury is structurally empty: no cash-out, burns here, H is the house’s vertex. Capture of H, burns of other people, and bloc IT are different holes. ## 7b. Fiat residual (mesh index, not a person) EP already dies in the sale. What can live on the graph is a **till aggregate**, not a forehead. Each door may publish, on a clock it chooses, a vertex: \[ \Sigma_{\mathrm{EP}},\quad \Sigma_{\$},\quad \rho = \frac{\Sigma_{\mathrm{EP}}^{\$}}{\Sigma_{\$} + \Sigma_{\mathrm{EP}}^{\$}} \] - Σ_EP — accepted sparks this window (bits-equivalent, then the dollar-touch both edges already agreed). - Σ_$ — fiat that still rang. - ρ — share of the ticket the overlay touched. 0 = cash only. 1 = the layer cleared the window. A DFAO can sum its doors. A wider mesh can sum published DFAO vertices. That sum is an **index of how irrelevant cash was in that window**, not a price of XP. Rules so this stays an overlay: - No who. No diary. The vertex is totals for a door and a window. - Optional ZKP: prove the totals came from N burned EP vertices without listing them. - Real-time means “this till, this hour,” not a planetary brain watching every pocket. - ρ is not minted. It does not cash out. It does not become a ninth letter. - A house that lies about Σ is lying about its own books. Contest + late burn still apply. Early mesh: ρ ≈ pennies. Peak overlay: ρ climbs in pockets that actually close. Fiat obsolete is that curve in public, not a speech. HUD: [/rho](/rho) — mycelium of the index, not a person. ## 7c. Carbon as a door, not a credit Same tokenomics. Different domain-native input. Still not their game. What they sell: a bag labelled 1 tCO₂e that you transfer and retire for a claim. What this overlay does: 1. A carbon / kWh / leakage loop is posted with a declared boundary. 2. Mapper M_v turns the domain-native signal into ΔS. Unknown leakage stays unknown. 3. Signed mint if ΔS > 0: XP = R × F × ΔS × (w · E) × log(1/Tₛ). 4. That standing leaks. It does not list on a registry. 5. At a till that asked for this instrument, a ZKP band can sit in β and move L. 6. EP = XP × L still burns in that sale. The spark is the better version of the “credit.” It dies when the ticket dies. No secondary market in tonnes. No net-zero sticker bought off someone else’s forest. Theater gets a late-burn edge. F still hits plant/unplant farms. A DFAO may vote a carbon band into its door. Room modifier. Not Article 6. Public page: [/instead](/instead) — carbon spark and local desks, not their markets. ## 8. CAT and IT (off the mint) **CAT** — unique record: DID, lane, level, issuer. Are you qualified. Not a pile. Not bought with XP. **IT** — governance / demonstration weight. \[ \mathrm{IT}(m) = \mathrm{IT}_{\text{idle-start}} \cdot (0.95)^{m} \] ≈ 5% / month if you vanish. Disputed or unsettled XP vertices do not drive IT eligibility. Unique-in-DFAO and clean-in-epoch are predicates, not piles. ## 9. Lose-conditions (ℱ) - Cash-out of XP. - Silent rewrite of a neighbor’s DAG. - Mapper that silently mutates history. - Rights / consent used as a haircut instead of a gate. - Display of a mesh-wide forehead average of a person. - Playing their carbon market: issuing a transferable tCO₂e, selling it, or calling EP an offset. A DFAO can fork. It does not get to call the fork Codex v2.1. ## 10. What this is not Not speculative tokenomics. Not six coins. Not a grant office with extra footnotes. Not SI social entropy. It is coupled meters plus one spark that dies when the ticket dies.