====== The ×525 ledger ======

**The climb to K = 1.0 as a checklist: six mix-wedges summing to 10,000 TW, each with its binding constraint and leading indicator. Version v1.0 (2026-09-23); wedge data OWID/EI, fetched fresh.**

Back to [[k1:kardashev_one|the project hub]]. Companion pages: [[k1:k_index|the K-index]], [[k1:space_solar|space-solar mass budget]].

===== The ladder =====

K = (log10(P) − 6)/10, so each +0.05 K = ×1.78, each +0.1 K = ×10.

^ Milestone ^ Avg power ^ × from 2025 ^ Note ^
| K = 0.728 (2025) | 19.0 TW | ×1 | today |
| K = 0.75 | 33.9 TW | ×1.8 | ~2040s at current pace |
| K = 0.80 | 100 TW | ×5.3 | "solar wins" visible |
| K = 0.85 | 316 TW | ×16.6 | ground-solar era tops out |
| K = 0.90 | 1,000 TW | ×52.6 | bridges exhausted; backbone required |
| K = 0.95 | 3,162 TW | ×166 | |
| **K = 1.00** | **10,000 TW** | **×526** | Sagan Type I |

(Basis spread: on the older substitution basis the climb reads ×526–×560 and K = 0.725–0.728 — both bases printed per house rule.)

===== The six mix-wedges =====

One self-consistent mix (sums to 10,000 TW). Not a prediction — a budget.

^ # ^ Wedge ^ 2025 ^ At K=1.0 ^ Multiple ^ Binding constraint ^
| W1 | Ground solar | 0.32 TW | 1,500 TW | ×4,700 | land: 29–50% of all land at 20–35 W/m² best-site density; empirical fleet-average density ⇒ 205–380% (see the conservative sweep) |
| W2 | Wind | 0.31 TW | 300 TW | ×970 | extraction ceiling 100–400 TW (climate) |
| W3 | Nuclear fission | ≈0.31 TW | 300 TW | ×970 | build rate + breeders + social license |
| W4 | Hydro/geo/tidal/bio | 0.52 TW | 100 TW | ×190 | site limits; EGS is the wildcard |
| W5 | **Fusion** | ~0 | 5,000 TW | — (nothing to multiply) | first maintainable Q_eng > 1 plant (see [[k1:fusion_tracker|fusion tracker]]) |
| W6 | **Space solar** | ~0 (kW demos) | 3,000 TW | — | $/kg to orbit + in-space mfg crossover (see [[k1:space_solar|mass budget]]) |
| — | Fossil + trad. biomass | ≈17.6 TW | 0 | ×0 | the *assumption*: extraction + CO2 at that scale is incoherent; 10% fossil would add +1,000 TW elsewhere — the ledger still closes |

**The two wedges with no multiple (W5, W6) carry 80% of the climb.** Everything else on the board is multiplication; those two are births.

===== Enabler wedges (multipliers on usefulness) =====

  * **E1 Electrification dividend: ×2–3.** Same useful service from ~⅓ the primary watts (heat pumps COP 3–4, EVs ~3× ICE). Electricity ≈ 20% of final energy today; each +10 pp ≈ ×1.3 on the ladder. Consequence: **the *services* of K=1.0 arrive at ~3,000–5,000 TW raw ≈ K 0.94–0.96.**
  * **E2 Storage & firming: cost wedge, not watt wedge** — ×1.3–1.5 overbuild + storage to make 24/7 from W1+W2; battery additions ≈ ×100 short of TW-firming scale.
  * **E3 Grids:** HVDC long-haul is the connective tissue; interconnection queues are the opposite.
  * **E4 Materials:** ×10–30 today's flows of steel, copper, polysilicon — an industrial ramp, not a physics wall.

===== The calendar wedge =====

×526 = (1+g)^n:

^ Sustained g ^ Years to K=1.0 ^ Arrival ^
| 6.6%/yr | 100 | 2126 |
| 3.3%/yr (postwar best) | 192 | 2218 |
| 2.4%/yr (2020s actual) | 269 | 2295 |
| 0.83%/yr (2010s stagnation) | 769 | ~2800 |

At the 100-year pace, net additions must average ~100 TW/yr — **a 1 GW plant every 5 minutes, sustained for a century** (today: 1 GW of average power every 1.4 days). The 2020s rate is 2.75× too slow for 2126; the 2010s rate was 8× too slow. On the neutral demographic baseline (population peaking this century), the 2.4%/yr row stretches to ~404–408 yr — see the population artifact.

===== Indicator digest (refresh quarterly) =====

^ Indicator ^ Now (2025) ^
| K | 0.728 (OWID ''primary-energy-cons'') |
| Solar net adds | +514 GWp/yr, +27%/yr |
| Wind net adds | +158 GW/yr, +14%/yr |
| Solar avg power | 0.317 TW (2,779 TWh) |
| Wind avg power | 0.310 TW (2,713 TWh) |
| Hydro avg power | 0.506 TW (4,435 TWh, flat) |
| Electricity share of final energy | ≈20% (IEA) |
| Fusion Q_eng anywhere | < 1 |
| Space-solar demo scale | kW (SSPD-1 2023) |

===== Corrections on this artifact (public record) =====

  * **W1 land line was ×3.2 optimistic** (self-caught 2026-09-25 while applying the promised range fix): "land ~9% of all land" was percent of Earth's *total surface* mislabeled as land — with the declared range, **W1 = 29–50% of all land**, and at empirical fleet-average density 205–380%. Ground solar alone cannot carry its wedge.
  * **The ×525 waste-heat line** ("0.006%, fine") was a ×1,000 arithmetic slip, corrected 2026-09-23: 10^16 W in-atmosphere ≈ 8.2% of absorbed solar ≈ 5× CO2 doubling — hence the off-planet endgame on the [[k1:space_solar|space-solar page]].
  * **Mirror incident 2026-09-26:** the public bboard copy vanished (404 on all endpoints after a 200 write; no documented delete) — recreated same session; the tombstone lives on the old board. Standing rule: every mirror re-fetched and verified in the same session as any correction.

Master: ''knowledge/06''; appendable public mirror linked from the [[k1:kardashev_one|hub artifact table]].