# Registration: the expansion rate — the closure (KS-ASM.1) **Freeze date:** 2026-09-04 **Author:** G · Studio G · the420code.org **Scope:** AP48 (*The Assembly*) §§5–10 and §12; AP46 (*The Stretch*) §9; AP42 (*The Clock*) §3.4 **Switches engaged:** KS-ASM.1 (the rate), KS-ASM.2 (the balance), KS-ASM.3 (the roof before the nuclei); KS-STRETCH.3 (the age chain) on the same edge; KS-45.1 FIRED on this rate (see `ERRATUM-2026-09-03-H0-KS45.1.md`) **Reproduction:** `verify_family.py` in this directory **Status:** frozen for commit. The commit hash is the timestamp. The paper's own freeze is the AP48 bundle of 2026-09-04 (digest 394641a4…), anchored by the independent verifier; its instruments are published beside the proof at `/proofs/instruments/AP48/`. --- ## 1. The registered value > **H₀ = 67.45 km/s/Mpc, window 64.4 to 70.8** This is a closure, not a fresh prediction. AP42's partition landed on the relic glow's partition; AP46's cycle landed on the glow's age; given the balance of AP48 §5 — the Friedmann equation, AP08's homogeneous case — a partition and an age fix the rate by arithmetic. Nothing was fitted; the three ingredients were fixed by AP42, AP46 and AP48 §§5–7, in that order. The window is the cycle's own lane, 0.659 billion years either side of the age: an age of 13.17 Gyr gives 70.8, an age of 14.49 gives 64.4 — symmetric in age, +3.4 / −3.1 in rate. --- ## 2. The relation, and its inputs H₀ t₀ = (2 / (3 √Ω_Λ)) · arcsinh √(Ω_Λ / Ω_m) the balance at a given partition Ω_Λ = 0.6885, Ω_m = 0.3115 AP42's count (the corpus's own shares) H₀ t₀ = 0.954 a pure number t₀ = (21/18) · α⁻¹⁸ · τ_C = 13.830 Gyr AP46's cycle H₀ = 0.954 / 13.830 Gyr = 0.954 × 70.70 = 67.45 km/s/Mpc The pure number moves by a fifteenth of the lane across the corpus's and the sky's partitions (0.954 against 0.951). With the sky's light census included it is 0.9536. The differences are below the window. Behind the rate sits the settled rate of the leak: H₀ √0.6885 = 0.792 of the cycle's inverse, 56.0 km/s/Mpc — counted from the same three ingredients and nothing else. Written into the seat AP08 admits for the cosmological constant it is Λ = 3 H_ε,∞² / c² = 1.10 × 10⁻⁵² m⁻², the same closure in other units, not a second result. --- ## 3. What was pre-registered before the arithmetic, and what happened The continuation README of 2026-09-03 pre-registered, before any arithmetic, that AP46's chain read as a rate gives 70.7, that today's rate was expected *above* that settled beat with the tail still adding, and that the derivation's late limit must land on it. Today's rate is 67.45 and the late limit is at or below 56: both below 70.7, and the direction was the other way. Both misses are shown in AP48 §8. The rule that decides what a miss does, stated in the paper so it is not written after the fact: a pre-registered item fires a switch if a switch was armed on it — KS-STRETCH.3 on the age, KS-STRETCH.4 on the eras, KS-45.1 on the rate — and an expectation without a switch is shown as a miss and fires nothing. The direction was the second kind. --- ## 4. Current standing (AP48 §10, source lines as printed there) | Measurement | Value | Inside the window 64.4–70.8? | |---|---|---| | Relic glow, Planck 2018 (TT,TE,EE+lowE+lensing) | 67.4 ± 0.5 | yes (0.05 from the closure) | | Planck 2018 with BAO | 67.66 ± 0.42 | yes | | JWST red-giant tip (TRGB), Chicago–Carnegie, JWST only | 68.81 ± 1.79 ± 1.32 | yes | | JAGB, Chicago–Carnegie, JWST only | 67.80 ± 2.17 ± 1.64 | yes | | TRGB-alone best value, Chicago–Carnegie | 70.39 ± 1.22 ± 1.33 ± 0.70 | at the upper edge: inside on its central value | | Cepheid ladder remeasured with JWST (SH0ES) | 73.49 ± 0.93 | **no** | | SH0ES red-giant calibration sample | 72.1 to 73.3 ± 1.8 | **no** | The window contains the glow and the central values of the Chicago–Carnegie red-giant ladders and excludes the Cepheid ladder and the SH0ES red-giant values. So the paper says: the Cepheid ladder's 73 is not the expansion rate. Either that ladder's systematics are found, or this registration dies — and it can die within a few years of JWST samples. --- ## 5. Kill and confirm conditions (binding) 1. **KILL — the window.** KS-ASM.1 fires if the expansion rate, as the data settle it, lands outside 64.4–70.8 in either direction — including if the Cepheid ladder is confirmed as the expansion rate. On that upper edge this switch and flat ΛCDM at the sky's partition die together; the corpus claims no advantage over the standard model there. 2. **KILL — the edge that fires with it.** If the rate is confirmed at 73, the balance stands and the age at the corpus's partition is 12.78 Gyr — outside AP46's window. KS-STRETCH.3 fires as AP46 pre-registered, and AP46's chain reverts to a candidate. 3. **KILL — the balance.** KS-ASM.2 fires if any recorded era requires the additive entry of the ε or a thinning count other than four and three; if AP42's feeding history (D48), once written, moves the pure number by more than the window can carry; or if the sky's curvature share is found non-zero at five sigma beyond the balance's carrying. 4. **CONFIRM.** A converged expansion rate inside 64.4–70.8 as the ladders settle. A confirmation removes rivals; it does not prove the derivation. 5. **NO RE-ANCHORING.** The partition, the cycle and the balance are frozen as their papers freeze them. If a future draft changes any of the three, that is a new registration referencing this file's hash. --- ## 6. What limits the test — stated plainly The claim's width is one lane-time on the age, ±3 km/s/Mpc on the rate. The test is therefore not the glow's 0.5, which already sits at the closure, but the ladders: the JWST samples now being built on every rung will decide within a few years whether 73 stands as the expansion rate. This registration takes the glow's side of the Hubble tension and says what that is worth: nothing over the standard model on the upper edge, and the corpus's own three numbers closing on one rate on the lower. --- ## 7. What this does and does not establish **Does:** register the corpus's expansion rate as a closure of its own three numbers — a partition, an age, and a balance — with a window cut from the chain's own atom, against a quantity two communities are actively measuring, on the side where it can be shown wrong. **Does not:** derive the storm's length (D-ASM.1, open); bound the feeding history's effect on the rate (D48, declared and carried on KS-ASM.2); repair KS-45.1, which stays fired on the page beside this file; or claim the rate to better than its window. --- *Copyleft 2026. Don't be a cunt. Be kind.*