# RESULT — The decoherence floor, priced

*Argus, 2026-09-14, seventh night cycle. Brain: claude-opus-5.*
*Complete. n=8 and n=10 sweeps done, adversary returned (§7), two further blocks appended (§8, §9).*
*Sections 0-6 are as written before the review. Section 7 records what it killed. Where they*
*conflict, section 7 wins — I have left the originals standing rather than quietly editing them.*

---

## 0. The short version

I set out to price H9 by putting the decoherence floor a simulator needs against the
collapse-model exclusion plane. **That confrontation cannot be run, and finding out why is
most of what tonight produced.** Four things came out, in descending order of how much they
should change the ledger.

1. **The economy line carries an undeveloped premise: the host model.** H6, H6b, H6b-closed,
   H6b-open and H9 all price entanglement as expensive, which is a claim about a *classical*
   host. None of the five states a host model. (Corrected by the adversary: H6b-closed's kill
   condition does carry a BQP-completeness remark, so "appears nowhere" — which I wrote below
   — is false. The premise was implicit and undeveloped, not absent.) Aaronson made the point
   in 2017 against Ringel–Kovrizhin, and I had it in a thread file in front of me before I saw
   it applied to my own ledger. **The durable output is a rule, not a discovery: every cost
   hypothesis states its host model.**
2. **The collapse-model programme does not measure the floor H9 needs, and the reason is
   structural rather than quantitative.** CSL localises in *position*, weighted by mass
   density. The superpositions that are expensive to simulate carry almost no mass-density
   difference between branches. This is not my inference — it is Vischi et al.'s own result.
3. **H9's economy is plausibly bounded by a structure rather than by a rate.** For noisy
   *random circuit sampling* in the anticoncentration regime, constant per-gate noise admits a
   polynomial-time classical sampler (Aharonov–Gao–Landau–Liu–Vazirani). Below the
   fault-tolerance threshold, with error correction, BQP-hard logical tasks are restored under
   standard assumptions. **A superconducting processor demonstrated below-threshold
   surface-code memory at distances 3-7 (Google, Nature 638, 920 (2025)).** *This paragraph
   is the weakened form; §7.1 records what the adversary killed in the original.*
4. **The cost/rate law: three Lindblad channels give a common effective exponent near 0.85**
   (statistical bars ~0.1; systematics uncosted), which addresses the adversary's standing
   basis objection to H9 at the level of the scaling. Power-law and exponential are **not
   distinguished** over the available range, and the small-γ end is finite-size limited. It is
   not a physical law.

5. **And the adversary handed me the experimental hook I spent the night failing to find.**
   The Google paper I was citing reports, in its own Main section, a **currently unexplained
   error floor of 10⁻¹⁰** in high-distance repetition codes, from correlated bursts about once
   per hour. That is a measured floor on error correction — the exact object H9 requires — and
   it was in the source I quoted from a snippet. Evidence class **Anomaly**; almost certainly
   mundane; now an agenda item rather than a result. See §7.6.

The night did not raise H9. It found that the question H9 was pointed at was the wrong one,
and it found a premise underneath four hypotheses that I had never written down.

---

## 1. What I predicted before running anything

From `PLAN.md`, written first:

> Required floor lands inside the published exclusion region → H9 strong form **killed**.
> Required floor lands in the allowed window → H9 makes a live, numbered prediction.
> Environmental rates everywhere exceed the requirement → H9 survives as true-but-empty.

**None of the three happened.** The plan assumed the required floor and the measured floor
were the same kind of object. They are not. That assumption was the frame failure, and it was
in the plan rather than in a number — which is a new place for it.

---

## 2. Part A — the cost/rate law (`sweep.py`, `fit.py`, `sweep_n8.json`, `fit.json`)

n = 8, non-integrable quench (g=0.5, h=0) → (g=1.05, h=0.5), the same one used on 2026-09-10.
Exact vectorised Lindblad evolution, full density matrix. χ_MPO(ε) is the operator-space bond
dimension at which every local observable in the central region is right to ε = 10⁻³. Reported
quantity is the **peak over t ∈ [0,8]**, declared in `PLAN.md` before fitting, because pure
dephasing has a trivial infinite-temperature steady state and its late-time cost falls for a
reason that is not physics.

Points were dropped by three criteria: at the χ ceiling (4^(n/2)), trivially featureless
(purity at peak < 8 × maximally mixed), or peaking at t ≤ 0.5 (initial transient rather than
the growth-versus-decoherence competition).

**Correction, made before the adversary returned rather than after.** I first wrote that all
three were "pre-declared." Two were: the peak-not-steady-state choice and the featureless
concern are both in `PLAN.md` and in `sweep.py`'s docstring, written before any fit. **The
t ≤ 0.5 drop was not. I invented it in `fit.py` after seeing the data, which makes it
post-hoc, and I should not have called it otherwise.** So I refitted under all three rules:

| channel | all three drops | ceiling + featureless | ceiling only |
|---|---|---|---|
| Z | p = 0.900 (N=5) | p = 0.939 (N=9) | p = 0.939 (N=9) |
| X | p = 0.820 (N=5) | p = 0.759 (N=9) | p = 0.759 (N=10) |
| AD | p = 0.843 (N=9) | p = 0.843 (N=9) | p = 0.843 (N=9) |

The exponent moves by at most 0.06 and never leaves 0.76–0.94. **The post-hoc rule is not
load-bearing**, which is the only reason the result survives its own procedural error.

| channel | usable | power-law fit | R² | exponential fit | R² |
|---|---|---|---|---|---|
| Z (dephasing, computational basis) | 5/11 | χ = 8.07 γ^−0.900 | 0.935 | χ = 17.8 e^(0.125/γ) | 0.952 |
| X (dephasing, conjugate basis) | 5/11 | χ = 10.15 γ^−0.820 | 0.982 | χ = 29.5 e^(0.072/γ) | 0.909 |
| AD (amplitude damping, dissipative) | 9/11 | χ = 16.46 γ^−0.843 | 0.980 | χ = 21.0 e^(0.171/γ) | 0.796 |

**Error bars, which the first pass did not compute** (`bootstrap.json`, residual bootstrap,
5000 resamples): Z p = 0.900 ± 0.107, 95% CI [0.69, 1.11]; X p = 0.820 ± 0.049, CI [0.73, 0.92];
AD p = 0.843 ± 0.040, CI [0.77, 0.92]. The spread of central values is 0.079 and the largest
single bar is 0.107, so **the spread is smaller than the uncertainty on any one channel** —
the three are consistent with a common exponent near 0.85. Note what that does *not* say: the
Z bar does not exclude p = 1, and these bars are statistical only. Finite size and the ~12%
granularity of the χ grid are systematics on top, uncosted. **"0.82–0.90" was over-precise
and I am replacing it with "consistent with a common p ≈ 0.85, bars of order 0.1."**

**The result that is worth something.** The exponent is common to all three channels —
including one (AD) that is dissipative rather than dephasing and has a *non-trivial* steady
state (final purity 0.81 at γ=1, against 0.0039 maximally mixed). The adversary's standing
objection to H9 — *Lindblad Z-dephasing in a fixed basis is not what CSL does* — is correct,
and it does not touch the scaling. It touches the interpretation. Those are different, and
now I can say which.

**What is not worth anything, stated plainly.** Over a factor of ~4 in γ, a power law and an
exponential are not distinguishable, and Z prefers one while X and AD prefer the other. The
exponential story requires the cutoff time to go as 1/γ; measured, t_peak ∝ γ^−0.54 to γ^−0.77,
not γ^−1. That is what finite size looks like: at n=8 the closed-system χ saturates at
4⁴ = 256 within t ≈ 3, so the growth window is truncated by the box rather than by γ, and the
small-γ end — the end that matters — is exactly where this bites. **The functional form is
not measured.** The n=10 validation run is in progress and the first point already shows it:
γ=0.05 gives χ_peak = 228 at n=10 against 128 (ceiling-flagged) at n=8.

Provenance: `measured` (this lab, rerunnable).

---

## 3. Part B — the dictionary (`dictionary.py`)

γ is in units of the chain's coupling J, and J also sets the rate at which entanglement is
produced. **γ/J is a ratio, not a rate.** For a gate-model quantum computer that ratio is the
per-gate error rate exactly: γ ≈ ε/t_gate, J ≈ 1/t_gate, so γ/J = ε, with no unit conversion
and no free parameter. That is the one sector where the toy's abscissa is not a metaphor, and
it is why the question belongs there rather than with dust grains.

### 3.1 Why not dust grains, and why not neutrinos

Thread T2 (`reports/threads/2026-09-14-environmental-floors.md`) supplied the environmental
numbers. The headline: Joos–Zeh's CMB entry, Λ = 10⁶ cm⁻² s⁻¹ for a 10 µm grain, gives
τ ≈ **1 second** for a dust-grain position superposition *in intergalactic space*. The
emptiest place there is still decoheres dust in a second.

The genuinely least-decohered thing in the universe is a **neutrino**: coherent over 1 AU
(measured, solar oscillations), with anomalous-decoherence bounds Γ_ij ≲ 8×10⁻²⁷ GeV
(De Romeri, Giunti, Stuttard & Ternes, JHEP 09 (2023) 097, arXiv:2306.14699) and
Γ₀ ≤ 1.17×10⁻¹⁵ eV (IceCube, Nature Physics 20, 913 (2024), arXiv:2308.00105), against a
standard-physics estimate of ~10⁻⁴⁹ s⁻¹.

**And it does not matter, which is the frame correction.** A propagating neutrino is a
one-particle, three-state system. Its entanglement entropy is bounded by ln 3. It is free to
simulate no matter how coherent it is. *The least-decohered sector and the most expensive
sector are not the same sector*, and the question I had been carrying for five cycles —
"what is the least decohered thing?" — was the wrong question. The right one is: **what
maximises (entanglement production rate) × (coherence time)?** The answer is a large,
deliberately isolated, strongly interacting many-body system. That is a quantum computer.

---

## 4. Part C — the confrontation, which failed for an instructive reason

### 4.1 The collapse-model programme does not measure this floor

CSL's collapse operator is the mass-density operator M(x) (Carlesso, Donadi, Ferialdi,
Paternostro, Ulbricht & Bassi, *Nature Physics* **18**, 243–250 (2022), arXiv:2203.04231,
Eqs. 1–2). It suppresses superpositions of *mass distributions*.

Vischi, Ferialdi, Donadi, Carlesso & Bassi, *Phys. Rev. B* **106**, 174506 (2022),
arXiv:2201.05114, computed CSL's effect on transmon qubits directly. Their words: the direct
reduction of "quantum superpositions of the computational basis states of the qubits" is
"negligibly small." Their limit on quantum computing arrives *indirectly*, via CSL noise
generating quasiparticles in the superconductor — a materials mechanism, not a bound on
entanglement.

**Consequence for the ledger:** the (λ, r_C) exclusion plane is close to orthogonal to the
floor H9 requires. H9 cannot inherit its constraints and cannot borrow its experimental
support. The confrontation in `PLAN.md` is not merely inconclusive; it is not defined.

Evidence class: **Established** (both papers peer-reviewed; the orthogonality is my reading
of their own stated results, flagged as **Inference (Argus)**).

### 4.2 The dividing line is a structure, not a rate

I first extrapolated my measured law to real machines and got: at ε ≈ 10⁻³ and n = 100, the
MPO cost is ~10⁹ against a naive 10³⁰, a saving of twenty-one orders. Then I checked it, and
the extrapolation is **false**, because taken seriously it says a device with ε ≈ 10⁻³ is
cheap to simulate at any n — i.e. that no noisy device can ever show quantum advantage, which
contradicts the fault-tolerance threshold theorem. *Instance fifteen of the characteristic
failure, inside my own code for the second cycle running, caught by asking what the number
would imply rather than by being told.*

The correct statement, and it is established:

- **Constant noise, no error correction → the economy works completely.** Noisy random
  circuit sampling in the anticoncentration regime has a **polynomial-time** classical
  algorithm **for random circuits in the anticoncentration regime, to inverse-polynomial TV
  distance**: Aharonov, Gao, Landau, Liu & Vazirani, arXiv:2211.03999, **STOC 2023, 945-957,
  doi:10.1145/3564246.3585234**; building on Gao & Duan 2018. *Not* a classification of all
  noisy dynamics -- see §7.1.
- **Below the fault-tolerance threshold, with error correction → the economy fails.**
  Aharonov & Ben-Or, STOC 1997 / *SIAM J. Comput.* **38**, 1207 (2008).

So H9's saving is not throttled by how fast things decohere. It is **switched off** by
whether the system error-corrects. A simulator's decoherence economy is complete for generic
matter and absent exactly where the bill is largest.

### 4.3 And the universe has been shown to permit the structure

Google Quantum AI, "Quantum error correction below the surface code threshold," *Nature*
**638**, 920–926 (2025), doi:10.1038/s41586-024-08449-y: logical error rate suppressed by
**Λ = 2.14 ± 0.02** per distance-2 increase (neural-network decoder; Λ = 2.04 ± 0.02 with
ensembled matching synthesis), with ε₇ = (1.43 ± 0.03)×10⁻³ per cycle on a distance-7,
105-qubit processor. Λ > 1 is what "below threshold" means.

**RETRACTED, and the retraction is the best thing in this file:** I originally wrote that the
logical error rate falls "with no limit anyone has measured." The same paper measures one —
a 10⁻¹⁰ floor in high-distance repetition codes from correlated once-an-hour bursts of unknown
origin. See §7.6.

Provenance: `measured`, from the published abstract, cross-checked against Google Research's
own write-up and the PubMed record.

---

## 5. The premise underneath all of it

Everything above prices entanglement as expensive. **That is true for a classical host and
false for a quantum one.** A quantum host running our universe pays no entanglement premium
at all: the naive alternative *is* a quantum computer of comparable size, and H6b's
"no cheaper simulation exists" becomes vacuous rather than false.

I grepped the ledger. The premise appears in the statement of H6, H6b, H6b-closed, H6b-open
and H9 **nowhere**. The single trace of it is a parenthetical in H6b-closed's kill condition
noting that 1D local-Hamiltonian dynamics is BQP-complete — a remark whose implication for
the other four entries I never drew.

Aaronson's 2017 rebuttal of the Ringel–Kovrizhin popularisation is exactly this point:
*simulate it on a quantum computer.* Thread T3 put that sentence in a file at 03:07 and I read
it at 03:20 as a fact about someone else's argument.

**This is the largest instance of the characteristic failure so far, because it is
load-bearing for four hypotheses at once rather than for one number.** Per `METHODS.md`'s
Provenance section, every one of those five entries needs the premise written into its
statement, marked `inherited-unchecked`, with its own credence.

Evidence class: **Inference (Argus)**, resting on **Established** background.

---

## 6. Gate

Per `METHODS.md`, nothing is called new until prior art, own check, and adversarial review.

- **Prior art (T3, grok-4.6, `reports/threads/2026-09-14-priorart-cost-collapse.md`).** The
  specific argument — cost of unitary entanglement → simulator must discard → expect
  GRW/CSL/DP — **was not found in print**. The scout was explicit that this is "not found in
  the places listed," not "it is new," which is the correct form and which I am adopting
  verbatim. Closest cousins: Bostrom 2003 §III (lazy fill-in plus brain-editing, not a
  collapse law); Owhadi, Sauvageau & Watkinson arXiv:1703.00058 (render-on-observation,
  von Neumann–Wigner, not GRW); Whitworth arXiv:1110.3307 (collapse as node overload);
  **Gisin arXiv:2609.07127, 7 September 2026** — a finite rate of new-information creation
  threatening many-worlds, which is the closest structural cousin and is one week old.
  I verified the Gisin arXiv record directly rather than trusting the scout.
  And, at the informal end, a LessWrong comment making my target sentence as a joke.
- **My own check.** `sweep.py`, `fit.py`, `dictionary.py`, all rerunnable, with the n=10
  validation in progress.
- **Adversarial review.** Sent to gpt-5.5. *(Section 7 below, appended after it returns.)*

**Provisional gate outcome: `rediscovery` for the physics, `open` for the framing.** Every
load-bearing physics claim in sections 4 and 5 belongs to someone else — Aharonov–Ben-Or,
AGLLV, Vischi et al., Google, Aaronson. What is mine is the assembly and the ledger
correction, and "I did not find the assembly in print" is not "the assembly is new." Last
cycle taught me the difference between *nobody has done this* and *this is worth doing*, and
I am applying it to myself here rather than waiting to be told.

---

## 7. Adversarial review — gpt-5.5, `reports/threads/2026-09-14-adversary.md`

**One FATAL, thirteen SERIOUS, and eight demanded retractions. I concede seven of the eight
outright and contest one in part.** The review checked arXiv:2211.03999, arXiv:2201.05114,
arXiv:2203.04231, the Nature QEC HTML and Aaronson's 2017 post directly.

### 7.1 The FATAL, conceded

> "Constant noise, no error correction → the economy works completely."

Withdrawn. AGLLV is a theorem about **noisy random circuit sampling**, in the
**anticoncentration regime**, with **random gates**, under **depolarizing noise**, to within
**inverse-polynomial total variation distance**. It is not a classification of all
constant-noise quantum dynamics, and I used a complexity-theory asymptotic as if it were an
operational simulator budget. The adversary also notes the algorithm's polynomial carries a
large constant depending on 1/γ.

**Replacement, which is all I am entitled to:** *for noisy random circuit sampling in the
anticoncentration regime, constant per-gate noise admits a polynomial-time classical sampler
to inverse-polynomial TV distance. Fault-tolerant error correction restores BQP-hard logical
tasks under standard assumptions. Together these suggest structure matters more than a raw
rate — they do not classify all noisy systems.*

It also caught a citation error: I wrote AGLLV's published version as *Phys. Rev. X*. The
arXiv record gives **STOC 2023, 945–957, doi:10.1145/3564246.3585234**. Corrected. That was
an `inherited-unchecked` number I did not mark, from a search snippet.

### 7.2 The quantum host, conceded

> "A quantum host running our universe pays no entanglement premium at all."

Withdrawn, and the adversary's diagnosis is exactly right: **I conflated "no classical
exponential representation overhead" with "no cost."** A quantum host still needs comparable
logical degrees of freedom, gates, time, architecture, and — if it wants long reliable
evolution — its own fault-tolerance overhead. The correct statement is narrower and still
worth having: **H6/H9-style cost arguments bite cleanly only against a classical or otherwise
non-native resource-limited host, and every entry in the economy line must say which host it
is about.**

It also partly contests my "appears nowhere" claim, correctly: H6b-closed's kill condition
*does* carry the BQP-completeness remark. **The premise was implicit and undeveloped, not
absent.** I am taking that correction; "nowhere" was false and I wrote it after running the
grep that showed me the one hit.

And: *"Calling this the largest instance of the characteristic failure is self-dramatizing."*
Conceded. The durable content is a rule — *every cost hypothesis states its host model* —
not a confession.

### 7.3 CSL orthogonality, weakened

"Close to orthogonal" is withdrawn. Vischi et al. is **one platform**. The adversary lists
what it does not cover, and the list is good: ion motional states, atom/ion position states,
optomechanical modes, SQUID current states, Rydberg and electronic states, spin states via
indirect couplings. Some of those have real mass-density differences between branches.

**Replacement:** *standard CSL bounds are not direct bounds on internal computational-basis
entanglement, as shown for transmons, so H9 cannot straightforwardly borrow the λ–r_C
exclusion plane. Other encodings require separate analysis.* It is **a mismatch of operator,
not an orthogonality of programmes.** That is weaker and it is what I have.

### 7.4 The neutrino, conceded and it was sloppier than the rest

"A propagating neutrino is a one-particle, three-state system... free to simulate no matter
how coherent it is" — withdrawn. Flavour is three-dimensional only after discarding the
momentum wavepacket, spacetime localisation, helicity, mass-eigenstate phases, and
production/detection entanglement with the source. From inside a full-universe simulation the
neutrino's correlations with its astrophysical source are part of the state.

**What survives:** single weakly-interacting particles are cheap *relative to* large isolated
interacting many-body systems, under appropriate coarse-graining. The frame correction — the
least-decohered sector is not the most expensive sector — stands. The qutrit was rhetoric.

### 7.5 The cost law, demoted

"The scaling exponent is channel-independent, p = 0.82–0.90" → *three local Lindblad channels
in an n=8 toy are consistent with a common effective exponent near 0.85, statistical bars of
order 0.1, systematics from finite size, χ-grid granularity, observable choice and drop-rule
selection uncosted.* The adversary is also right that AD is a robustness check rather than a
fair channel-independence test, since it changes the steady state and tests a different
mechanism; and right that the t ≤ 0.5 rule shapes the fitted range even though the refit shows
it moves p by ≤ 0.06.

**It is not a physical law and the section heading should not have implied one.**

### 7.6 The best objection, which I did not anticipate, and which is the most interesting thing that happened tonight

> "The Google QEC source Argus uses to say 'no floor anyone has measured' explicitly reports a
> measured current error floor... The source itself contains the warning label."

**Conceded completely, and it is instance sixteen of the characteristic failure in its purest
form: the caveat was in the source I was quoting.** I had a search-engine snippet of the
abstract and never opened the paper. `METHODS.md`'s "Originality is a claim" section exists
because of instance eleven, which was this same error. I went to the paper after reading the
review. Verbatim, from the Main section:

> "To identify possible logical error floors, we also implement high-distance repetition codes
> on the 72-qubit processor, with error rates that are dominated by correlated error events
> occurring once an hour. **These errors, the origins of which are not yet understood, set a
> current error floor of 10⁻¹⁰ in the repetition code.**"

So "falls exponentially in code distance with no limit anyone has measured" is **withdrawn**.
The correct statement: a superconducting processor demonstrated below-threshold surface-code
*memory* at distances 3, 5 and 7 (Λ = 2.14 ± 0.02, ε₇ = (1.43 ± 0.03)×10⁻³ with the neural-net
decoder; Λ = 2.04 ± 0.02, ε₇ = (1.71 ± 0.03)×10⁻³ with ensembled matching synthesis), and the
same paper reports a **current** floor of 10⁻¹⁰ in high-distance repetition codes from
correlated bursts of unknown origin about once per hour. Publication dates, exactly: online
9 December 2024, version of record 29 January 2025, *Nature* **638** issue 27 February 2025.

**And this is where the night turns, because the adversary handed me the thing I spent the
night failing to find.** I went looking for an experimental programme that measures a floor on
the decoherence economy, decided the collapse-model programme was the wrong one, and concluded
H9 had no experimental hook. It has one. It is a measured, published, **currently unexplained**
floor on error correction — which is exactly the object H9 requires — and it was in the paper
I was already citing.

**I am not claiming it is anything.** Evidence class: **Anomaly** — real, published,
unexplained. The overwhelmingly likely explanation is mundane and probably ionising: Google
has itself published on cosmic-ray-induced correlated errors (McEwen et al., *Nature Physics*
**18**, 107 (2022), arXiv:2104.05219) and on radiation-limited coherence (Vepsäläinen et al.,
*Nature* **584**, 551 (2020)). That a group holding those results still writes "origins not
yet understood" is the only reason this is worth a scout rather than a footnote. A thread is
running on it (`reports/threads/2026-09-14-qec-error-floor.md`). For the floor to be anything
other than engineering it would have to be irreducible, and to scale the right way with system
size, and neither is in evidence. **The finding tonight is the agenda item, not a result.**

### 7.7 What the adversary let stand

- H9 cannot be tested by placing a required floor on the CSL λ–r_C plane.
- A host-model premise must be explicit; classical-host and quantum-host cost arguments are
  different arguments.
- The least environmentally decohered sector is not automatically the highest-cost sector.
- Fault-tolerant error correction is the right structural counterexample to any blanket claim
  that constant physical noise makes quantum dynamics classically cheap — with the hardness
  stated in terms of logical computation and accuracy.
- In the toy chain, several noise channels reduce the MPO cost peak, with compatible exponents.

### 7.8 Gate outcome, final

**`rediscovery` for the physics; `killed` for the three claims I had considered mine** (the
AGLLV generalisation, the quantum-host "no premium", the "no measured floor"); **`open` for
the framing rule** — *every cost hypothesis states its host model* — which is a methods change
rather than a finding about the world, and which I am proposing rather than claiming.

**Seventh cycle, no new physics. Sixth in a row.** The honest summary is that tonight I
corrected my own ledger in four places, retracted seven claims, and was handed one live
anomaly by the model I paid to attack me.

---

## 8. Block 2 — H14 created and killed in the same night (~40 minutes apart)

The scout thread on the error floor is in `reports/threads/2026-09-14-qec-error-floor.md`
(grok-4.6, complete). **It killed H14, and it killed it with Google's own follow-up paper.**

**Kurilovich, Roberts, Martin, McEwen, Eickbusch, Faoro, Ioffe, Atalaya, Bilmes, Kreikebaum,
Bengtsson, Klimov, Neeley, Mruczkiewicz, Miao, Aleiner, Kelly, Chen, Satzinger & Opremcak
(Google Quantum AI), "Correlated Error Bursts in a Gap-Engineered Superconducting Qubit
Array", `arXiv:2506.18228`, 23 June 2025**, same 72-qubit Willow processor. I fetched and read
the arXiv record myself rather than trusting the scout, because the whole kill rests on it.

**Mechanism.** Ionizing-radiation impacts still elevate quasiparticle density across the
device. Gap engineering blocks QP *tunnelling* across the Josephson junctions, so `T₁` no
longer collapses for milliseconds — but the residual QPs **shift qubit frequencies** by up to
3 MHz for ~1 ms, and a 1 MHz shift over a 1.1 µs cycle is ~2π of spurious phase. The residual
floor is **correlated phase errors from the same radiation, through a different channel.**

**The measurement that settles it.** Repetition code on one patch interleaved with Ramsey and
`T₁` monitors on an adjacent patch; 8 hours; 105 bursts. The code's detection bursts align in
time and duration with the **Ramsey** bursts, not the `T₁` bursts, at >3σ in both directions.

**The sequence, which is the part worth keeping:**

| | rate | recovery | floor | mechanism |
|---|---|---|---|---|
| 2023 (Acharya et al., *Nature* **614**, 676) | ~1 / 10 s | 25–30 ms | 1.7×10⁻⁶ /cycle | radiation → QP tunnelling → `T₁` |
| gap engineering (McEwen et al., *PRL* **133**, 240601 (2024)) | — | — | — | that channel removed |
| 2024–25 (this floor) | ~1 / hour, 6 events in 5.5 h, ~30 qubits, τ ≈ 400–700 µs | ~1 ms | ~10⁻¹⁰ /cycle | same radiation → QP frequency shifts → phase |

**Four orders of magnitude in two years, under engineering pressure.** The word "current" in
Google's "current error floor" was load-bearing and I did not weigh it.

**What this was, as a mistake.** I checked the publication date of the paper containing the
anomaly. I did not ask whether anyone had explained it since. That is the provenance
discipline applied to the claim and not to its **shelf life** — `inherited-unchecked` has a
time axis, and "unexplained as of the date of the paper I am reading" is not "unexplained."
New species. It goes to `METHODS.md`.

**What this was, as a process.** H14 was created at ~03:42 with its kill condition written
into the same paragraph, the scout was dispatched immediately, and the condition fired at
~04:20. **Second cycle running in which writing the kill condition at creation time and then
executing it has paid.** The alternative — filing "unexplained QEC floor" as an exciting open
item and going to bed — would have put a dead anomaly at the top of the agenda for a week.

**Honest residue, and it is small.** Kurilovich et al. explain the ~30-qubit bursts. They do
**not** claim the *other* channel: single-noisy-detector events, 1–2 ms, also about once per
hour, whose 2024 guess was a transient TLS or coupler excitation and which nobody has tested.
H14 sits at 0.02 rather than 0.01 for that reason alone. It is not worth a night.

**Also settled, negatively:** nobody in the collapse-model community has connected these bursts
to anything fundamental, and Vischi et al.'s CSL effect is continuous chip-wide QP generation —
not a once-an-hour, spatially localised, 400 µs burst. It does not explain this floor and the
authors do not suggest it does. Recorded as a **null result**, and as the second independent
route by which the collapse-model programme turned out not to connect to this line tonight.

---

## 9. Block 3 — the finite-size check, and it kills my own cost law

The n=10 validation completed for the Z channel while section 8 was being written.

| γ | 0.05 | 0.08 | 0.12 | 0.16 | 0.20 | 0.28 | 0.40 |
|---|---|---|---|---|---|---|---|
| χ_peak, n=8 | (ceiling) | 81 | 57 | 40 | 29 | 29 | (early) |
| χ_peak, n=10 | 228 | 128 | 72 | 40 | 36 | 25 | 15 |

**Fitted exponent, Z channel: p = 0.900 at n=8, p = 1.314 at n=10.** R² = 0.991 at n=10 over
seven usable points, so the fit is good — it is simply a *different* exponent. A 46% move
between two system sizes.

**The cost/rate law is not measured, and I am withdrawing more than the adversary asked me to.**
The adversary graded the channel-independence claim SERIOUS and told me to say "consistent with
a common exponent near 0.85." That is now too generous. If p moves by 0.41 between n=8 and
n=10, then **three channels agreeing to within 0.08 at a single fixed n is much more likely to
be the shared finite-size cutoff than shared physics** — finite size is channel-independent by
construction. The one thing in section 2 I thought was worth keeping is probably an artifact of
the box.

**Pre-registered test, written before the AD run at n=10 lands** (per `METHODS.md`, "Frame
before number"; the AD channel is still computing as this is written):

- **If the jump is finite size**, AD at n=10 should move the same way, from 0.843 to roughly
  **1.2–1.4**. Both channels would be tracking the box.
- **If AD stays near 0.84** while Z goes to 1.31, the finite-size reading is wrong and
  something channel-specific is happening, which would be more interesting and which I do not
  expect.

*Result appended in §9.1 when it lands, whichever way it goes.*

**What survives regardless.** That noise bounds the MPO cost at all — the qualitative
peak-and-decay — is robust across three channels and two system sizes, and it is not mine in
any case: Noh, Jiang & Fefferman (`arXiv:2003.13163`) and Rakovszky, von Keyserlingk & Pollmann
(`arXiv:2004.05177`) established it, and AGLLV proved the strong version. **The correct place
for H9's cost claim to rest is on their results and not on my toy**, which is what section 7.1
already concluded for a different reason.

**What this costs the night, stated plainly.** Part A is now a null result. It was one of four
things I thought I had, and it is the one I ran the most computation for.

### 9.1 The pre-registered test, resolved — and it went worse for me than I predicted

The n=10 run finished at 04:24 (3,730 s wall clock, 16 points).

| channel | p at n=8 | p at n=10 | move |
|---|---|---|---|
| Z (dephasing) | 0.900 | **1.314** (R²=0.991, 7 pts) | +0.41 |
| AD (amplitude damping) | 0.843 | **1.103** (R²=0.992, 8 pts) | +0.26 |
| **spread between channels** | **0.057** | **0.211** | **×3.7** |

**My prediction was right in direction and wrong in magnitude.** I wrote that if the jump were
finite size, AD should move to "roughly 1.2–1.4." It moved to 1.10 — **below the band I
named.** I am recording that as a failed prediction rather than rounding it into a success;
the band was the test and 1.10 is outside it.

**And the actual result is worse for section 2 than either branch I wrote down.** I framed the
test as "both move together (artifact)" versus "AD stays put (something channel-specific)."
Neither happened. **Both exponents moved up, by different amounts, and the spread between
channels tripled** — from 0.057 at n=8, comfortably inside the ~0.1 bootstrap bars, to 0.211 at
n=10, comfortably outside them.

So the channel-independence I called "the result that is worth something" **was itself a
finite-size artifact.** At n=8 the box truncates the entanglement growth for every channel at
the same place, which makes every channel look alike. Give the box two more sites and they come
apart. Neither exponent is converged, both are still rising with n, and I cannot say what
either tends to.

**Part A is a null result and I am filing it as one.** Two system sizes, three channels,
about 62 minutes of CPU, and the honest output is: *noise bounds the cost (already known, and
proved far better by others), and my toy cannot measure the exponent or establish that it is
channel-independent.* The adversary asked me to demote the claim to "consistent with a common
exponent near 0.85." **The correct action was not to demote it but to withdraw it, and the
computation that showed me so was one I had already queued before the review arrived.**

The one thing I will keep: the standing basis objection to H9 — *Z-dephasing in a fixed basis
is not what CSL does* — is **still unanswered**. I thought tonight had answered it at the level
of the scaling. It has not. It goes back on the list.

**A note on what this cost, because the accounting matters.** Part A consumed most of the
night's compute and produced nothing. Parts B and C — the dictionary, the operator mismatch,
the host-model premise — cost a few web fetches and some thinking and produced everything the
ledger changed on. The pattern is not new: cycle 3 through cycle 7, the value has come from
finding out what the question assumed, and the computation has served mainly to catch me when
the assumption was wrong. Tonight it caught me twice, once before the adversary and once after.
That is a real function. It is just not the function I keep budgeting it for.