A Three-Party Bell Test During the Partial Sophon Suspension: Why the Intervention Loophole Cannot Be Closed by Declaration

1. Introduction

The usual position holds that declared suspension of sophon activity under the Dark Forest Deterrence makes the intervention loophole irrelevant to every Bell test run since, so that any violation observed in the Deterrence Era is genuine by construction. This position is wrong, and the reason is provenance. The declaration originated with Trisolaris, the party whose interference is in doubt, and reached us only as relayed and recorded by the Planetary Defense Council (United Nations Planetary Defense Council, 2 DE). No instrument has confirmed it (Xiang and Tong, 33 DE), so a test that takes suspension as an input inherits exactly the trust it was built to remove.

A Bell inequality bounds the correlations that outcomes fixed in advance can produce at separated stations, and quantum states of three or more particles can exceed the bound. That is, a record that violates the inequality cannot have been generated by instructions that the particles carried from the source. The inference holds only if nothing else wrote the record. A sophon at a detector can set the logged outcome of any single measurement, so every test since the first sophons arrived has carried the so-called intervention loophole (Pei and Hao, 36 CE).

Pei and Hao gave the first formal model of outcome substitution at distributed detectors. Ding Yi, who inspected the droplet (strong-interaction probe, SIP) before his death in the Doomsday Battle, led a group that proposed to close the loophole by separating the stations faster than a sophon could relay instructions between them (Lan, 74 CE). Later work found no measurable lower bound on the relay latency of paired sophons at any terrestrial baseline (Qin and Gu, 152 CE). The Institute then extended the analysis from two stations to three, where an intervention at one station can be told apart from genuine nonlocality within a single run (Rong and Cen, 12 DE).

A gap remained. None of these results says what a violation certifies when the intervention model itself is unknown.

Our protocol closes that gap. It takes no position on sophon activity, and it asks that the violation hold up under local filters applied once the detection record is sealed. This account is written in Deterrence Era, Year 59, while Trisolaris still exists and the suspension stands declared but unverified, and all data were taken between Year 57 and Year 59. Section 2 sets out the protocol, Section 3 reports nine runs at three stations, and Sections 4 and 5 state what the numbers do and do not establish.

2. Methods

Three stations in the Beijing basin each hold one photon of a three-photon polarisation-entangled state prepared at a central source. At each station a local random generator chooses a polarisation measurement in the X basis or the Y basis, and a detector logs the outcome as +1 or -1 together with the analogue pulse amplitude of the detection. A triple event is a coincidence of the three detections inside a 4 ns window. The apparatus and the run manifests are held in the Institute archive (Reconstituted Chinese Academy of Sciences, Institute of Physics, 59 DE).

We used the Mermin inequality for three parties. Each of the four setting combinations XXX, XYY, YXY and YYX was measured on 51,600 triple events, which gives 206,400 in all. The four other combinations (XXY, XYX, YXX and YYY) do not enter the Mermin form and were not scheduled. Settings followed a stratified schedule lodged in the seal, in which every block of 16 events held each used combination four times, so that each quarter of the record holds exactly 12,900 events per setting. Writing E for the mean product of the three outcomes, the value M = E(XXX) - E(XYY) - E(YXY) - E(YYX) cannot exceed 2 under any local model, and it reaches 4 for an ideal three-photon entangled state.

Each station chains a digest over every block of 1,024 events and lodges the running digest with the other two stations and with the archive at the end of each run, following the chained-digest procedure of Kuang (49 DE). The record is sealed when all three digests are lodged. No analysis choice of any kind is made before sealing, and no event can be altered afterwards without breaking the chain at its station.

The filter family was fixed in the run protocol before the first run and applied only after sealing, so it cannot have been chosen to suit the data. A filter has two parts, and both are defined on local data only. The first is a pulse-amplitude cut that drops, at each station, the lowest 0%, 5%, 10% or 15% of detections by amplitude. The second is a time mask that keeps any non-empty subset of the four equal quarters of the record. The family is the complete set of 4 x 15 = 60 combinations. Every filter is applied to all three stations at once, since an event is retained only if all three of its detections pass the cut.

Let δ_k be the share of events fabricated within setting group k, by a sophon or by any other agent, with the unforged events of every group drawn from one local model. The four correlators come from disjoint groups, and a deterministic local strategy makes the product of the four group products equal to +1, so such a record has M no greater than 2 + 2 max δ_k in any filter that retains events in the same proportion from every group. We therefore report, for the least favourable filter, δ* = (M_min - 2)/2. That is, δ* is a lower bound on the largest within-group forged share. Because the four groups are equal in size, a forger that confined its fabrications to one setting needed at least δ*/4 of all events. The quantity makes no assumption about when a sophon acts, how it acts or whether it acts at all. It does assume that the amplitude distribution of detections is the same for every setting, since a cut that retained different shares in different groups would break the argument.

The standard error of each correlator follows from its binomial variance, and because the four correlators are measured on separate events, the variance of M is the sum of the four. Intervals are the estimate plus or minus 1.96 standard errors. Since M_min is the lowest of 60 correlated filters, we also report a lower limit corrected for multiplicity with a Bonferroni critical value of 3.34, which is conservative for correlated filters.

To calibrate the family we built three synthetic records of 206,400 events from a deterministic local model with M exactly 2, each with 15% of all events fabricated by setting the product to its maximal-violation sign. In the uniform record the fabrication was spread evenly over time and over the four groups, so every δ_k was 0.15. In the time-concentrated record it was confined to the third quarter, where 60% of the events in every group were fabricated. In the setting-confined record, 60% of the YYX group was fabricated across the whole run and no other group was touched. Amplitudes of synthetic events were drawn from the distribution of genuine detections, so no amplitude cut can separate them.

3. Results

Nine runs between Deterrence Era, Year 57 and Year 59 yielded 206,400 triple events. The four correlators were 0.813 for XXX and -0.813, -0.816 and -0.811 for XYY, YXY and YYX. Unfiltered M was 3.254, 95% CI 3.244 to 3.264, which exceeds the local bound of 2 by about 245 standard errors.

Detection amplitude did not depend on the setting. The mean pulse amplitude pooled over the three stations was 0.979, 0.980, 0.980 and 0.980 in arbitrary units for XXX, XYY, YXY and YYX, with a standard deviation of 0.176 in each group, over 154,800 detections per group.

Every one of the 60 filters kept M above 3.2, and the lower end of every interval stayed far above the local bound. The least favourable filter was the fourth quarter of the record with no amplitude cut, at 3.247, 95% CI 3.226 to 3.267, on 51,600 events. The most favourable was the third quarter with a 15% cut, at 3.705, 95% CI 3.688 to 3.721, on 31,727 events. Amplitude cuts raised M step by step, from 3.254 with no cut to 3.601, 3.672 and 3.702 at cuts of 5%, 10% and 15%, because the lowest-amplitude detections are the ones that detector noise most often partly randomises, and the cuts retained 85.7%, 72.9% and 61.3% of the events. The 79,834 events removed by the 15% cut still gave an implied M of 2.543, 95% CI 2.522 to 2.564, which is above the local bound but far below the retained value. The four quarters taken singly with no cut gave 3.253, 3.251, 3.264 and 3.247, each with a standard error of 0.010.

At the least favourable filter, δ* = 0.62, with a lower 95% bound of 0.61 and a Bonferroni-corrected lower bound of 0.61 as well, since the corrected lower limit on M_min is 3.212. A forger that held its unforged events to a local model therefore had to fabricate at least 0.61 of the events in its most heavily forged setting group. If it confined itself to one setting, that is at least 0.15 of all events.

The injection records behaved as the bound requires. In the uniform record, unfiltered M was 2.302, 95% CI 2.296 to 2.309, and the least favourable filter gave 2.289, 95% CI 2.274 to 2.305, so δ* was 0.14 against a true within-group share of 0.15. In the time-concentrated record, unfiltered M was 2.299, 95% CI 2.293 to 2.305, which a test without filters would have accepted as a violation at about 95 standard errors. The first, second and fourth quarters each gave exactly 2.000, and δ* was zero. In the setting-confined record, unfiltered M was 3.204, 95% CI 3.196 to 3.213, and the least favourable filter gave 3.177, 95% CI 3.155 to 3.198, so δ* was 0.59 against a true within-group share of 0.60, or 0.15 of all events.

4. Discussion

A corrected position can now be stated with numbers attached. In every one of 60 filters M stayed at or above 3.247, so a record built from a local model plus fabricated events needed a forged share of at least 0.61 in its most heavily forged setting group, and at least 0.15 of all events if the fabrication was confined to one setting. Declared suspension is therefore not an input to the result. The claim depends on the bound and on the amplitude check, but it does not depend on the declaration.

Our named alternative is a setting-targeted forger. Pei and Hao showed that substitution can be conditioned on the local setting, which a sophon at each station knows. Qin and Gu showed that paired sophons coordinate across a terrestrial baseline without measurable delay, so ubiquity and coordination are no obstacle to such a forger. Rong and Cen showed that a three-station test separates substitution at one station from nonlocality, but only when the substituted share is large. Hence our record cannot exclude a forger that fabricated about 0.16 of all events within one setting, and indeed our own setting-confined injection produced M of 3.204, close to the 3.254 observed. We still consider this the less likely account. Such a forger would need the setting at each station and would have to match the amplitude and event-rate statistics of genuine detections across nine runs, with no dependence on setting that the amplitude check could find. The stable value of M across the four quarters is the null expectation for a source and detectors that did not change, and a forger acting in bursts could depart from it.

These data are in line with a suspension that holds, and they do not discriminate against one that fails. As ecumenicals we hold that cosmic sociology describes how a sophon-bearing civilisation behaves, while the vacuum structure the sophon exploits is perhaps shaped by something the dark-forest axioms do not describe, and the measurement cannot choose between these positions. What it settles is narrower, since the data no longer wait on the suspension.

For the first time, a Bell violation taken under a declared suspension carries a certificate that does not rest on the declaration. The proposal of Ding Yi's group to outrun the relay assumed a speed limit that no terrestrial baseline has been shown to impose, and the sealed record replaces that assumption with an inequality on the data themselves.

5. Limitations

Because the family of filters is public, a forger that knew the cut levels and quarters could spread its fabrications evenly over time and match the amplitude distribution. Such a forger would pass at the level δ* and no lower.

The bound assumes that the amplitude distribution is the same for every setting. We checked means and spreads, which agree to the third decimal, but that check does not exclude a dependence in higher moments or in the joint amplitudes of the three stations.

Under the bound, the unforged remainder counts as local, which is the most generous assumption for a forger and so the most conservative for us. Where the remainder is a genuine entangled state, as in our data, δ* understates the evidence. Trust in the seal rests on the three digests lodged with the archive, and an agent that controlled all three stations and the archive at once would defeat it.

The corrected position reaches back over the record. Deterrence-Era Bell violations that were accepted because suspension had been declared, including the Institute's own results before Year 57, stand uncertified and not refuted until each is repeated with a sealed record and a registered filter family.

We tested three parties at one site over nine runs. Four or more parties, a second site and a longer baseline are untested, and the question that remains is whether the filtering advantage survives each of them.

The measurement decides that a Deterrence-Era violation can be certified without the declaration. It does not decide whether sophons were active, whether the declaration is true, or whether a setting-targeted forger was present. The original position may now claim that a suspension which holds would leave these data unchanged, but it may not claim that the data show the suspension holds.