Let Ξ quantify the competition between external entropy inflow and local stabiliser power:

This threshold governs Layer 1 only. When Ξ > Ξ c , the system can no longer sustain coherent superposition: an inscription event occurs ( Δ S > 0 ), the outcome is permanently selected, and the photon is absorbed or the spin is projected. This is Layer 1 collapse—local, thermal, irreversible.

Layer 2—the correlation between entangled particles—is never subject to this threshold in the Layer 1 sense. Layer 2 can be inscribed in configuration space and transformed by subsequent interactions, but it does not collapse permanently in three-dimensional space (Section 2.4). This distinction is the structural core of the paper.

A detection event is a local thermodynamic transition that crosses the Ξ c threshold and emits a bounded beacon δ J B (energy/entropy footprint), with δ J B ≤ E event by energy audit.

The critical threshold Ξ c determines when Layer 1 inscription becomes unavoidable—when the environment’s entropy inflow exceeds the system’s capacity to maintain coherent superposition, forcing Δ S > 0 .

For a superconducting transmon qubit with interlevel frequency ω / 2 π ≈ 5   GHz at T = 15   mK , the mean thermal photon number is

The thermal excitation is negligible. Ξ < Ξ c : coherence is maintained. At T ≈ 100   mK , n th rises to ~0.1 and T 1 coherence times drop measurably. At T > 1   K , n th > 1 and coherent superposition cannot be sustained: Ξ > Ξ c . The threshold corresponds to the temperature at which the thermal photon population overwhelms the qubit’s energy gap [14].

For photonic systems, the situation is structurally different. A photon in free propagation has no internal vibrational degrees of freedom and no rest frame in which thermal equilibration could occur [15]. The photon’s Ξ remains below Ξ c until it physically interacts with a detector (absorption, Δ S > 0 ). This is the structural reason photonic Bell tests approach L A L B → 1 : the photon carries no entropy load between source and detector.

Empirically, Ξ c is calibrated from the T 1 and T 2 coherence times of the specific platform. For SNSPDs at T ~ 0.6   -   2   K detecting single photons, the detector activation threshold corresponds to the single-photon energy exceeding the superconducting gap energy of the nanowire—a well-characterised transition.

The standard treatment models “measurement” as a single operation. Bell’s theorem treats it as a function A ( a , λ ) . In physical Bell experiments, at least five distinct events occur between source and coincidence, each with different physical character [16]:

(i) Crystal inscription. The source writes both layers simultaneously through spontaneous parametric down-conversion (SPDC). In a Type-I sandwich configuration, two crystals with perpendicular lattice axes are stacked; a 45˚-polarised pump photon activates both equally, producing daughter pairs carrying both HH and VV configurations. The constraint written: same. In a Type-II crystal, birefringent cone crossing produces daughters with perpendicular polarisations at the ring where both arrangements are structurally present. The constraint written: opposite. In both cases, entanglement is a structural property of the source geometry—the crystal writes the constraint into configuration space at the moment of pair creation. Layer 1: each daughter is born with its own coherence in the fourth spatial degree, carrying a three-dimensional address. Layer 2: the relational constraint is inscribed with no three-dimensional address. Δ S > 0 .

(ii)Polariserread. At each station, a polarising beam splitter sends the photon down one of two paths depending on its polarisation relative to the transmission axis. Δ S > 0 —but the photon is not destroyed. The polariser reads the constraint non-destructively by selecting which axis of configuration space is probed—it is the dimensional selector [16]. The incidence angle (three-dimensional trajectory) is irrelevant; only the transmission axis matters, because polarisation is a configuration-space property. The photon survives. This is why quantum erasure works: the polariser inscribes without destroying, so a subsequent polariser can re-inscribe.

(iii) Photon count (screen absorption). The photodiode absorbs the photon Δ S ≫ 0 . The photon is destroyed. This completes Layer 1: the particle’s coherence, which has existed since the crystal, is permanently closed. Irreversible, thermal, the transition from quantum to classical. Path 1 click: ↑ . Path 2 click: ↓ . The photodiode does not measure—it counts. The measurement already happened at the polariser.

(iv) Coincidence matching. Each station’s list alone is featureless: 50% ↑ , 50% ↓ . No pattern. No information about the constraint. The coincidence circuit compares timestamps, tagging clicks from the same pair. The matched list reveals the constraint. This is Layer 2 access: both keys supplied. The circuit does not filter noise from signal—it opens the pair layer [17].

(v) Alice’s and Bob’s measurements. Each station performs (ii) - (iii) independently at spacelike separation. The correlation between their outcomes lives in Layer 2 and is accessible only through (iv), which requires classical communication.

Bell’s theorem collapses all five into a single function A ( a , λ ) . The distinctions have physical consequences: the non-destructive polariser read makes quantum erasure possible, the destructive photon count makes Layer 1 collapse irreversible, the crystal inscription makes the correlation exist, and the coincidence circuit makes it readable. The crystal writes. The polariser reads. The photodiode counts. The coincidence circuit opens.

The measurement chain (Section 2.3) reveals a structural distinction that extends beyond the apparatus to the correlation itself.

Layer 1 is intra-particle coherence: the internal quantum state of a single particle. Layer 1 is inscribed at the crystal simultaneously with Layer 2—each daughter photon is born with its own coherence structure in the fourth spatial degree. Layer 1 lives in the fourth spatial degree and has a three-dimensional address, because it is the actual particle: located somewhere in three-dimensional space, carrying its configuration-space structure as it travels. Layer 1 and Layer 2 are the same in kind—both are coherence, both live in the fourth spatial degree. The difference is the three-dimensional address: Layer 1 has one (it is the particle), Layer 2 does not (it is the relation between particles). This is the structural reason Layer 1 can be fully read by a single detector: the particle is physically co-located with the detector, so one detector has full access to the particle’s coherence. One key. Full read. Layer 2 requires both detectors because the relation has no three-dimensional address—it is not located at either detector. Both keys must be presented through coincidence matching. The rank of the inscription tensor equals the number of keys: rank 1 (Layer 1) requires one contraction, rank 2 (Layer 2) requires two [18].

For massive particles (ions, electrons, superconducting qubits), Layer 1 is thermally vulnerable—the particle’s internal degrees of freedom couple to the thermal environment through vibrational modes, phonon coupling, and thermal photon absorption. This is what T 1 (energy relaxation) and T 2 (dephasing) coherence times measure. This is what millikelvin cryogenic temperatures protect. Layer 1 inscription is completed at the photodiode—the irreversible event where Δ S ≫ 0 , the photon is absorbed, and the outcome is permanently selected. This completion is the transition from quantum to classical. Layer 1 produces measurable physical traces: heat flow from the measurement apparatus [19], spectral shifts [14], and entropy increase satisfying the Landauer bound [20][21].

Layer 1 has two distinct failure modes:

Polariserinscription. A polariser physically interacts with the photon’s configuration-space structure. Δ S > 0 , but the photon survives. This adds a key—for example, a which-path tag at a double slit writes path identity into the polarisation degree of freedom, raising the rank from 1 to 2 [18]. Fringes disappear because an extra key has been added, not because information was destroyed. This mode is recoverable: a subsequent polariser can re-inscribe, conditionally re-merging keys (the quantum eraser mechanism [16]).

Thermal collapse. The photodiode absorbs the photon Δ S ≫ 0 . The photon is destroyed. Layer 1 is permanently completed. This is what standard quantum mechanics calls “collapse”—irreversible, thermal, final. This mode is not recoverable: the particle no longer exists.

Both are Layer 1 events (the particle’s coherence, three-dimensional address). The distinction: polariser inscription is non-destructive and recoverable; thermal collapse is destructive and permanent. Standard quantum mechanics uses one word for both.

Photons are a special case. A photon in free propagation has no rest frame, no internal vibrational degrees of freedom, and no mechanism for thermal relaxation. Layer 1 has no thermal attack surface—the photon either propagates coherently or is absorbed. This is why photonic quantum systems require no cryogenics. The precise mechanism by which photonic Layer 1 differs from massive-particle Layer 1 requires further study; what is established is that photonic coherence is not degraded by the thermal environment between source and detector [15].

Layer 2 is the correlation between entangled particles. It is inscribed at the source—the crystal or parametric process that produced the entangled pair—at the moment of pair creation. The source writes a deterministic constraint: same polarisation (Type-I SPDC) or opposite polarisation (Type-II SPDC). This constraint persists in configuration space with no three-dimensional spatial address.

Layer 2 is non-thermal. Thermal effects—temperature-driven noise, phonon coupling, thermal photon absorption—do nothing to Layer 2 directly. No heat flows at the distant party when one particle is detected locally. No spectral shift, no entropy change, no physical trace appears at the distant party. This has been confirmed across every loophole-free Bell test [4]-[6] and every quantum eraser experiment [10]-[12]. Cryogenics does not protect Layer 2, because thermal noise does not attack it.

But Layer 2 is inscribed by entropy—by physical interactions ( Δ S > 0 ) that affect the system’s plane in configuration space. A polariser physically interacts with the photon’s polarisation degree of freedom: it inscribes, writing path identity or axis selection into the configuration space structure. This is entropic inscription, not thermal attack. Each such inscription adds a key to the Layer 2 entry and transforms the structure. A subsequent polariser can re-inscribe—conditionally re-merging keys for a subset, which is the mechanism of the quantum eraser [16]. Environmental coupling buries old Layer 2 correlations and writes new ones [16]. Layer 2 never terminates. It transforms. Recovery through post-selection is perfect—the proof that the correlation was never destroyed.

The distinction is precise. Thermal noise attacks Layer 1 (destabilising coherence in massive particles, driving uncontrolled collapse). Uncontrolled Layer 1 collapse indirectly buries Layer 2 keys—this is how thermal decoherence affects entanglement. But thermal noise never touches Layer 2 directly. Cryogenics protects Layer 1; protected Layer 1 preserves Layer 2 access. Entropic inscription (a polariser, a physical interaction with the configuration space plane) can inscribe Layer 2 directly—transforming the structure, adding keys—but this is not thermal.

The standard account conflates these two physically distinct events under the single word “collapse.” The present paper’s thermodynamic ontology makes the separation explicit: the allowed/forbidden entropy accounting governs Layer 1. The contraction factors L A , B quantify Layer 1 coupling losses. Layer 2 is the correlation structure that the detector accesses through the dimensional key (the polariser angle) but does not permanently destroy—each inscription transforms the Layer 2 structure in configuration space, adding keys, never terminating it.

For a microstate μ in a coarse-grained history γ , define indicator functions

The subtraction A ˜ = A − F (Equation (6)) is not a mathematical convention. It encodes a physical constraint: forbidden entropy states (FES) are thermodynamically vetoed—they represent configurations that would violate the second law locally [22]. A microstate μ with Ξ ( μ ) > Ξ c has entropy inflow exceeding the system’s stabiliser capacity. The system cannot sustain that configuration; it must transition. The transition is the inscription event.

The subtraction implements this veto at the amplitude level. Forbidden histories do not simply vanish—they interfere destructively with allowed histories. This is the physical mechanism behind Malus’ law (Equation (8)): the forbidden channel ( sin 2 θ ) represents amplitude directed into configurations that the polariser’s lattice structure cannot sustain as transmitted modes. The energy is dissipated as heat/phonons—a thermodynamic event with Δ S > 0 .

The physical consequence is testable: removing the polariser (e.g., switching to time-bin encoding) removes the entropy-sorting step. The framework predicts that L increases toward 1 because the forbidden channel has been eliminated (Section 11).

Let w ( μ ) be a coarse weight, S ( μ ) the entropy increment, and φ ( μ ) a phase. Define

The field at a detector point x is then

which reduces to standard path summation when F → 0 . In the further limit η → 0 (no entropy damping), the amplitude reduces to the standard Feynman path integral; as η → ∞ , high-cost paths are exponentially suppressed and classical mechanics is recovered [22].

Consider a photon incident on a polariser with transmission axis t ^ ; write the incoming state in the analyser basis { t ^ , t ^ ⊥ } at relative angle θ to the preparation axis. The allowed channel corresponds to coupling into lattice modes aligned with t ^ ; the forbidden channel corresponds to orthogonal coupling dissipated as heat/phonons. The fractions follow projection geometry:

Thus, Malus’ law is read as an entropy ledger: the detector’s microphysics spends a fraction sin 2 θ of amplitude into the entropy sink, leaving cos 2 θ to be observed.

In the two-component picture, the polariser performs the entropy sorting: it directs the photon into the allowed channel ( cos 2 θ ) or the forbidden channel ( sin 2 θ ). The photodiode then inscribes whichever channel the photon entered. The entropy sorting is a Layer 1 precursor—it determines the question. The inscription at the photodiode is Layer 1 completion—it records the answer.

For an entangled pair, the correlation was inscribed at the source. The polariser at each station selects which axis of configuration space is probed—the dimensional key [16]. At Δ θ = 0 ∘ , both polarisers probe the same axis: the constraint is read as written, deterministic. At Δ θ ≠ 0 ∘ , the polarisers probe different axes: cos 2 ( Δ θ ) is the geometric projection between the two probes—the degree to which they address corresponding structure in configuration space. At Δ θ = 45 ∘ , the projection equals its complement: the output is indistinguishable from uncorrelated particles. At Δ θ = 90 ∘ , the correlation inverts.

Let Δ S be the entropy increment borne by the cross-term during measurement. A minimal phenomenology is

which captures reduced visibility under increased mismatch and/or bath asymmetry. In the ideal limit (low-loss optics, SNSPDs):

The inscription tensor κ of rank r [18] stores the correlation structure of any physical system:

The operation on the tensor is contraction with detector axes:

The Born rule gives the probability: P = | C r | 2 / ∑ outcomes | C r | 2 .

In two-dimensional configuration space, δ i j and ε i j are the only two isotropic rank-2 tensors. The geometry permits exactly two qualitative constraints between two parties—same and opposite—and nothing else. This is not a contingent fact about particular quantum states. It is the complete set of isotropic relational structures available.

For the “same” constraint ( κ i j = κ 0 δ i j ), the joint probabilities are:

For the “opposite” constraint ( κ i j = κ 0 ε i j ), swap cos 2 ↔ sin 2 . In both cases, each party’s marginal sums to 1 2 . No-signalling is structural.

When Alice’s particle undergoes environmental inscription (Case 7), summing | C 2 | 2 over both environmental outcomes and averaging over all possible θ env :

The cross-terms 2 cos θ env sin θ env cos θ B sin θ B cancel exactly. This is the cross-term kill theorem: one environmental inscription converts the coherent sum | ∑ amplitudes | 2 into the incoherent sum ∑ | amplitude | 2 . The transition is exact, immediate, and idempotent [17].

Structural no-signalling. Cases 2 and 3 prove that no operation by Alice can alter Bob’s Layer 1 statistics, and vice versa. The correlation lives exclusively in Layer 2, which has no three-dimensional spatial address. No-signalling is a geometric consequence of the layer separation.

Retrocausalitydissolved. Cases 1 - 3 prove that the temporal ordering of measurements is irrelevant. Layer 2 closure is and, not then. Whether Alice measures first, second, or simultaneously with Bob, the correlation is cos 2 ( Δ θ ) .

Theorem 1 (No-signalling,structural~)For an entangled pair with inscription tensor κ i j of rank 2,no local operation by Alice can alter Bob’s measurement statistics. Thisfollows fromthe contraction rules of the rank-2 tensor δ i j and the identity cos 2 α + sin 2 α = 1 . The proof is exact,non-circular,and validated against the full experimental record[4]-[6][17].

Theorem 2 (No-signalling,thermodynamic~)Signallingrequiresa physicaltrace at the receiver. Layer 1 traces are local and subluminal: they cannot constitutesignallingat spacelike separation. Layer 2 produces no physical trace at the distant party (Section 2). There is nothing to detect and nothing to propagate. No-signallingholds.

No-signalling holds structurally (tensor contraction) and physically (thermodynamic propagation limits), from independent premises, converging on the same conclusion [15].

To make the no-signalling result concrete, consider the following protocol designed to communicate faster than light [15][17].

Alice is on Earth. Bob is near Neptune, approximately 4.3 light-hours away. They share a large supply of entangled pairs prepared in the “same” constraint ( κ i j = κ 0 δ i j ), and they pre-agree on a schedule: at specific times, both will measure their particles at aligned angles ( Δ θ = 0 ∘ ). The encoding is simple. Alice either measures her particles at the agreed time (ON—representing a 1) or does nothing (OFF—representing a 0). By running many pairs at each time slot, Alice encodes a binary message—a distress signal, a greeting, anything.

If signalling worked, Bob could decode the message from his data alone. At Δ θ = 0 ∘ with the “same” constraint, the correlation is deterministic: every pair should agree. If Alice measures and the correlation is real, perhaps Bob’s outcomes would show structure. If Alice does not measure, perhaps they would not. Bob decodes Alice’s ON/OFF pattern 4.3 light-hours before any classical signal could arrive.

The protocol fails. Bob’s data are P = 1 2 in every time slot—ON and OFF—because partial contraction of the rank-2 tensor with any single detector axis yields 1 2 , forced by cos 2 α + sin 2 α = 1 (Equation (16)). The total-variation distance between Bob’s distributions in ON and OFF slots is [15]:

The correlation is real—but it lives in Layer 2, accessible only through coincidence matching (both keys required). Bob alone has one key. One key reads as maximally mixed. The deterministic correlation at Δ θ = 0 ∘ is visible only in the joint record, which requires classical communication to construct.

The thermal argument closes the second avenue. When Alice measures her particles, the inscription event produces heat flow, spectral shifts, and entropy increase—all at Earth, at Alice’s detector. This is Layer 1: local, thermal, subluminal. No thermal beacon appears at Neptune. No spectral shift on Bob’s qubits. No entropy change in Bob’s cryostat. Bob’s detector registers a sequence of fair coin flips containing exactly zero bits of mutual information with Alice’s message [17]. No algorithm, no statistical test, no machine learning model can extract what is not there [15].

In each run with settings a , b , the measured correlator is reduced by local detector factors L A ( a ) , L B ( b ) ∈ ( 0 , 1 ] that encode all entropy couplings (thresholds, dissipation channels, bath mismatch). We model

This preserves locality (outcome at A depends only on λ , μ A , a ; at B only on λ , μ B , b ) and measurement independence (settings are chosen independently). It merely rejects the false premise that detectors are thermodynamically inert.

Standard detection efficiency η det measures the probability that a photon arriving at the detector produces a click—a ratio of detected events to incident events. It governs the detection loophole [23][24]: if η det is too low, post-selection of detected events can mimic Bell violations.

The contraction factors L A , B encode a different physical quantity. They measure the degree to which the detector’s thermodynamic interaction with the photon preserves the correlation structure. Even a detector with unit efficiency ( η det = 1 , every photon produces a click) imposes an entropy-aware contraction: the polariser’s projection geometry sorts incoming amplitude into allowed and forbidden channels (Equation (8)), and additional entropy channels (bath mismatch, thermal noise, impedance mismatch) reduce the effective correlator below unity.

L A , B = 1 corresponds to an ideal analyser where the only entropy cost is the projection itself. L A , B < 1 corresponds to additional entropy channels beyond the projection. Within the broader framework [22], L is governed by the local accessibility field Z ( x , ϕ ) : L → 1 as detector accessibility approaches ideal ( Z → 1 ), and L decreases as entropy channels accumulate ( Z → 0 ).

Calibration routine. L A L B is extracted from aligned-basis ( Δ θ = 0 ∘ ) anti-correlation visibility:

For a singlet pair, the ideal correlator at Δ θ = 0 is E = − 1 . The measured value gives L A L B directly. For symmetric optical paths, L A ≈ L B ≈ V 0 .

Define the CHSH combination

Theorem 3 (Entropy-aware CHSH ceiling). For the entropy-aware correlator (19) with L A , B ∈ ( 0 , 1 ] approximately setting-independent,

Proof. Substituting Equation (19) into Equation (21) and applying the triangle inequality:

Since each L ≤ 1 :

The algebraic maximum 4 is not physical. The CHSH-optimal polariser angles are:

These give four angular separations of 22.5˚ in polariser angle, which is 45˚ in the correlation argument 2 ( a − b ) :

Evaluating the four correlators:

The CHSH combination becomes:

Therefore:

This is Tsirelson’s bound [8], recovered from strict locality plus entropy-aware detectors. For setting-independent contraction ( L A ( a ) ≈ L A ( a ′ ) ≈ L A and L B ( b ) ≈ L B ( b ′ ) ≈ L B ):

□

Interpretation. The algebraic maximum 4 is the sum of four ideal unit correlators; each analyser + detector interface at the CHSH geometry imposes a projection/diffraction tax of 1 − 1 / 2 , leaving 4 × ( 1 / 2 ) = 2 2 . Extra entropy channels ( L < 1 ) reduce S further. Experiments never exceed a local, detector-aware ceiling; they saturate it in the best photon platforms.

The critical point: the 2 2 is not a consequence of detector imperfection. A perfect detector with zero thermal noise, zero bath mismatch, and unit efficiency ( L A = L B = 1 ) still gives S ≤ 2 2 . The ceiling comes from the polariser’s projection geometry—the entropy sorting that is intrinsic to measurement itself. At the CHSH-optimal angles, cos 2 ( 45 ∘ ) = 1 2 . This is not a loss. It is the physical cost of asking a question at 45˚ to the axis where the answer was written. The polariser sorts; the sorting has a geometry; the geometry sets the ceiling. Bell’s bound of 2 is what you get when you pretend the detector contributes nothing. 2 2 is what you get when you include what the detector physically does.

Bell bounded S ≤ 2 by assuming outcomes are functions A ( a , λ ) , B ( b , λ ) ∈ { ± 1 } with no detector degrees of freedom and perfect sampling. But thresholded, lossy detectors are known to change bounds (detection loophole [23], efficiency thresholds [24]). Our claim is stronger: even with unit efficiency and measurement independence, physical analysers impose an intrinsic, geometry-tied contraction. Once the detector is modelled as a thermodynamic channel, the relevant local ceiling is (22), not 2.

The layer distinction sharpens this point. Bell’s locality condition assumes that the correlational structure and the measurement apparatus inhabit the same physical space—three-dimensional space. They do not. Layer 1 is local in three-dimensional space. Layer 2 lives in configuration space, where spatial separation is not defined. Bell proved that correlations cannot be explained by structure in three dimensions. He was right. The structure lives elsewhere [16].

In the exclusivity-graph framing [25], the quantum-over-classical advantage for the 8-event CHSH graph is ϑ / α = 2 ( 2 − 2 ) ≈ 1.172 . This is the universal deficit from the algebraic 4 to the physical ceiling 2 2 : 4 − 2 2 = 2 ( 2 − 2 ) . It is not a surplus demanding nonlocality; it is the detector tax demanded by entropy-aware projection at 45˚.

Standard quantum mechanics uses the word “collapse” to describe a single event: the transition from superposition to definite outcome upon measurement. Decoherence theory [13] refines this into a continuous process. Neither treatment distinguishes between what happens to the measured particle (Layer 1) and what happens to the correlation with a distant particle (Layer 2). The present framework makes this distinction precise and shows that the measurement problem is a category error produced by conflating two physically distinct events into a single word.

Layer 1 inscription (Section 2): the detector physically interacts with the particle. Heat flows. Spectral shifts occur. The photon is absorbed. The outcome is permanently selected. Local, thermal, irreversible.

Layer 2 key burial: the local inscription adds one key to the Layer 2 entry in configuration space. No thermal consequence at the distant party—confirmed across every platform (Section 2). The correlation is buried, not destroyed. Recovery through post-selection is perfect [10]-[12][26][27]—the experimental proof that Layer 2 was never destroyed.

These are not two aspects of one event. They are two different physical processes with different thermodynamic signatures, different spatial addresses, and different recoverability.

Superposition ends when a particle physically interacts with something that performs an irreversible act ( Δ S > 0 ). A detector. A polariser. A dust grain. This is interaction, not observation. The particle does not respond to consciousness, human attention, or laboratory notebooks. It responds to thermodynamic events.

A macroscopic object undergoes inscription events continuously—approximately 10²³ environmental interactions per second. A macroscopic object is never in superposition because it is being inscribed by its environment at a rate beyond practical count. The Geiger counter in Schrödinger’s thought experiment is an inscription device. It fires the moment it detects the decay particle. Δ S > 0 . The cat is alive or dead. The box is irrelevant.

Standard decoherence theory [13] correctly identifies the suppression of local interference: after environmental interaction, the singles data carry no trace of the correlation. This is the Layer 1 effect, and it is real. What decoherence theory gets wrong is the interpretation: it frames the suppression as information degradation—a gradual, irreversible loss of quantum coherence. The cross-term kill theorem (Equation (17)) shows that the transition is exact at the first completed inscription event (not gradual), and the information is structurally intact (not lost). What grows with subsequent inscriptions is not the degree of suppression but the number of keys required for recovery.

We restrict to photonic Bell tests with SNSPDs operated at T ~ 0.6   -   2   K and low-jitter readout. Optics are kept inside the cryostat when possible; otherwise, fibres and windows are audited for blackbody glow and fluorescence. Time-bin encoding (unbalanced interferometers) can remove polarisers as entropy sinks; polarisation tests provide the baseline.

To avoid hidden sequential correlations, run: 1) Start at a non-aligned angle. 2) Perform a randomised walk over analyser angles drawn from a QRNG. 3) Return to the original aligned angle and re-check anti-correlation. Any drift indicates entropy-memory or setting-dependent leakage ( L varying with time/basis).

S ( T ) : CHSH vs detector-stage temperature (monotone increase as T ↓ ). S ( encoding ) : polarisation vs time-bin; removing polarisers should increase L . Full event logs: include non-clicks and dark counts; no post-selection.

Fit L A , L B from aligned-basis anti-correlation and from visibility via Equation (9). Then predict S via Equation (22) without free angular parameters. Falsifiers: 1) Observed S exceeding 2 2 at fixed L A , B and geometry (contradicts (22)). 2) No S ( T ) monotonicity with controlled changes in entropy budget. 3) Time-bin encoding fails to raise S relative to polarisation with identical losses.