Empirical/CSD/Crypto: B92 — false conclusive clicks from a dynamical intercept #
Category: CSD bridge (dynamical). An instantiation of the BB84Sequential engine on the
B92 unambiguous-discrimination round — recorded as such: the dynamical theorem is the same
calibrated-swap fact, re-read on B92's conclusive-click semantics.
The round #
B92 encodes bit 0 in |0⟩ and bit 1 in |+⟩. Bob's conclusive detector for bit 0 is the
|−⟩ click: honest carriers of bit 1 (|+⟩) can never trigger it (⟨−|+⟩ = 0,
b92_unambiguous_zero on the QM side). This module gives that unambiguity its ontic form and
then shows what an intercepting Eve does to it:
b92_honest_false_click_null— the conclusive-bit-0basin is a null set for a|+⟩carrier: unambiguity is an ontic impossibility (a zero-width context-fixed basin), the same shape as the eraser's dark fringe. The Z-side counterpartb92_honest_false_click_null_z(a|0⟩carrier never triggers the conclusive-bit-1click) ismomentMap_vertex.b92_conclusive_basin_half— the honest conclusive rate½(b92_conclusive_rate_one's X-side counterpart) as a basin measure.- ★
b92_eve_false_click— Eve Z-intercepts a|+⟩carrier (the calibrated-swap dynamics); Bob's conclusive-bit-0basin now has probability½, whatever Eve recorded — false conclusive clicks at rate½where honestly there is nothing inΣto produce one. - ★
b92_eve_detectable— the strict contrast: the intercept raises the false-click probability strictly above its honest value0. Eavesdropping announces itself in the conclusive statistics.
⚠️ Honest scope #
One sifted round; the dynamical content is bb84_wrong_basis_error re-read (stated, not
hidden); Eve's basis choice stays classical bookkeeping. Inherits the calibrated-swap witness's
scope notes via SequentialMeasurement.lean. The unambiguous-discrimination optimality
(IDP bound) and full key-rate analysis remain on the QM side and the recorded QKD tranche.
References #
Empirical/QM/Crypto/B92.lean (b92_unambiguous_zero, b92_conclusive_rate_one,
ketMinus_inner_ketPlus, ketPlus_unit); Empirical/CSD/Crypto/BB84Sequential.lean (the
engine: xBasisON, xContext_rate_vertex, bb84_wrong_basis_error);
SigmaLayer/RotatedContext.lean (basisContext_rate_mk); Bennett 1992; specs/BACKLOG.md.
The honest X-context rates at the two carriers #
Unambiguity as a null basin #
Unambiguity is an ontic impossibility. For a |+⟩ (bit-1) carrier, the
conclusive-bit-0 basin (|−⟩ click) is a null set: the context-fixed fibre arc has width
zero at that base point. No microstate of an honest bit-1 carrier produces a false conclusive
click — the same shape as the eraser twin's dark fringe.
The Z-side unambiguity: a |0⟩ (bit-0) carrier never triggers the conclusive-bit-1
click (|1⟩ in the computational basis) — momentMap_vertex at the off-index.
The honest conclusive rate: a |0⟩ carrier triggers the conclusive-bit-0 click with
basin measure ½ — B92's ½ conclusive rate as a fibre-arc width.
The intercepted round #
★ Eve creates false conclusive clicks. Alice sends |+⟩ (bit 1); Eve measures in the
computational basis and the calibrated-swap dynamics resends her eigenstate; Bob's
conclusive-bit-0 basin now has probability ½ — whatever Eve recorded. The dynamical
fact is bb84_wrong_basis_error, re-read on B92's click semantics: where honestly no
microstate could produce this click, the intercept produces it half the time.
★ The intercept is detectable in the conclusive statistics: for every Eve outcome, the false-click probability is strictly above its honest value (zero).