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REVIEW 3 major objections 4 minor 72 references

VIGIL: Verifying Identity via Gated Intermittent Likelihoods for Continuous Biometric Authentication

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read VIGIL is a continuous-authentication framework whose core rule is that only actual biometric observations may increase the probability a user is genuine; without them, trust decays monotonically and attackers cannot simply wait out verifica

desk verdict Sound anti-backflow math undercut by a walkthrough that contradicts VIGIL's own transition rule. read the letter →

arxiv 2607.16651 v1 pith:NRQFKFJT submitted 2026-07-18 cs.CR

Aldridge Fonseca , Udayan Atreya , Amith Kamath Belman , Frank Sicong Chen This is my paper · ORCID
classification cs.CR
keywords continuousauthenticationmultimodalbiometricstemporalfusionstatetransitionmachineunidirectionalmatrixadaptiveverificationwindowmonotonicdecaybackflowelimination
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to prove that continuous authentication can be made both faster and more usable by enforcing a single rule: the system's belief that the current user is genuine may only increase when real biometric observations arrive, and must decay monotonically when they do not. To implement this, it proposes VIGIL, a dual-state Markov framework whose transition matrices are unidirectional, so probability mass cannot flow back from Suspense to Normal without evidence. The authors argue this closes a loophole in prior temporal-fusion systems, where an attacker could wait out a verification window and regain a trusted state for free. They further claim that a three-zone decision model, which allows multiple verification rounds when evidence is inconclusive, together with an adaptive window that shrinks on each repeat entry, shortens the time to detect persistent attackers while preserving usability for legitimate users. The evaluation is analytical; the paper itself identifies empirical validation on real datasets as the natural next step.

What carries the argument

The central mechanism is the unidirectional state transition matrix used in both state transition machines (STM1 for cruise and STM2 for verification). In STM1, the Suspense state is absorbing during temporal fusion: probability mass leaving Normal cannot return without a Bayesian update from actual biometric observations. In STM2, entry transfers all Suspense mass to Alert, and the decay function q(Δt) governs Normal-to-Alert erosion. This, together with the three-zone decision model and the penalty-based adaptive window W_current = max(W_min, W_base − penalty), carries the argument: no-observation periods monotonically reduce P(N), and repeated inconclusive verification rounds compound pre

What would settle it

Measure VIGIL end-to-end on a real multimodal dataset (e.g., face plus voice or keystroke) with natural sensor dropout and a simulated persistent attacker: if the false-alarm rate for genuine users whose observation gaps exceed the minimum window (1 s) is unacceptably high, or if the time-to-alert for an attacker who produces neutral evidence is not shortened relative to a static-window baseline, then the claim that VIGIL reduces detection time while preserving usability is falsified.

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Extended reading notes

Core claim

The central claim is that a continuous authentication system should treat biometric evidence as the only permissible cause of an increase in the posterior probability P(N) that the current user is genuine. VIGIL enforces this with unidirectional transition matrices in both of its state transition machines: in cruise mode (STM1), the Suspense state is absorbing during temporal fusion, so P(N) can only fall as time passes without observations; in verification mode (STM2), all Suspense mass is transferred to Alert at entry and only a fresh Bayesian update from actual observations can raise P(N). The paper proves monotonic decay and shows analytically that a baseline approach with a Suspense-to-

Load-bearing premise

The load-bearing premise is that legitimate users, in real deployments, will supply enough biometric observations with strong enough fused scores that the monotonic decay of P(N) and the alert-on-no-observations rule will not lock them out — an assumption about real sensor dropout and score distributions that the paper does not test empirically.

Editorial extensions

If this is right

  • A persistent attacker who triggers suspicion cannot wait out a static window and return to Normal: the no-observations branch in P2 alerts immediately, and re-entry into P2 shortens the active window.
  • Suspicion does not reset over time: because P(N) decays monotonically without observations, the system requires progressively stronger biometric evidence to recover in later rounds.
  • Operators can select fusion strategies (product, weighted sum, weighted geometric mean) per active sensor subset, so a weak sensor cannot collapse the fused likelihood the way the plain product rule does.
  • The penalty mechanism gives legitimate users a full window after stable Normal behavior (penalty decays at rate λ), so the claimed usability cost is bounded.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct corollary the paper does not spell out is that the unidirectional principle transfers to any continuous trust system—zero-trust access, anomaly detection, fraud scoring—where the absence of positive evidence should lower confidence, not merely leave it unchanged.
  • Because the monotonic decay proof is independent of the fusion function, the security benefit of VIGIL holds for any per-modality combination rule; operators can therefore tune fusion for accuracy or robustness without weakening the no-backflow guarantee.
  • The framework's parameters are hand-set (table S1), so a testable extension is automated parameter tuning: a deployment could search over (T_stay, T_back, T_alert, W_base, δ, λ) on a validation set to explicitly trade off false alarms against time-to-detection.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes VIGIL, a continuous multi-modal biometric authentication framework built on two state-transition machines. The main technical contribution is a unidirectional temporal-fusion design: in both cruise mode (STM1) and verification mode (STM2), probability mass can leave the Normal state but cannot return to it without new biometric evidence, eliminating the S-to-N backflow that the authors identify in the baseline SSPRA model. The paper also introduces a configurable subset-level fusion strategy, a three-zone P2 decision model with multi-round verification, and an adaptive shrinking verification window. The evaluation is entirely analytical: monotonic decay is proved from the transition matrices, and six numerical walkthrough scenarios are presented in the supplementary material to illustrate recovery, gradual alert, no-observation alert, max-round exhaustion, and penalty decay.

Significance. The core mathematical observation is sound and useful: replacing SSPRA's S-to-N recovery path with an absorbing Suspense state gives strict monotonic decay of P(N) under no observations, and the derivation in Eqs. (3)-(6) and (12)-(14) is clean and easy to verify. The paper is also honest in Section 4 about the lack of empirical validation and about the hand-set nature of the parameters. If the internal inconsistency described in the major comments were resolved, the unidirectional temporal-fusion idea would be a legitimate incremental improvement over SSPRA. However, the abstract's stronger claims, specifically that VIGIL 'reduces the time to detect intrusions while maintaining high usability,' are not supported by the current analytical walkthroughs, and one of those walkthroughs contradicts the paper's own mode-transition rule. The significance of the contribution is therefore real but narrower than the paper claims.

major comments (3)
  1. [§3.3 / Supplementary Scenario J.2 and Table 6] The P1-to-P2 transition rule is stated as occurring 'when P(N) drops below the stay threshold T_stay during cruise mode.' Using Eq. (4) with the default τ_p=10s and T_stay=0.70, a user at P(N)=0.95 (the value entering the 20s Normal period in Scenario J.2) drops below T_stay after approximately 4.4s without observations. Scenario J.2 and Table 6 nevertheless assume 10-20s Normal periods with no observations. If the rule is continuously enforced, those periods are impossible and the user would enter P2, where the no-observation rule triggers an immediate alert—contradicting the claimed usability benefit. If the rule is event-driven (checked only when an observation arrives), an attacker who withholds all observations never enters P2, so the stalling-prevention claim in Section 3.3.5 is vacuous. Either interpretation invalidates the walkthrough's demonstration of penalty decay and window r
  2. [Abstract and §4] The abstract claims VIGIL 'reduces the time to detect intrusions while maintaining high usability.' This is not derived or measured anywhere in the paper. The six scenarios in the supplementary material assign strong likelihoods to genuine users and weak likelihoods to attackers, so the outcomes are forced by the input scores; they do not quantify time-to-detection, false-alarm rates, or lockout probability under realistic sensor dropout. Section 4 explicitly states that 'Empirical validation on multimodal datasets is a natural next step.' The categorical claim in the abstract should be qualified to a design objective or supported by a formal performance bound.
  3. [§3.3.4 / Table 7] The adaptive-window penalty mechanism is presented as the usability-preserving component, but its operation depends on the same inconsistent Normal-period assumption. Table 7 sets λ=0.1s⁻¹ and W_min=1.0s, and Table 6 shows the penalty decaying during 10s and 20s in Normal. Because, under the default decay parameters, a continuous P1 check would force P2 after roughly 4.4s without observations, the claimed restoration of the full window for 'a genuine user who maintains stable behavior' is not actually demonstrated. The paper needs to specify when P1 thresholds are evaluated and then show that legitimate sensor dropouts of the durations used in the walkthroughs do not cause lockouts.
minor comments (4)
  1. [§1] The introduction refers to 'Section II,' 'Section III,' and 'Section IV,' but the sections are numbered 2, 3, and 4. Please use consistent numeric labels.
  2. [References] Reference [6] contains spacing artifacts ('V . V . Phoha' should be 'V.V. Phoha'). Several other references have similar spacing issues; a final proofread is recommended.
  3. [§3.1] The notation P(M_t | s_t) in Eq. (2) is defined only loosely. Since the paper stresses per-modality likelihoods P_N^j and P_¬N^j, the relationship between the two notations should be clarified or unified.
  4. [Table S3] In Scenario E, the statement 'Shorter windows reduce per-round decay (q closer to 1), but the cumulative effect is decisive' is not a general result; it depends on the particular sequence of window lengths and decay half-life. The table is correct, but the interpretive sentence should not be phrased as a theorem.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: VIGIL's unidirectional-decay derivation is self-contained; the walkthrough scenarios are illustrative, not fitted predictions; self-citation [6] is not load-bearing.

full rationale

VIGIL's load-bearing mathematical content is the unidirectional temporal-fusion update (Eqs. 3–6 for STM1, Eqs. 12–14 for STM2, plus the Bayesian update). The transition matrices remove the S→N path by construction, and π_N = p(Δt)·P_N immediately gives monotonic decay; this is a design property, not an empirical prediction, and it is justified by the reproduced equations rather than by the cited SSPRA paper [6]. The walkthrough scenarios (A–F, Tables 6/S3–S4) use hand-assigned per-modality likelihoods, and the paper itself limits them in §4: 'Empirical validation on multimodal datasets is a natural next step.' Thus the scenario outcomes are illustrative consequences of chosen inputs, not fitted parameters renamed as predictions. The comparison with SSPRA is derived in-text (Eqs. 7–10, 15–17), so VIGIL's anti-backflow claim does not reduce to the self-citation. No uniqueness theorem or ansatz is imported via [6] or any other citation. The main substantive concern is a consistency defect, not circularity: under τ_p=10s and T_stay=0.70, P1 without observations crosses T_stay in about 4.4s, yet Supplementary Scenario F lets a 20s no-observation Normal period elapse before re-entering P2 (P(N)=0.2380). That undermines the illustrative walkthrough's usability claim but does not make the derivation circular. Overall, no load-bearing step is equivalent to its own input.

Assumptions & free parameters 10 free parameters · 6 assumptions · 1 invented entities

All decisive quantities—thresholds, half-lives, window lengths, penalty rates, and fusion weights—are hand-set defaults (Table 7/Table S1) rather than calibrated to data. The mathematical claims about monotonic decay follow from the chosen transition matrices, but the security/usability claims additionally depend on unfalsified assumptions about real likelihood accuracy and sensor-dropout patterns.

free parameters (10)
  • STM1 decay half-life tau_p = 10 s
    Hand-set in Table S1; controls how fast P(N) decays during cruise without observations; no calibration.
  • STM2 decay half-life tau_q = 20 s
    Hand-set in Table S1; controls verification-mode decay; no calibration.
  • T_stay / T_back thresholds = 0.70
    Stay and recovery thresholds are hand-set to match each other (Table 7); no empirical tuning.
  • T_alert threshold = 0.30
    Hand-set as symmetric complement of T_back; creates the inconclusive band (Table 7).
  • W_base = 5.0 s
    Base verification window; hand-set (Table 7/Table S1).
  • W_min = 1.0 s
    Minimum window; hand-set to ensure at least one observation cycle (Table 7).
  • delta penalty increment = 1.0 s
    Hand-set; shrinks window by 1 s per P2 entry (Table 7).
  • lambda penalty decay = 0.1 s^-1
    Hand-set; penalty decays to zero after roughly 40 s in Normal (Table 7).
  • Max verification rounds = 5
    Hand-set; forces alert after five inconclusive rounds (Table S1).
  • Per-subset fusion weights = inverse-EER normalized values (e.g., 0.35, 0.46, ... in Table 3)
    Weights are derived from hypothetical validation-set EERs; no real data are supplied.
assumptions (6)
  • standard math State probabilities are normalized and updated by Bayes' rule with the given transition matrices and likelihoods.
    Used throughout §3.3 and the supplement; standard probability update.
  • domain assumption Per-modality likelihoods P_j^N and P_j^notN can be estimated from labeled validation data and remain well-calibrated during deployment.
    Section 3.1 states VIGIL is agnostic to how likelihoods are produced; correctness of the fused scores depends on this.
  • domain assumption Multiplicative or weighted geometric combination of per-modality scores is a valid fusion model.
    Section 3.1 and Table 2; product and geometric rules implicitly assume some conditional independence; no calibration is provided.
  • domain assumption Temporal evidence strength decays exponentially with a fixed half-life.
    Section 3.2 uses f(dt)=e^{-ln2/tau * dt}; the exponential form is cited to [22], but tau values are hand-set.
  • ad hoc to paper Only cross-modal fusion should increase P(N); no-evidence recovery is always undesirable.
    This is the design principle behind the unidirectional matrices in §3.2; it is a policy premise, not derived from data.
  • ad hoc to paper At P2 entry, all Suspense mass transfers deterministically to Alert.
    Section 3.3.1, Eq. (12); design choice that maximizes pressure accumulation; no empirical justification.
invented entities (1)
  • Penalty accumulator (adaptive window state)
    purpose: Tracks repeated P2 entries and shrinks the verification window via W_current = max(W_min, W_base - penalty).
    Internal bookkeeping variable with hand-set delta and lambda; no standalone falsifiable prediction outside the paper.

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Cite this review

Pith. "Pith review of VIGIL: Verifying Identity via Gated Intermittent Likelihoods for Continuous Biometric Authentication." pith.science (2026). https://pith.science/paper/NRQFKFJT

@misc{pith2026260716651,
  author       = {Pith},
  title        = {Pith review of: VIGIL: Verifying Identity via Gated Intermittent Likelihoods for Continuous Biometric Authentication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NRQFKFJT}},
  note         = {Machine review of arXiv:2607.16651}
}
read the original abstract

Continuous multi-modal authentication has emerged as a necessity for securing modern environments against persistent threats. Existing temporal fusion techniques fail to identify a persistent attacker from a genuine user with poor signal strength. In this study, we propose VIGIL (Verifying Identity via Gated Intermittent Likelihoods for Continuous Biometric Authentication), a highly adaptive continuous authentication framework. We introduce configurable cross-modal fusion with per-modality weighting, enabling operators to select their choice of integration strategy. We improve temporal fusion using dual-state State Transition Machines (STM) with unidirectional transition matrices. A three-zone verification decision model that enables multi-round verification when evidence is inconclusive is used in combination with an adaptive shrinking verification window. Monotonic decay, backflow elimination and analytical evaluation demonstrate that the proposed framework effectively addresses the limitations of existing approaches and reduces the time to detect intrusions while maintaining high usability for legitimate users.

Figures

Figures reproduced from arXiv: 2607.16651 by the authors.

Figure 1
Figure 1. VIGIL system architecture. Active modalities [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. P1 state transition diagrams. (a) Baseline SSPRA in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. STM1 P(N) trajectory with no observations. Baseline SSPRA exhibits a transient spike above the initial P(N) due to S → N backflow; VIGIL decays monotonically from the first time step. 3.3.1 VIGIL STM2 Design At P2 entry, any Suspense state probability mass from P1 is directly transferred to Alert. This gives a starting state [P N , 0, P A]. VIGIL’s STM2 uses the separate decay func￾tion q(∆t) = e − ln 2 τq ·∆t with … view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: VIGIL multi-round P2 verification flow. Three paths [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Multi-round P2 scenarios (Wbase = 5.0 s, δ = 1.0 s, Wmin = 1.0 s). (a) Legitimate user recovers after three rounds. (b) Attacker exhausts max rounds; forced alert at Wmin. (c) User recovers in round 2, penalty decays during 20 s in Normal, sec￾ond P2 entry uses full re…

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Reference graph

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    Per-modality scores: ModalityP N j P ¬N j M1 (face) 0.92 0.08 M2 (iris) 0.95 0.05 M3 (voice) 0.55 0.45 M4 (keystroke) 0.50 0.50 M5 (gait) 0.48 0.52

  17. [25]

    Cross-modal fusion(Weighted Geometric Mean): LN = 0.920.35 ×0.95 0.46 ×0.55 0.09 ×0.50 0.06 ×0.48 0.05 = 0.8312 L¬N = 0.080.35 ×0.05 0.46 ×0.45 0.09 ×0.50 0.06 ×0.52 0.05 = 0.0900

  18. [26]

    Temporal fusion(∆t= 0s, sop= 1.0):π N = 1.0×0.95 = 0.9500,π S = 0.0×0.95 + 0.05 = 0.0500 11

  19. [27]

    Bayesian update:P(N) post = LN ·πN LN ·πN +L¬N ·πS = 0.9943

  20. [28]

    Decision:0.9943≥T stay = 0.70→Stay in P1. C.2. Observation 2 —{M 1, M2}att= 2s Only physiological sensors available. Weighted Geometric Mean withˆw= (0.43,0.57)

  21. [29]

    Per-modality scores: ModalityP N j P ¬N j M1 (face) 0.90 0.10 M2 (iris) 0.93 0.07

  22. [30]

    Cross-modal fusion(Weighted Geometric Mean): LN = 0.900.43 ×0.93 0.57 = 0.9170 L¬N = 0.100.43 ×0.07 0.57 = 0.0816

  23. [31]

    Temporal fusion(∆t= 2s,p=e − ln 2 10 ×2 = 0.8706):π N = 0.8706×0.9943 = 0.8656,π S = 0.1294×0.9943 + 0.0057 = 0.1344

  24. [32]

    Bayesian update:P(N) post = LN ·πN LN ·πN +L¬N ·πS = 0.9864

  25. [33]

    Decision:0.9864≥0.70→Stay in P1. C.3. Observation 3 —{M 3, M4, M5}att= 5s — Triggers P2 Only behavioral sensors active. Noisy environment, poor readings. Weighted Sum withˆw= (0.46,0.30,0.24)

  26. [34]

    Per-modality scores: ModalityP N j P ¬N j M3 (voice) 0.40 0.60 M4 (keystroke) 0.35 0.65 M5 (gait) 0.30 0.70

  27. [35]

    Cross-modal fusion(Weighted Sum): LN = 0.46×0.40 + 0.30×0.35 + 0.24×0.30 = 0.3610 L¬N = 0.46×0.60 + 0.30×0.65 + 0.24×0.70 = 0.6390

  28. [36]

    Temporal fusion(∆t= 3s since Obs 2,p=e − ln 2 10 ×3 = 0.8123):π N = 0.8123×0.9864 = 0.8012,π S = 0.1877×0.9864 + 0.0136 = 0.1988

    1988

  29. [37]

    Bayesian update:P(N) post = LN ·πN LN ·πN +L¬N ·πS = 0.6948

  30. [38]

    Decision:0.6948< T stay = 0.70→Enter P2. D. P2 Entry At P2 entry, Suspense mass transfers to Alert: P(N) = 0.6948, P(A) = 1−0.6948 = 0.3052 Penalty= 0(first entry). Window=W base = 5.0s. Six scenarios branch from here. E. Scenario A: Immediate Recovery Genuine user provides st...

  31. [40]

    Per-modality scores and fusion: ModalityP N j P ¬N j M1 (face) 0.93 0.07 M2 (iris) 0.96 0.04 M3 (voice) 0.60 0.40 LN = 0.930.38 ×0.96 0.51 ×0.60 0.10 = 0.9053,L ¬N = 0.070.38 ×0.04 0.51 ×0.40 0.10 = 0.0643

  32. [41]

    STM2 temporal fusion(q=e − ln 2 20 ×5.0 = 0.8409):π N = 0.8409×0.6948 = 0.5843,π A = 0.1591×0.6948 + 0.3052 = 0.4157

  33. [42]

    Bayesian update:P(N) post = LN ·πN LN ·πN +L¬N ·πA = 0.9519

  34. [43]

    Outcome:Return to P1 withP(N) = 0.9519,P(S) = 0.0481

    Decision:0.9519≥T back = 0.70→RECOVER. Outcome:Return to P1 withP(N) = 0.9519,P(S) = 0.0481. Penalty→1.0s. F. Scenario B: Multi-Round Recovery Borderline behavioral evidence in R1 (inconclusive), then strong face-dominant evidence in R2. F.1. Round 1(W= 5.0s) —{M 3, M5}, Wtd. Sum

  35. [45]

    Per-modality scores and fusion(ˆw= [0.65,0.35]): P N j P ¬N j M3 (voice) 0.52 0.48 M5 (gait) 0.48 0.52 LN = 0.65×0.52 + 0.35×0.48 = 0.5060,L ¬N = 0.65×0.48 + 0.35×0.52 = 0.4940

  36. [47]

    Bayesian update:P(N) post = 0.5901

  37. [48]

    Carry forward, shrink window

    Decision:0.30<0.5901<0.70→INCONCLUSIVE. Carry forward, shrink window. F.2. Round 2(W= 4.0s) —{M 1, M3, M4}, Wtd. Sum Face becomes available.ˆw= (0.71,0.18,0.12)

  38. [49]

    Entry state:P(N) = 0.5901,P(A) = 0.4099

  39. [50]

    Per-modality scores and fusion: P N j P ¬N j M1 (face) 0.91 0.09 M3 (voice) 0.58 0.42 M4 (keystroke) 0.52 0.48 LN = 0.71×0.91 + 0.18×0.58 + 0.12×0.52 = 0.8129 L¬N = 0.71×0.09 + 0.18×0.42 + 0.12×0.48 = 0.1971

    1971

  40. [51]

    STM2 temporal fusion(q=e − ln 2 20 ×4.0 = 0.8706):π N = 0.8706×0.5901 = 0.5137,π A = 0.1294×0.5901 + 0.4099 = 0.4863 13

  41. [52]

    Bayesian update:P(N) post = 0.8133

  42. [53]

    Outcome:Return to P1 withP(N) = 0.8133

    Decision:0.8133≥0.70→RECOVER. Outcome:Return to P1 withP(N) = 0.8133. Penalty= 2δ= 2.0s. If re-entered immediately:W eff = max(1.0,5.0− 2.0) = 3.0s. G. Scenario C: Gradual Alert An attacker with limited biometric capability. Each round uses a different subset as the attacker t...

  43. [54]

    Entry state:P(N) = 0.6948,P(A) = 0.3052

  44. [55]

    Fusion:Single modality, Product rule.L N = 0.40,L ¬N = 0.60

  45. [56]

    STM2 temporal fusion(q= 0.8409):π N = 0.5843,π A = 0.4157

  46. [57]

    Bayesian update:P(N) post = 0.4837

  47. [58]

    Decision:0.30<0.4837<0.70→INCONCLUSIVE. G.2. Round 2(W= 4.0s) —{M 3, M5}, Wtd. Sum

  48. [59]

    Entry state:P(N) = 0.4837,P(A) = 0.5163

  49. [60]

    LN = 0.4060,L ¬N = 0.5940

    Fusion(ˆw= [0.65,0.35]):M 3:(0.42,0.58),M 5:(0.38,0.62). LN = 0.4060,L ¬N = 0.5940

  50. [61]

    STM2 temporal fusion(q= 0.8706):π N = 0.8706×0.4837 = 0.4211,π A = 0.1294×0.4837 + 0.5163 = 0.5789

  51. [62]

    Bayesian update:P(N) post = 0.3321

  52. [63]

    Decision:0.30<0.3321<0.70→INCONCLUSIVE. G.3. Round 3(W= 3.0s) —{M 3, M4, M5}, Wtd. Sum

  53. [64]

    Entry state:P(N) = 0.3321,P(A) = 0.6679

  54. [65]

    LN = 0.3912,L ¬N = 0.6088

    Fusion(ˆw= [0.46,0.30,0.24]):M 3:(0.42,0.58),M 4:(0.38,0.62),M 5:(0.35,0.65). LN = 0.3912,L ¬N = 0.6088

  55. [66]

    STM2 temporal fusion(q=e − ln 2 20 ×3.0 = 0.9013):π N = 0.9013×0.3321 = 0.2993,π A = 0.0987×0.3321 + 0.6679 = 0.7007

  56. [67]

    Bayesian update:P(N) post = 0.2153

  57. [68]

    Outcome:Session locked

    Decision:0.2153≤T alert = 0.30→ALERT. Outcome:Session locked. Total P2 duration:5.0 + 4.0 + 3.0 = 12.0s. P(A)progression:0.3052→0.5163→0.6679→0.7847. Compounding pressure forces the outcome. H. Scenario D: No Observations

  58. [69]

    Window= 5.0s

    Entry state:P(N) = 0.6948,P(A) = 0.3052. Window= 5.0s

  59. [70]

    None arrive

    System waitsfor observations. None arrive

  60. [71]

    This prevents an attacker from stalling by avoiding sensors entirely

    Decision:No observations→ALERT(immediate, no further rounds). This prevents an attacker from stalling by avoiding sensors entirely. 14 I. Scenario E: Max-Rounds Exhaustion Attacker produces perfectly neutral evidence (L N =L ¬N = 0.04) every round. Equal likelihoods mean the B...

  61. [72]

    LN = 0.910.43 ×0.94 0.57 = 0.9270,L ¬N = 0.090.43 ×0.06 0.57 = 0.0714

    Fusion(ˆw= [0.43,0.57]):M 1:(0.91,0.09),M 2:(0.94,0.06). LN = 0.910.43 ×0.94 0.57 = 0.9270,L ¬N = 0.090.43 ×0.06 0.57 = 0.0714

  62. [73]

    STM2 temporal fusion(q= 0.8409):π N = 0.8409×0.55 = 0.4625,π A = 0.1591×0.55 + 0.45 = 0.5375

  63. [74]

    Bayesian update:P(N) post = 0.9178

  64. [75]

    Penalty→1.0s

    Decision:0.9178≥0.70→RECOVER. Penalty→1.0s. Key insight:The penalty fully decayed during 20 s of Normal, so the second P2 uses the full 5.0 s window. VIGIL is fair to genuine users who maintain stable behavior between P2 episodes. K. Adaptive Window Session Timeline Table S4 t...

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.