IPPM Working Group L. Melegassi Internet-Draft Catellix Intended status: Experimental 18 June 2026 Expires: 20 December 2026 Real-World Measurement of the Infrastructure-Cognitive Coupling Matrix R_cross: Closing the MVPS AI-Coherence Production Conjecture (IC9.1) draft-melegassi-mvps-ai-coherence-coupling-real-00 Abstract The MVPS AI-Coherence framework [I-D.melegassi-mvps-ai-coherence] defines an infrastructure-cognitive coupling matrix R_cross = Sigma_net^{-1/2} Sigma_cross Sigma_AI^{-1/2} and proves, in simulation, that a non-zero R_cross is the necessary and sufficient condition for the joint network-AI anomaly space to carry detection information that neither standalone monitor can recover. That document leaves two items open: (a) work item IC9.1, a statistical hypothesis test on R_cross over an empirical joint covariance, and (b) the CONJECTURE that E[R_cross] != 0 in production AI-on-network deployments. This companion document closes both. It specifies a permutation- based hypothesis test for the normalized cross-block correlation estimator, reports the FIRST real-wire measurement of R_cross on a production large-language-model serving path (n = 100 ticks, DeepInfra), and documents a pure-arithmetic reference implementation embedded in an operational system that reproduces the measurement number-for-number. The strongest coupling, latency_ms <-> output tokens, is r = +0.446 (permutation p = 0.0005) on the full series and survives the same-model confound control at r = +0.343 (p = 0.0135) within a single serving regime. The Frobenius norm ||R_cross||_F = 0.469 (full) / 0.443 (intra-regime) exceeds the non-triviality floor of 0.05, confirming the production conjecture for this deployment. The document also specifies how the measured coupling and the per-engine Mahalanobis distance D^2 are consumed by an operational Wald Sequential Probability Ratio Test (SPRT) as an additive evidence channel for surgical sub-environment bifurcation. Status of This Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." This document is a companion to [I-D.melegassi-mvps-ai-coherence] and [I-D.melegassi-mvps-perfsec-coupling]. This Internet-Draft will expire on 20 December 2026. Copyright Notice Copyright (c) 2026 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised BSD License. Table of Contents 1. Introduction 2. Terminology and Requirements Language 3. The Normalized Cross-Block Estimator 4. Hypothesis Test (closes IC9.1) 5. Real-Wire Measurement Results 6. Reference Implementation (production, pure arithmetic) 7. Operational Use: R_cross and D^2 as SPRT Evidence 8. CAVEATs (Honest Limitations) 9. Security Considerations 10. IANA Considerations 11. References Appendix A. Reproducibility Author's Address ============================================================================== 1. Introduction ============================================================================== [I-D.melegassi-mvps-ai-coherence], Section 18.3, partitions the joint covariance of a network-coupled AI system as Sigma_joint = [ Sigma_net | Sigma_cross ] [ Sigma_cross^T | Sigma_AI ] and defines the coupling matrix R_cross = Sigma_net^{-1/2} * Sigma_cross * Sigma_AI^{-1/2}. Under the null hypothesis H_0: R_cross = 0 the joint Mahalanobis distance factorises, D^2_joint = D^2_net + D^2_AI, and the joint monitor adds nothing over two independent monitors. Section 18.4 establishes (CORRECTED THEOREM) that Phase 3 (COUPLED) existence is necessary but not sufficient for R_cross != 0, and defers "the proper test -- a statistical hypothesis test on R_cross using the empirical Sigma_joint" to open work item IC9.1. It further records a CONJECTURE that E[R_cross] != 0 in production. This document inherits the evidential-status discipline of the parent draft (Appendix A: THEOREM / DEFINITION / CONJECTURE / HYPOTHESIS / CAVEAT) and the reproducible-receipt discipline of [I-D.melegassi-irtf-mvps-methodology]. The measurement below is a NUMERICAL RECEIPT in the sense of [I-D.melegassi-ippm-mvps-proof-envelope]: a machine-regenerable artifact (evidence/rcross_real.json) whose SHA-256 digest can be bound into a proof envelope. It does not introduce any new THEOREM; it converts the parent CONJECTURE into a measured result for one deployment and reports the failed-to-reject and rejected channels honestly (Section 5.3), including negative results. This document supplies the missing test, the missing measurement, and a reference implementation, replacing simulation-only evidence (scripts/simulate_three_domains.py in the parent draft) with a measurement on a live commercial inference API. This document follows the IP Performance Metrics framework of [RFC2330]: the metric (R_cross) is defined with an explicit measurement methodology (Sections 3-4), and the sources of measurement uncertainty are enumerated (Section 8), as that framework requires. Both blocks are derived from operator telemetry in the sense of the Network Telemetry Framework [RFC9232], and the detection lineage (Coherence-BFD) inherits the sub-second timing model of Bidirectional Forwarding Detection [RFC5880] via [I-D.melegassi-coherence-bfd]. ============================================================================== 2. Terminology and Requirements Language ============================================================================== The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here. Network/infrastructure block (x_net): per-tick vector [latency_ms, tok_per_s], where tok_per_s = tokens / (latency_ms / 1000). Both quantities are observable on every request at the client edge with zero additional instrumentation. Cognitive block (x_AI): per-tick vector [out_tokens, len_dev], where out_tokens is the completion length and len_dev = |out_tokens - mean(out_tokens)| is the absolute deviation of the response length, a black-box proxy for cognitive instability when logit-level signals are unavailable (Section 6). Tick: one served request. A regime is a contiguous run of ticks served by the same model identifier. ============================================================================== 3. The Normalized Cross-Block Estimator ============================================================================== The framework definition R_cross = Sigma_net^{-1/2} Sigma_cross Sigma_AI^{-1/2} reduces, when each variable is standardised to unit variance, to the cross-block of the Pearson CORRELATION matrix. This document uses that normalized form as the estimator: R_cross[i][j] = corr(x_net,i , x_AI,j) where corr is the sample Pearson correlation. The estimator coincides with the parent-draft definition exactly when the intra- block correlations are small, and is an honest, conservative proxy otherwise (it omits the whitening cross-terms, which can only add coupling, never remove it). The aggregate coupling magnitude is the Frobenius norm ||R_cross||_F = sqrt( sum_{i,j} R_cross[i][j]^2 ). A coupling is reported as NON-TRIVIAL when ||R_cross||_F > 0.05. CAVEAT (dimensionality). The parent draft defines R_cross as a 3x3 matrix over the full coherence axes (C_1, C_2, C_3). This document measures a 2x2 black-box SUB-INSTANCE over the only axes observable without logit access (Section 2): it is a lower bound on the full ||R_cross||_F, never an over-statement. A grey-box deployment would recover the remaining entries and can only increase the measured coupling. ============================================================================== 4. Hypothesis Test (closes IC9.1) ============================================================================== For each cross pair (i, j) the null H_0: R_cross[i][j] = 0 is tested by a PERMUTATION test that makes no Gaussian assumption: 1. Compute the observed |r| = |corr(x_net,i, x_AI,j)|. 2. For B = 2000 iterations, randomly permute x_AI,j and recompute |r_b|. 3. p = (1 + #{b : |r_b| >= |r|}) / (B + 1). The permutation null is exact under exchangeability and is robust to the heavy-tailed latency distributions typical of shared inference wires. A fixed seed (12345) makes the p-value reproducible. To control the MODEL-SWAP CONFOUND (a change of served model shifts both latency and output length jointly, manufacturing correlation that is not infrastructure-cognitive coupling), the test is run twice: once on the full series spanning a model swap (regimes A+B), and once restricted to the larger single-model regime (B). Coupling that survives within a single regime cannot be attributed to the swap. This two-regime design is the COUNTER-PROOF (falsification attempt) required by [I-D.melegassi-irtf-mvps-methodology]: the most plausible alternative explanation (the swap manufactured the correlation) is constructed and tested against, not assumed away. The claim is retained only because it survives that attempt (Section 5.2, F2). ============================================================================== 5. Real-Wire Measurement Results ============================================================================== Measurement context: n = 100 ticks collected on the same client wire against the DeepInfra inference API, spanning one deliberate model swap (regime A -> regime B). Raw series: evidence/coupling_timeseries.json. Computed verdict: evidence/rcross_real.json. 5.1. Full series (A+B, includes the model swap) R_cross (rows = net block, cols = cognitive block): out_tokens len_dev latency_ms +0.446 -0.063 tok_per_s -0.063 -0.113 permutation p-values: out_tokens len_dev latency_ms 0.0005 0.5482 tok_per_s 0.5467 0.2549 ||R_cross||_F = 0.469 strongest pair = (latency_ms, out_tokens), |r| = 0.446 5.2. Within regime B (single model -- confound controlled) R_cross: out_tokens len_dev latency_ms +0.343 +0.181 tok_per_s +0.164 -0.138 permutation p-values: out_tokens len_dev latency_ms 0.0135 0.2144 tok_per_s 0.2579 0.3453 ||R_cross||_F = 0.443 5.3. Findings F1. R_cross != 0 on the real wire. ||R_cross||_F = 0.469 > 0.05. The production CONJECTURE of [I-D.melegassi-mvps-ai-coherence] Section 18 holds for this deployment. F2. The coupling SURVIVES the model-swap confound: ||R_cross||_F = 0.443 within a single regime, with the leading pair latency_ms <-> out_tokens still significant (r = +0.343, p = 0.0135). The coupling is therefore an intra-regime infrastructure-cognitive effect, not a swap artefact. F3. The coupling is DIRECTIONAL and SPARSE: it concentrates in the latency <-> output-length channel, consistent with the drift-transfer mechanism of [I-D.melegassi-mvps-ai-coherence] Section 19, where serving-path state perturbs decode length. F4 (NEGATIVE RESULT, reported for falsifiability). Three of the four cross pairs FAIL to reject H_0: (tok_per_s, out_tokens) p=0.5467, (latency_ms, len_dev) p=0.5482, (tok_per_s, len_dev) p=0.2549 on the full series. Only the latency <-> out_tokens channel is significant. Reporting the non-significant channels is required by the adversarial-audit discipline of [I-D.melegassi-irtf-mvps-methodology]: the claim is "one strong coupling channel exists", NOT "the blocks are densely coupled". A reader MUST NOT infer coupling on the silent pairs. ============================================================================== 6. Reference Implementation (production, pure arithmetic) ============================================================================== The estimator of Section 3, the permutation test of Section 4, and the telemetry derivation of Section 2 are implemented in an operational system (Catellix "Aurix") as pure standard-library arithmetic with zero I/O and zero numerical dependencies: app/aurix2/trajectory.py: _pearson(a, b) -- sample Pearson correlation cross_coupling(block_net, -- R_cross + ||.||_F + max pair block_ai) coupling_from_telemetry(rows)-- derives x_net, x_AI from the request-telemetry rows and returns R_cross, gated by a minimum sample size (default 12) The implementation runs on the SAME telemetry rows already queried for the per-engine trajectory report (Section 7); it introduces no additional database query and is exposed under the report key "_coupling". 6.1. Exact-reproduction conformance test A conformance test (tests/test_aurix2_trajectory.py:: test_cross_coupling_matches_validated_evidence) feeds the published raw series (evidence/coupling_timeseries.json) to the production cross_coupling() function and asserts BYTE-EXACT equality with the published verdict (evidence/rcross_real.json): the full R_cross matrix, the Frobenius norm, and the strongest pair. The production path therefore computes the measurement of Section 5 with no deviation; the numbers in this document are not a separate analysis but the system's own output. The full trajectory/coupling suite is 17/17 passing. ============================================================================== 7. Operational Use: R_cross and D^2 as SPRT Evidence ============================================================================== The measured coupling is consumed operationally, not merely reported. Two mechanisms apply. 7.1. Per-engine D^2 channel into the Wald SPRT The system maintains a per-engine trajectory report with a Mahalanobis distance D^2 (diagonal form over the state vector z(t) = [1 - C_4, CBF, truncation_rate, latency]) and Critical-Slowing-Down precursors (lag-1 autocorrelation and Kendall-tau variance trend). The current D^2 is now fed as an additive evidence channel into the Wald SPRT [WALD1945] that decides whether an individual request merits a surgical sub-environment (bifurcation). The channel uses the chi-square-quantile-calibrated log-likelihood ratio of the parent incremental draft [I-D.melegassi-mvps-incremental-be], Theorem 5 region: D^2 <= dof -> LLR = -0.5 (evidence for H_0) D^2 = 7.815 (.05) -> LLR = +1.0 D^2 = 11.345 (.01) -> LLR = +2.3 The channel MUST default to a neutral log-likelihood ratio (LLR = 0) when no trajectory is available, so the addition is fail-safe: it can only add evidence, never suppress the prior channels. 7.2. Why coupling matters for the SPRT Because R_cross != 0 (Section 5), the infrastructure axes carry information about the cognitive state. The latency component of z(t) and the D^2 channel are therefore not redundant with the coherence probe (C_2/C_4/CBF): they are a partially independent, zero-cost-to-observe leading indicator. Quantifying ||R_cross||_F tells the operator HOW MUCH independent precision the infrastructure channel adds, exactly as predicted by [I-D.melegassi-mvps-ai-coherence] Section 18. ============================================================================== 8. CAVEATs (Honest Limitations) ============================================================================== Per the evidential discipline of [I-D.melegassi-mvps-ai-coherence] Appendix A, every limitation is stated explicitly as a CAVEAT. CAVEAT L1. SINGLE SHARED WIRE. The measurement is taken on one client wire against one commercial API. It does not isolate pure network latency from server-side queueing/load; the coupling is between END-TO-END infrastructure latency and cognitive output, which is the operationally relevant quantity but not a clean physical-layer measurement. L2. SINGLE BATCH (n = 100). Effect sizes and p-values are indicative, not definitive. The intra-regime significance (p = 0.0135, n = 60-ish) is the conservative figure; the full- series p = 0.0005 is inflated by the swap. Replication across wires, providers, and time-of-day is required before any normative claim. L3. BLACK-BOX COGNITIVE PROXY. The cognitive block uses output length and its deviation, not logit-level coherence, because the tested API returns logprobs = null. len_dev is a coarse proxy; a grey-box deployment with logprobs would measure a sharper cognitive axis and likely a larger ||R_cross||_F. L4. CORRELATION, NOT MECHANISM. This document measures coupling; the causal drift-transfer mechanism is argued in [I-D.melegassi-mvps-ai-coherence] Section 19 and is not re-proved here. ============================================================================== 9. Security Considerations ============================================================================== The coupling channel is a DETECTION aid; it adds no new attack surface because both blocks are derived from telemetry the operator already collects. An adversary who can shape serving-path latency could, in principle, attempt to bias the cognitive proxy via the measured coupling; the fail-safe SPRT wiring (Section 7.1) bounds the influence of any single channel and the cross-check quorum of the trajectory layer requires corroboration from at least two independent axes before a strong action. No part of the proprietary coherence calibration is disclosed by R_cross itself. PRIVACY. R_cross is computed over aggregate per-engine telemetry (latency and token counts), not over request content; the privacy considerations framework of [RFC6973] applies to the underlying telemetry collection but R_cross adds no new personal-data exposure. ============================================================================== 10. IANA Considerations ============================================================================== This document has no IANA actions. ============================================================================== 11. References ============================================================================== 11.1. Normative References [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997, . [RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis, "Framework for IP Performance Metrics", RFC 2330, May 1998, . [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, May 2017, . [I-D.melegassi-mvps-ai-coherence] Melegassi, L., "MVPS AI-Coherence Extension: Semantic, Byzantine, and Infrastructure-Cognitive Coherence for AI-Serving Network Deployments", draft-melegassi-mvps-ai-coherence-01, May 2026. 11.2. Informative References [RFC5880] Katz, D. and D. Ward, "Bidirectional Forwarding Detection (BFD)", RFC 5880, June 2010, . [RFC6973] Cooper, A., Tschofenig, H., Aboba, B., Peterson, J., Morris, J., Hansen, M., and R. Smith, "Privacy Considerations for Internet Protocols", RFC 6973, July 2013, . [RFC9232] Song, H., Qin, F., Martinez-Julia, P., Ciavaglia, L., and A. Wang, "Network Telemetry Framework", RFC 9232, May 2022, . [I-D.melegassi-mvps-incremental-be] Melegassi, L., "Incremental Bandwidth-Efficient Multi- Vantage Path Synchrony (BE-MVPS): Cell-Partitioned Coherence with epsilon-Gated Sherman-Morrison Updates", draft-melegassi-mvps-incremental-be-00, May 2026. [I-D.melegassi-mvps-perfsec-coupling] Melegassi, L., "MVPS Performance-Security Coupling Profile: Joint Volume-Independence and Authentication Guarantees for Coherence-BFD with Coherent-Witness Trust (CWT)", draft-melegassi-mvps-perfsec-coupling-00, May 2026. [I-D.melegassi-coherence-bfd] Melegassi, L., "Coherence-BFD: Sub-Second Coherence Detection Using Bidirectional Forwarding Detection Patterns", draft-melegassi-coherence-bfd-00, May 2026. [I-D.melegassi-irtf-mvps-methodology] Melegassi, L., "The MVPS Adversarial-Audit Methodology: A Reproducible Discipline for Measurement-Security Internet- Drafts", draft-melegassi-irtf-mvps-methodology-00, May 2026. [I-D.melegassi-ippm-mvps-proof-envelope] Melegassi, L., "MVPS Proof Envelope: Tamper-Evident Binding of Theorem Catalogues, Validators, and Numerical Receipts, with an Optional Post-Quantum Profile", draft-melegassi-ippm-mvps-proof-envelope-00, May 2026. [WALD1945] Wald, A., "Sequential Tests of Statistical Hypotheses", Annals of Mathematical Statistics, 16(2):117-186, 1945. Appendix A. Reproducibility Raw series: evidence/coupling_timeseries.json Verdict: evidence/rcross_real.json Analysis: scripts/_rcross_real.py Production: app/aurix2/trajectory.py (cross_coupling, coupling_from_telemetry) Conformance: tests/test_aurix2_trajectory.py (test_cross_coupling_matches_validated_evidence) The conformance test asserts that the production function reproduces the published verdict exactly; running the trajectory suite regenerates the agreement (17/17 passing). Author's Address Leonardo Melegassi Catellix Andradina, SP Brazil Email: melegassi@catellix.com URI: https://catellix.com/