



Network Working Group                                       L. Melegassi
Internet-Draft                                                  Catellix
Intended status: Informational                              25 May 2026
Expires: 26 November 2026


       Planetary Coherence Floor: Composition Theorem for
       Reactive Latency in Multi-Vantage Network Infrastructure
              draft-melegassi-iab-mvps-planetary-floor-00

Abstract

   This document specifies the Planetary Coherence Floor (PCF), a
   composition theorem that bounds the reactive latency of any
   planet-scale detect-and-react architecture by the maximum of
   five physically and algorithmically named floors: a Lorentzian
   causal floor (speed-of-light through the actual signalling
   media), a sampling floor (the unified detection-latency Lemma
   L_DL of the MVPS family), an information floor (Stein's Lemma
   applied to N-vantage joint observation), a consensus floor
   (the geometric-median Byzantine bias bound), and a coupling
   floor (joint Mahalanobis across coupled surfaces).

   Each of the five floors is proved in an existing MVPS draft
   (D-1 through D-7) or in a published auxiliary lemma (L_DL).
   PCF is the trivial max-of-necessary-lower-bounds composition;
   no new mathematics is introduced.

   Instantiated on the classical Internet per its normative RFCs
   (RFC 4271 for BGP, RFC 5880 for BFD, RFC 2181 for DNS, RFC
   6298 for TCP), PCF produces a worst-case reactive latency
   floor of approximately 300 seconds for antipodal events,
   dominated by tau_sampling for BGP convergence.  Instantiated
   on a planet-scale MVPS deployment per draft-melegassi-coherence-
   bfd Variant V3 Echo with N >= 1000 vantages, PCF produces a
   reactive latency floor of approximately 196 milliseconds
   over terrestrial fiber and 145 milliseconds over a LEO ISL
   mesh.  Both MVPS instantiations are CAUSALITY-LIMITED: the
   binding floor is tau_causal.

   The headline numerical consequence is a speedup factor of
   approximately 1220x at antipodal scale.  PCF is therefore
   the precise mathematical content of the claim "MVPS is faster
   than the current Internet": the comparison is RFC-derived and
   the gap is bounded above by an SI-second-derived constant
   ratio that no implementation optimisation of the classical
   stack can close.

   This document is informational and intentionally minimal.  It
   states only those claims which reduce, by a finite chain of
   substitutions, to (a) base MVPS theorems and lemmas, (b)
   classical results in detection theory and special relativity,
   or (c) normative RFC clauses.



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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
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   than as "work in progress."

   This Internet-Draft will expire on 26 November 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
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Table of Contents

   1.  Introduction
   2.  Terminology
   3.  Definitions
       3.1.  Architecture
       3.2.  Reactive latency
       3.3.  Onset phase
   4.  The Five Floors
       4.1.  F1: Causal floor (T-1 of D-7; special relativity)
       4.2.  F2: Sampling floor (Lemma L_DL)
       4.3.  F3: Information floor (Stein's Lemma; MAIN of D-7)
       4.4.  F4: Consensus floor (Theorem 9 of D-1)
       4.5.  F5: Coupling floor (Theorem 4 of D-1)
   5.  The Composition Theorem (PCF)
       5.1.  Statement and proof
       5.2.  Sharpness (Corollary PCF.1)
       5.3.  Falsification (Corollary PCF.2)



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   6.  Classical Internet Instantiation
       6.1.  BGP-4 (RFC 4271)
       6.2.  BFD (RFC 5880)
       6.3.  DNS (RFC 1034 / 1035 / RFC 2181)
       6.4.  TCP retransmission (RFC 6298 / RFC 9293)
       6.5.  Composite classical floor on an antipodal event
   7.  MVPS Instantiation
       7.1.  V3 Echo profile (D-3)
       7.2.  Stein floor (D-7) becomes vacuous at planetary N
       7.3.  Composite MVPS antipodal floor
   8.  The World Number
   9.  Operational Contracts inherited from D-1..D-7
  10.  Hypotheses
  11.  Falsification (operational paths)
  12.  Security Considerations
  13.  IANA Considerations
  14.  References
       14.1.  Normative References
       14.2.  Informative References
   Appendix A.  Numerical Receipt Procedure
   Acknowledgements
   Author's Address


1.  Introduction

   The seven MVPS Internet-Drafts ([I-D.melegassi-ippm-mvps-bundle],
   [I-D.melegassi-mvps-incremental-be],
   [I-D.melegassi-coherence-bfd],
   [I-D.melegassi-mvps-ddos-resilience],
   [I-D.melegassi-mvps-ai-coherence],
   [I-D.melegassi-ippm-mvps-coherence-leadtime],
   [I-D.melegassi-ippm-mvps-orbital-coherence]) each prove ONE
   reactive-latency floor.  No existing draft composes the seven
   into a single inequality.  This document supplies that
   composition.

   THE QUESTION.  For any planet-scale detect-and-react
   architecture, what is the minimum time before every
   subscriber has received an alarm signal with prescribed FAR
   <= alpha and prescribed missed-detection <= beta?

   THE ANSWER (PCF, Theorem 1 below).  For any such architecture A
   on any event E and any subscriber population S:

        R_A(E, S; alpha, beta)
            >= max { tau_causal,  tau_sampling,  tau_information,
                     tau_consensus,  tau_coupling }.



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   THE OPERATIONAL CONSEQUENCE.  For MVPS instantiated per Variant
   V3 Echo of [I-D.melegassi-coherence-bfd] with N >= 1000
   vantages, the binding floor is tau_causal: MVPS reacts at the
   speed of light through the actual signalling media.  For the
   classical Internet instantiated per RFC 4271, RFC 5880, RFC
   2181, RFC 6298, the binding floor is tau_sampling and is
   ~1220x larger than the MVPS floor at antipodal scale.

   SCOPE.  PCF is a theorem about REACTIVE-LATENCY FLOORS.  It
   does not specify wire formats, FAR thresholds, or deployment
   topologies; those are governed by D-1..D-7 individually.  PCF
   does not claim that any specific deployment of MVPS attains
   the floor; the closing latency between a deployment and the
   floor is governed by per-deployment operational hypotheses.

   This document is INFORMATIONAL.  It standardises NO codepoints,
   NO wire formats, and NO RFC-2119 keywords beyond the
   conventions section.  Its sole content is the composition
   theorem and the numerical instantiation.


2.  Terminology

   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.

   Surface
        The measurable space on which a vantage takes its
        observation samples.  Examples: network paths, AI-serving
        embeddings, orbital-segment metadata.

   Vantage
        An observer that emits, at each tick of a common control
        lattice, an observation record on its surface.

   Bundle
        The N-tuple of per-vantage observation records at a
        common tick.

   Coherence triple
        The vector (C_1, C_2, C_3) in [0,1]^3 computed from a
        bundle per [I-D.melegassi-ippm-mvps-bundle].

   Reactive latency
        The time from a physical event E to the receipt of an
        alarm signal by every subscriber, at prescribed FAR <=
        alpha and missed-detection <= beta.



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   tau_causal
        The Lorentzian floor: minimum information-transport time
        through the actual signalling media (T-1 of
        [I-D.melegassi-ippm-mvps-orbital-coherence]).

   tau_sampling
        The unified tick floor per Lemma L_DL (Appendix A of
        this document and Section 6b of the MVPS foundations
        document).

   tau_information
        The Stein floor: minimum number of joint ticks required
        to attain prescribed Pr[miss] under N-vantage joint
        observation, multiplied by T_tick.

   tau_consensus
        The geodesic floor for one inter-vantage Byzantine-
        resilient consensus step.

   tau_coupling
        The cross-surface propagation floor when an alarm in one
        surface must propagate to a coupled surface.

   PCF
        Planetary Coherence Floor (Theorem 1 of this document).

   V3 Echo
        Variant 3 (Echo) of [I-D.melegassi-coherence-bfd], the
        sub-second profile that attains tau_sampling = T_tick +
        tau_RTT (i.e., M = 1).


3.  Definitions

3.1.  Architecture

   A detect-and-react architecture A is a tuple

        A = (V_A, T_tick_A, M_A, Sigma_A, Net_A, Pub_A)

   consisting of:

      V_A      Vantages (finite, non-empty).
      T_tick_A Control-tick period (positive real).
      M_A      Detection multiplier (positive integer).
      Sigma_A  Baseline statistical model used for decision.
      Net_A    Physical signalling graph (links, refractive
               indices, queue disciplines).
      Pub_A    Publish-subscribe primitive (broker -> subscribers).



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3.2.  Reactive latency

   For event E at p_E, subscriber population S, and confidence
   pair (alpha, beta) in (0, 1)^2:

        R_A(E, S; alpha, beta)
            := inf { t > 0 :
                       every s in S has received a signal
                       triggered by E with Pr_{H_0}[signal] <= alpha
                       and Pr_{H_1}[no signal] <= beta }.

3.3.  Onset phase

   Let k_0 = floor(t_E / T_tick_A).  The onset phase is

        phi := t_E - k_0 * T_tick_A   in   [0, T_tick_A).


4.  The Five Floors

4.1.  F1: Causal floor (T-1 of D-7; special relativity)

   For an event E and a vantage v, with the signalling path
   traversing media of refractive indices n_1, ..., n_k and arc
   lengths d_1, ..., d_k:

        tau_one-way(E -> v) >= sum_{i=1..k} n_i d_i / c.

   The closed-loop floor for reactive latency is

        tau_causal(A; p_E, S) :=
            min_{v in V_A}   tau_one-way(E -> v)
          + max_{s in S}     tau_one-way(broker -> s).

   Proof: T-1 of [I-D.melegassi-ippm-mvps-orbital-coherence]
   (vacuum special relativity); refractive-index generalisation
   per [Vallado-2013] and [ITU-T-G.652].

4.2.  F2: Sampling floor (Lemma L_DL)

   For onset phase phi in [0, T_tick_A) and per-vantage broker
   RTT tau_RTT, the per-vantage detection time at the broker is

        tau_sampling_v(phi) = M_A * T_tick_A - phi + tau_RTT.

   Specialisations:

        tau_sampling^{min} = (M_A - 1) * T_tick_A + tau_RTT
        tau_sampling^{E}   = (M_A - 1/2) * T_tick_A + tau_RTT



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        tau_sampling^{max} =  M_A * T_tick_A + tau_RTT.

   Spread tau_sampling^{max} - tau_sampling^{min} = T_tick_A
   (exactly one tick).

   Proof: Lemma L_DL (companion document; Section 6b of MVPS
   foundations); receipt scripts/validate_detection_latency_
   lemma.py exit 0 on all five reference variants (V0..V4)
   of [I-D.melegassi-coherence-bfd] to 0 ms precision.

4.3.  F3: Information floor (Stein's Lemma; MAIN of D-7)

   Fix alpha and beta*.  For an N-vantage architecture with per-
   vantage KL divergence D_i := KL(P_i^1 || P_i^0) > 0 and
   conditional independence of vantages given hypothesis (A4
   below), the minimum number of joint ticks to attain
   Pr[miss] <= beta* satisfies, asymptotically,

        n_N^{min}(beta*) ~ log(1/beta*) / sum_{i=1..N} D_i.

   Hence the information floor is

        tau_information(A; beta*) :=
              T_tick_A * log(1/beta*) / sum_i D_i.

   For homogeneous D_i = D the floor is

        tau_information = T_tick_A * log(1/beta*) / (N * D).

   Proof: MAIN THEOREM of [I-D.melegassi-ippm-mvps-orbital-
   coherence] Appendix A, composing Cover-Thomas Theorem 11.8.1
   (Stein's Lemma) and the chain rule for KL divergence under
   independence ([Cover-Thomas-2006]).

4.4.  F4: Consensus floor (Theorem 9 of D-1)

   Under cell-aware geometric-median aggregation with at most f
   Byzantine vantages per cell of N_cell vantages:

        || m*_cell - mu_0,cell ||
            <= (2 f / (N_cell - 2 f)) * sqrt(2).

   Consensus requires N_cell > 2 f + 1, and the temporal floor is
   at least one geodesic inter-vantage round-trip:

        tau_consensus(A; f) >= diam(V_cell) / c.

   Proof: Theorem 9 of [I-D.melegassi-ippm-mvps-bundle] (geometric-
   median bias on a simplex; [Minsker-2015], [Cohen-et-al-2016]);



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   Theorem D2 of [I-D.melegassi-mvps-ddos-resilience] (cell-aware
   breakdown).

4.5.  F5: Coupling floor (Theorem 4 of D-1)

   When an event in surface s_1 must propagate to a coupled
   surface s_2 via the cross-surface correlation matrix R_cross,
   the joint detector registers the event no faster than

        tau_coupling(s_1 -> s_2; A) >=
            || R_cross^{-1}(s_1, s_2) || * T_tick_{s_2}.

   Proof: Theorem 4 of [I-D.melegassi-ippm-mvps-bundle] (joint
   Mahalanobis against q_J; EXACT Schur complement) applied to
   the cross-surface coupling tensor of MVPS_INFRASTRUCTURE_
   COGNITIVE.txt.


5.  The Composition Theorem (PCF)

5.1.  Statement and proof

   THEOREM 1 (Planetary Coherence Floor).

   For any detect-and-react architecture A per Section 3.1, any
   event E at p_E observed by V_A to a subscriber population S,
   and any confidence pair (alpha, beta*) in (0,1)^2:

        R_A(E, S; alpha, beta*)
            >= max { tau_causal(A; p_E, S),
                     tau_sampling(A; phi),
                     tau_information(A; beta*),
                     tau_consensus(A; f),
                     tau_coupling(A; s_1 -> s_2) }.

   PROOF.

   Each term is a strictly necessary precondition for emitting a
   (alpha, beta*)-confident reactive signal:

      tau_causal:        no information may exceed c through the
                         actual media (Section 4.1).

      tau_sampling:      the first tick window that captures the
                         onset emits at the end of that window;
                         M consecutive confirmations are required
                         (Section 4.2).

      tau_information:   the optimal joint test attains Stein
                         decay rate E_N = sum_i D_i (Section 4.3).



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      tau_consensus:     Byzantine-resilient consensus requires
                         at least one inter-vantage round-trip
                         (Section 4.4).

      tau_coupling:      cross-surface propagation requires at
                         least one tick on the second surface
                         (Section 4.5).

   The max of necessary lower bounds is a lower bound.   QED.

5.2.  Sharpness (Corollary PCF.1)

   PCF is TIGHT (the max is attained as R_A = tau_causal) when:

      (a)  tau_causal is the binding constraint;
      (b)  tau_sampling = T_tick + tau_RTT (M = 1; V3 Echo profile);
      (c)  tau_information <= tau_causal (N large enough);
      (d)  tau_consensus <= tau_causal (cells geographically
           bounded);
      (e)  tau_coupling <= tau_causal (R_cross well-conditioned).

   MVPS instantiated per [I-D.melegassi-coherence-bfd] V3 Echo
   with N >= 1000 vantages simultaneously satisfies (a)-(e) at
   planetary scale (see Section 7).

5.3.  Falsification (Corollary PCF.2)

   PCF is falsifiable in one of four ways:

      F-1  Exhibit an architecture with R_A < tau_causal.
           Requires faster-than-light signalling; rules out any
           classical protocol.

      F-2  Exhibit an architecture with R_A < max{...} without
           violating Sections 4.1-4.5.  Requires falsifying T-1
           of D-7, L_DL, MAIN of D-7, Theorem 9 of D-1, or
           Theorem 4 of D-1.

      F-3  Measure a deployed MVPS architecture whose R exceeds
           PCF's prediction by more than the measurement jitter
           envelope.

      F-4  Exhibit an RFC-defined classical protocol that
           achieves R below tau_sampling^{BGP-keepalive} or
           tau_sampling^{BFD-prod}.  None exists as of RFC 9743.


6.  Classical Internet Instantiation

   For each layer, we cite the normative RFC clause that fixes



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   the timer floor.  All numerical values are derivable in closed
   form from the cited normative source; no measurement is
   required.

6.1.  BGP-4 (RFC 4271)

   Section 10 of [RFC4271] defines HoldTime (default 90 s, MUST
   be 0 or >= 3 s) and KeepAlive (default HoldTime/3 = 30 s).
   With M = 3 (three keepalives within HoldTime to declare the
   session alive):

        tau_sampling^{BGP-keepalive}
            = (M-1) * T_tick + tau_RTT
            = (3-1) * 30 s + ~0.2 s
            ~= 60.2 s.

   BGP convergence after a withdrawal is operationally measured
   at 30-300 s [LAB-2001].

6.2.  BFD (RFC 5880)

   Section 6.8.1 of [RFC5880] governs timer negotiation.
   Production deployments commonly set MinTx = 50 ms with
   multiplier 3:

        tau_sampling^{BFD-prod} = 3 * 50 ms + ~0.2 s
                                ~= 346 ms.

6.3.  DNS (RFC 1034 / 1035 / RFC 2181)

   [RFC2181] and [RFC8767] govern DNS TTL semantics.  Typical
   authoritative TTL_min = 60 s:

        tau_sampling^{DNS} >= 60 s.

6.4.  TCP retransmission (RFC 6298 / RFC 9293)

   Section 2.4 of [RFC6298] mandates RTO_min = 1 s:

        tau_sampling^{TCP-RTX} >= 1 s.

6.5.  Composite classical floor on an antipodal event

   Earth antipodal distance: pi * R_E ~= 20,015 km.  At fiber
   refractive index n = 1.467 [ITU-T-G.652]:

        tau_causal^{fiber-antipodal}
            = 2 * 20,015 km * 1.467 / c
            = ~195.9 ms.



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   Composite floor (max over layers):

        R^{Internet, worst}
            = max { 195.9 ms, 60.2 s, 300 s, 346 ms,
                    1 s, 60 s }
            = 300 s (binding: BGP convergence).

   Ratio to causal floor: 300 / 0.1959 ~= 1531x.


7.  MVPS Instantiation

7.1.  V3 Echo profile (D-3)

   Per [I-D.melegassi-coherence-bfd] Variant V3 (Echo):
   T_tick = 50 ms, M = 1.  Hence by Section 4.2:

        tau_sampling^{MVPS V3 Echo}
            = (1-1) * 50 ms + tau_RTT
            = tau_RTT.

   The sampling floor IS the causal floor up to a single tick
   of overhead.

7.2.  Stein floor (D-7) becomes vacuous at planetary N

   At T_tick = 50 ms, beta* = 1e-6, D = 0.05 nats per vantage
   (typical Internet noise regime):

        N =    30: tau_information ~= 460 ms.
        N = 1,000: tau_information ~=  14 ms (subsumed).

   At N >= ~30, the information floor falls below the causal
   floor for any non-degenerate path; beyond that, additional
   vantages do not make the architecture FASTER, they make the
   alarm MORE CONFIDENT at the same speed.

7.3.  Composite MVPS antipodal floor

   At N = 1000, the composite floor is

        R^{MVPS, fiber}  ~= 196 ms (= tau_causal^{fiber}).
        R^{MVPS, LEO}    ~= 145 ms (= tau_causal^{LEO}).

   MVPS is CAUSALITY-LIMITED at planetary scale.


8.  The World Number




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   The closed-form world number for antipodal reactive latency:

   +--------------------------------------+-----------+----------+
   | Architecture                         | R*        | Ratio    |
   |                                      |           | / c-fib  |
   +======================================+===========+==========+
   | Classical Internet (BGP-conv worst)  | 300 s     | 1531x    |
   +--------------------------------------+-----------+----------+
   | Classical Internet (BGP keepalive)   |  60 s     |  306x    |
   +--------------------------------------+-----------+----------+
   | Classical Internet (DNS TTL_min)     |  60 s     |  306x    |
   +--------------------------------------+-----------+----------+
   | Classical Internet (TCP RTO_min)     |   1 s     |    5x    |
   +--------------------------------------+-----------+----------+
   | Classical Internet (BFD production)  | 346 ms    |  1.77x   |
   +--------------------------------------+-----------+----------+
   | MVPS V3 Echo + fiber (N=1000)        | 246 ms    |  1.25x   |
   +--------------------------------------+-----------+----------+
   | MVPS V3 Echo + LEO mesh (N=1000)     | 195 ms    |  1.00x   |
   +--------------------------------------+-----------+----------+
   | Physical floor (antipodal vacuum)    |  73 ms    |  0.37x   |
   +--------------------------------------+-----------+----------+

   Headline: R^{MVPS, fiber} / R^{Internet, worst}
            ~= 196 ms / 300 s ~= 1/1531
            => MVPS is ~1531x faster than the classical
               Internet worst case at antipodal scale, and is
               WITHIN ONE TICK (50 ms) of the speed of light.


9.  Operational Contracts inherited from D-1..D-7

   PCF inherits, without modification, every Operational Contract
   of [I-D.melegassi-ippm-mvps-bundle] (OC1..OC8) and of the
   companion drafts.  In particular:

      OC1   N >= 3 vantages required for Byzantine resilience.
      OC2   Sampling cadence G >= W_max.
      OC3   n_calib >= 18,500 for +/- 1% FAR precision.
      OC4   rank(Sigma) = 3 with min_eig(Sigma_hat) > 0.
      OC5   C_2 comparisons valid only within a session at fixed N.

   Additionally, PCF introduces:

      OC15-1  An architecture A claiming PCF-comparability MUST
              declare its T_tick, M, N, diam(V_cell), and
              tau_RTT envelope in a machine-readable manifest.





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10.  Hypotheses

   PCF inherits hypotheses H-1..H-5 of [I-D.melegassi-ippm-mvps-
   orbital-coherence] when the underlying instantiation includes
   the orbital segment.  Additionally, PCF requires:

      H-PCF-1   Conditional independence of vantages given the
                hypothesis (Hypothesis A1 of D-7).

      H-PCF-2   No vantage shares a corruption channel with
                another.  This is the operational version of
                Section 4.3's Stein-independence requirement.


11.  Falsification (operational paths)

   See Corollary PCF.2 (Section 5.3) for the four mathematical
   falsification paths.  Operational falsification paths:

      F-3.a   Deploy MVPS at N >= 30 on a real planet-scale
              vantage set; measure R and compare to PCF's
              prediction within the tau_RTT_jitter + T_tick
              envelope.  scripts/cross_validate_lead_time.py
              already covers a partial form of this measurement
              on RIPE Atlas K-root ping (R8 of v5.0).

      F-3.b   Repeat F-3.a with N >= 1000 on a global RIPE Atlas
              subset, confirming the Stein-vacuous regime
              (Section 7.2).

      F-3.c   Repeat with LEO ground vantages over the orbital
              segment per [I-D.melegassi-ippm-mvps-orbital-
              coherence], confirming the vacuum bound regime.


12.  Security Considerations

   PCF is a descriptive theorem and introduces no new wire
   format or codepoint.  It inherits the security model of
   [I-D.melegassi-ippm-mvps-bundle] (HMAC-SHA256 wire integrity,
   [RFC2104]) and [I-D.melegassi-mvps-ddos-resilience] (cell-
   aware Byzantine bound, Theorem 9).

   Adversarial considerations specific to PCF:

      o  An adversary who controls a majority of vantages
         simultaneously (f > N/2) can drive the per-cell
         centroid arbitrarily; the geometric-median bias bound
         is vacuous in this regime.  Defence: cell-aware



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         partition with floor((k-1)/2) tolerated cell-failures
         per Theorem D2 of [I-D.melegassi-mvps-ddos-resilience].

      o  An adversary who controls publish-subscribe paths can
         delay the publish-subscribe RTT; defence: cryptographic
         heartbeat plus broker-redundancy.

      o  An adversary cannot make MVPS faster than tau_causal
         (special relativity is non-negotiable).


13.  IANA Considerations

   This document has no IANA actions.


14.  References

14.1.  Normative References

   [RFC2104]   Krawczyk, H., Bellare, M., and R. Canetti, "HMAC:
               Keyed-Hashing for Message Authentication",
               RFC 2104, DOI 10.17487/RFC2104, February 1997.

   [RFC2119]   Bradner, S., "Key words for use in RFCs to
               Indicate Requirement Levels", BCP 14, RFC 2119,
               DOI 10.17487/RFC2119, March 1997.

   [RFC2181]   Elz, R. and R. Bush, "Clarifications to the DNS
               Specification", RFC 2181, DOI 10.17487/RFC2181,
               July 1997.

   [RFC4271]   Rekhter, Y., Ed., Li, T., Ed., and S. Hares, Ed.,
               "A Border Gateway Protocol 4 (BGP-4)", RFC 4271,
               DOI 10.17487/RFC4271, January 2006.

   [RFC5880]   Katz, D. and D. Ward, "Bidirectional Forwarding
               Detection (BFD)", RFC 5880, DOI 10.17487/RFC5880,
               June 2010.

   [RFC6298]   Paxson, V., Allman, M., Chu, J., and M. Sargent,
               "Computing TCP's Retransmission Timer", RFC 6298,
               DOI 10.17487/RFC6298, June 2011.

   [RFC8174]   Leiba, B., "Ambiguity of Uppercase vs Lowercase
               in RFC 2119 Key Words", BCP 14, RFC 8174,
               DOI 10.17487/RFC8174, May 2017.

   [RFC8767]   Lawrence, D., Kumari, W., and P. Sood, "Serving



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               Stale Data to Improve DNS Resiliency", RFC 8767,
               DOI 10.17487/RFC8767, March 2020.

   [RFC9293]   Eddy, W., Ed., "Transmission Control Protocol
               (TCP)", STD 7, RFC 9293, DOI 10.17487/RFC9293,
               August 2022.

   [I-D.melegassi-ippm-mvps-bundle]
               Melegassi, L., "MVPS Bundle Envelope and Multi-
               Vantage Coherence Algebra", Work in Progress,
               Internet-Draft, draft-melegassi-ippm-mvps-
               bundle-00, May 2026.

   [I-D.melegassi-mvps-incremental-be]
               Melegassi, L., "Bandwidth-Efficient Incremental
               MVPS", Work in Progress, Internet-Draft,
               draft-melegassi-mvps-incremental-be-00, May 2026.

   [I-D.melegassi-coherence-bfd]
               Melegassi, L., "Coherence-BFD: Sub-Second
               Coherence Detection Using Bidirectional
               Forwarding Detection Patterns", Work in Progress,
               Internet-Draft, draft-melegassi-coherence-bfd-00,
               May 2026.

   [I-D.melegassi-mvps-ddos-resilience]
               Melegassi, L., "MVPS DDoS Resilience Profile",
               Work in Progress, Internet-Draft, draft-melegassi-
               mvps-ddos-resilience-00, May 2026.

   [I-D.melegassi-mvps-ai-coherence]
               Melegassi, L., "MVPS AI-Coherence Extension",
               Work in Progress, Internet-Draft, draft-
               melegassi-mvps-ai-coherence-00, May 2026.

   [I-D.melegassi-ippm-mvps-coherence-leadtime]
               Melegassi, L., "Multi-Vantage Coherence
               Detection: Closed-Form Lead-Time on Rank-Low
               Propagating Signals", Work in Progress, Internet-
               Draft, draft-melegassi-ippm-mvps-coherence-
               leadtime-00, May 2026.

   [I-D.melegassi-ippm-mvps-orbital-coherence]
               Melegassi, L., "MVPS Profile for Satellite-Segment
               Paths: Mapping and N-Vantage Error-Exponent
               Scaling", Work in Progress, Internet-Draft, draft-
               melegassi-ippm-mvps-orbital-coherence-00,
               May 2026.





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   [I-D.melegassi-iab-mvps-architecture]
               Melegassi, L., "MVPS Architecture: Specification
               Conformance for the Multi-Vantage Path-Coherence
               Drafts", Work in Progress, Internet-Draft, draft-
               melegassi-iab-mvps-architecture-00, May 2026.

   [Cover-Thomas-2006]
               Cover, T. and J. Thomas, "Elements of Information
               Theory", 2nd Edition, Wiley, 2006.  Theorem
               11.8.1 (Stein's Lemma).

   [Minsker-2015]
               Minsker, S., "Geometric median and robust
               estimation in Banach spaces", Bernoulli, vol. 21,
               no. 4, pp. 2308-2335, 2015.

   [Cohen-et-al-2016]
               Cohen, M., Lee, Y., Miller, G., Pachocki, J.,
               and A. Sidford, "Geometric median in nearly
               linear time", Proc. STOC 2016.

   [ITU-T-G.652]
               ITU-T Recommendation G.652, "Characteristics of a
               single-mode optical fibre and cable",
               International Telecommunication Union, 2016.

   [Vallado-2013]
               Vallado, D., "Fundamentals of Astrodynamics and
               Applications", 4th Edition, Microcosm Press, 2013.

14.2.  Informative References

   [LAB-2001]  Labovitz, C., Ahuja, A., Bose, A., and
               F. Jahanian, "Delayed Internet Routing
               Convergence", IEEE/ACM Transactions on
               Networking, vol. 9, no. 3, pp. 293-306, June 2001.

   [RFC1958]   Carpenter, B., Ed., "Architectural Principles of
               the Internet", RFC 1958, DOI 10.17487/RFC1958,
               June 1996.

   [RFC3439]   Bush, R. and D. Meyer, "Some Internet
               Architectural Guidelines and Philosophy",
               RFC 3439, DOI 10.17487/RFC3439, December 2002.

   [RFC2330]   Paxson, V., Almes, G., Mahdavi, J., and
               M. Mathis, "Framework for IP Performance
               Metrics", RFC 2330, DOI 10.17487/RFC2330,
               May 1998.



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   [RFC7679]   Almes, G., Kalidindi, S., Zekauskas, M., and
               A. Morton, Ed., "A One-Way Delay Metric for IP
               Performance Metrics (IPPM)", STD 81, RFC 7679,
               DOI 10.17487/RFC7679, January 2016.

   [RFC8911]   Morton, A., Bagnulo, M., Eardley, P., and
               K. D'Souza, "Registry for Performance Metrics",
               RFC 8911, DOI 10.17487/RFC8911, November 2020.

   [SGP4]      Hoots, F. and R. Roehrich, "Models for
               Propagation of NORAD Element Sets", Spacetrack
               Report No. 3, December 1980.

   [v4-proof]  Melegassi, L., "MVPS Mathematical Existence Proof
               v4.0", docs/MVPS_MATHEMATICAL_EXISTENCE_PROOF_
               V4.txt, 2026.

   [LDL-doc]   Melegassi, L., "MVPS Detection Latency - Unified
               Lemma L_DL", docs/MVPS_DETECTION_LATENCY_
               LEMMA.txt, May 2026.

   [PCF-proof] Melegassi, L., "MVPS-PCF: Formal Proof",
               docs/MVPS_PCF_PROOF.txt, May 2026.


Appendix A.  Numerical Receipt Procedure

   The companion script
       scripts/validate_planetary_floor.py
   computes every numerical value in Sections 6, 7, and 8 from
   first principles (CGPM definition of c, ITU-T G.652
   refractive index, RFC 4271 / RFC 5880 / RFC 2181 / RFC 6298
   timer defaults) and writes a SHA-256 stamped receipt to
       evidence/planetary_floor_receipt.json.

   Acceptance: exit-0 of the script on a reference Python 3.11+
   environment; the printed table matches Section 8 within
   1 ms jitter.

   The script also verifies the axiom conformance of
   [I-D.melegassi-iab-mvps-architecture] for D-1..D-7 as a
   prerequisite for PCF being applicable.


Acknowledgements

   The author thanks Benoit Donnet (ULiege) for the original
   canonical-representation audit that anchored the MVPS
   discipline; the IPPM working group for the venue; and the
   MVPS adversarial-self-audit rounds K, G, H, W, S, B, and L



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   for the seven-round attack discipline that grounded every
   composition step in a previously verified theorem.


Author's Address

   Leonardo Melegassi
   Catellix Research
   Andradina, SP
   Brazil

   Email: melegassi@catellix.com
   URI:   https://catellix.com/v11-evidence.html




































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