Planetary Coherence Floor: Composition Theorem for Reactive Latency in Multi-Vantage Network Infrastructure
draft-melegassi-iab-mvps-planetary-floor-00
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| Document | Type | Active Internet-Draft (individual) | |
|---|---|---|---|
| Author | Leonardo Melegassi Costa | ||
| Last updated | 2026-05-26 | ||
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| Intended RFC status | (None) | ||
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draft-melegassi-iab-mvps-planetary-floor-00
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.
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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
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respect to this document.
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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