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The Single-Stack 100/50 Principle: Formal Definitions for IPv4 Retirement in Dual-Stack Networks
draft-sun-single-stack-100-50-01

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Author Charles Sun
Last updated 2026-09-02
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draft-sun-single-stack-100-50-01
Network Working Group                                             C. Sun
Internet-Draft                          Alliance for Universal Computing
Intended status: Informational                          2 September 2026
Expires: 6 March 2027

     The Single-Stack 100/50 Principle: Formal Definitions for IPv4
                   Retirement in Dual-Stack Networks
                    draft-sun-single-stack-100-50-01

Abstract

   The Single-Stack 100/50 Principle defines two independent, formally
   derivable consequences of retiring the IPv4 protocol stack in a dual-
   stack (IPv4 + IPv6) network environment: (1) 100% elimination of
   executable attacks attributable to IPv4 under the document's
   definition, and (2) an exact 50% reduction in the count of
   concurrently exposed network-layer protocol-stack surfaces when IPv4
   is retired, stated by the Principle as a minimum structural floor.
   The analysis is bounded to the functional Layer 3 scope and parameter
   universe U_3 defined in this document.  Within that premise, Axiom 0
   and Axioms 1-15 stipulate protocol independence, operational state
   transitions, traffic termination, addressing/routing domains,
   protocol-associated control and resolution functions, header-
   processing paths, and protocol-specific vulnerability execution.
   Theorem I follows by removal of the necessary IPv4 Layer 3 execution
   precondition for every IPv4-attributable attack.  Theorem II follows
   by direct enumeration of two concurrently exposed protocol-stack
   surfaces before retirement and one after retirement.  Neither theorem
   depends on empirical attack volume, incident frequency, or
   statistical inference, and neither theorem claims that IPv6 is
   inherently more secure than IPv4.

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
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   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
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   time.  It is inappropriate to use Internet-Drafts as reference
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   This document is subject to BCP 78 and the IETF Trust's Legal
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   Please review these documents carefully, as they describe your rights
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Definitional Premise and Layer 3 Scope  . . . . . . . . . . .   4
     2.1.  Core Terminology  . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Prerequisite for IPv4-Attributable Attack Execution . . .   5
     2.3.  Parameter Universe and Completeness . . . . . . . . . . .   5
     2.4.  Native-Stack and Scope Boundary . . . . . . . . . . . . .   6
   3.  Statement of the Single-Stack 100/50 Principle  . . . . . . .   7
   4.  Axiomatic Foundation  . . . . . . . . . . . . . . . . . . . .   7
     4.1.  Axiom 0 - Protocol Independence at Layer 3  . . . . . . .   7
     4.2.  Axiom 1 - Enabling Either Protocol Is Non-Interfering . .   8
     4.3.  Axiom 2 - Enabling Both Protocols Is Non-Interfering  . .   8
     4.4.  Axiom 3 - Enabling IPv4 Does Not Affect IPv6  . . . . . .   8
     4.5.  Axiom 4 - Enabling IPv6 Does Not Affect IPv4  . . . . . .   8
     4.6.  Axiom 5 - Disabling Either Protocol Preserves the
            Other  . . . . . . . . . . . . . . . . . . . . . . . . .   8
     4.7.  Axiom 6 - Disabling IPv4 Preserves IPv6 . . . . . . . . .   9
     4.8.  Axiom 7 - Disabling IPv6 Preserves IPv4 . . . . . . . . .   9
     4.9.  Axiom 8 - Disabling a Protocol Terminates Its Traffic . .   9
     4.10. Axiom 9 - Disabling IPv4 Terminates All IPv4 Traffic  . .   9
     4.11. Axiom 10 - Disabling IPv6 Terminates All IPv6 Traffic . .   9
     4.12. Axiom 11 - Disabling Both Protocols Terminates All IP
            Networking . . . . . . . . . . . . . . . . . . . . . . .  10
     4.13. Axiom 12 - Disjoint Address-Space Isolation . . . . . . .  10
     4.14. Axiom 13 - Disjoint Control-Protocol State Machines . . .  10
     4.15. Axiom 14 - Disjoint Header-Parsing Execution Paths  . . .  10
     4.16. Axiom 15 - Absence of Transitive Vulnerability
            Inheritance  . . . . . . . . . . . . . . . . . . . . . .  11
     4.17. Operational-State Completeness  . . . . . . . . . . . . .  11
     4.18. Structural-Parameter Completeness . . . . . . . . . . . .  11
   5.  Layer 3 Vertical-Stack Mechanics  . . . . . . . . . . . . . .  12

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   6.  Theorem I: The 100% Clause  . . . . . . . . . . . . . . . . .  13
     6.1.  Basis . . . . . . . . . . . . . . . . . . . . . . . . . .  13
     6.2.  Formalization . . . . . . . . . . . . . . . . . . . . . .  13
     6.3.  Theorem I . . . . . . . . . . . . . . . . . . . . . . . .  14
   7.  Theorem II: The Minimum 50% Clause  . . . . . . . . . . . . .  14
     7.1.  Basis . . . . . . . . . . . . . . . . . . . . . . . . . .  14
     7.2.  Direct Enumeration  . . . . . . . . . . . . . . . . . . .  14
     7.3.  Theorem II  . . . . . . . . . . . . . . . . . . . . . . .  14
   8.  Comparative Summary . . . . . . . . . . . . . . . . . . . . .  15
   9.  Scope and Boundary Conditions . . . . . . . . . . . . . . . .  15
   10. Standards Basis . . . . . . . . . . . . . . . . . . . . . . .  16
   11. Security Considerations . . . . . . . . . . . . . . . . . . .  17
   12. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  17
   13. Conclusion  . . . . . . . . . . . . . . . . . . . . . . . . .  17
   14. Changes from -00  . . . . . . . . . . . . . . . . . . . . . .  18
   15. Normative References  . . . . . . . . . . . . . . . . . . . .  18
   16. Informative References  . . . . . . . . . . . . . . . . . . .  19
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  19

1.  Introduction

   This document formalizes two structural consequences of retiring IPv4
   from a native dual-stack IPv4/IPv6 environment.  The first concerns
   executability of attack vectors whose necessary execution path is
   IPv4.  The second concerns the number of concurrently exposed IP-
   version-specific Layer 3 protocol-stack surfaces.  Both results are
   definitional and structural; neither depends on empirical attack-
   volume measurement.

   This revision expands the formal model while retaining the two
   independent denominators of the Single-Stack 100/50 Principle.  The
   100% clause concerns the defined class of executable
   IPv4-attributable attack vectors.  The minimum 50% clause concerns
   the count of concurrently exposed network-layer protocol-stack
   surfaces.  The document does not claim that IPv6 is inherently more
   secure than IPv4, nor does it claim a 50% reduction in attack
   traffic, incident count, financial loss, or total organizational
   risk.

   This document defines no conformance requirements and uses no RFC
   2119 or RFC 8174 key words.

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2.  Definitional Premise and Layer 3 Scope

   To maintain mathematical and logical rigor, every definition, axiom,
   parameter, and derivation in this document is bounded to Layer 3 IP
   protocol mechanics and to the protocol-associated control/resolution
   functions expressly included in U_3 when they directly support Layer
   3 forwarding.  Layer 3 supplies network-layer addressing, packet-
   header processing, forwarding logic, and the IP delivery function
   between lower-layer connectivity and upper-layer transport
   [ISO7498-1].  This is a functional proof boundary.  It does not
   assign every auxiliary mechanism (for example, ARP) to OSI Layer 3 as
   a matter of formal layer classification; only the protocol-associated
   function expressly defined in U_3 is admitted.  No proposition
   outside that boundary is used as a proof premise.

   Formal status of the axioms.  Within the stipulated Layer 3/U_3
   premise, Axiom 0 and Axioms 1-15 are definitional or structural
   premises used by the derivations.  They are not empirical hypotheses
   and are not conditioned on observed attack traffic.  Their
   applicability is limited to the native IP protocol mechanics and
   explicit parameters defined in U_3; implementation coupling or cross-
   layer behavior outside U_3 is not asserted away.

2.1.  Core Terminology

   *Dual-Stack Mode of Operations*
      A network or host configuration in which both the IPv4 and IPv6
      protocol stacks are concurrently active and reachable at Layer 3.

   *Single-Stack Mode of Operations*
      A network or host configuration in which only one network-layer
      protocol stack - IPv4 or IPv6 - is active and reachable at Layer
      3.

   *Network-Layer Attack Surface*
      For this document, one active and reachable IP-version-specific
      Layer 3 protocol-processing surface, treated as a complete
      independently addressable stack and characterized by its own
      addressing/routing domain, header format, packet-processing path,
      protocol-associated control/resolution functions, and protocol-
      specific vulnerability execution conditions.

   *IPv4-Attributable Attack*
      Any attack vector whose execution requires IPv4 protocol mechanics
      at Layer 3.  The defining test is necessity: if execution does not
      require an active and reachable IPv4 Layer 3 processing path, the
      vector is not IPv4-attributable for purposes of Theorem I.

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   *Retirement*
      The disabled or removed state of the identified protocol stack at
      Layer 3, such that no active processing path for that protocol
      remains within the network or host boundary to which the Principle
      is applied.  If translation, tunneling, or another mechanism
      retains or reintroduces active IPv4 Layer 3 processing inside that
      same boundary, IPv4 is not retired there for purposes of Theorem I
      or Theorem II.

2.2.  Prerequisite for IPv4-Attributable Attack Execution

   An IPv4-attributable attack can execute only if an active and
   reachable IPv4 Layer 3 protocol instance can receive and process the
   IPv4 protocol data unit needed by that attack.  This necessary-
   condition relationship is the definitional basis of Theorem I.
   Theorem I addresses the Layer 3 execution prerequisite; it does not
   require an estimate of how frequently any attack is attempted.

2.3.  Parameter Universe and Completeness

   Let U_3 denote the bounded Layer 3 parameter universe used by this
   document.  U_3 comprises: (i) IPv4 and IPv6 enable/disable state;
   (ii) the traffic-flow consequence of each state; (iii) continuity of
   the remaining enabled protocol; (iv) protocol-specific addressing and
   routing lookup, including the IPv4 and IPv6 address domains A_4 and
   A_6 defined in Axiom 12; (v) protocol-specific control/resolution
   functions; (vi) protocol-specific header-parsing semantics; and (vii)
   protocol-specific vulnerability execution.  Axiom 0 and Axioms 1-15
   collectively state all domain-specific premises invoked for those
   parameters by Theorems I and II.  'Complete' therefore means proof-
   complete relative to U_3 and the stated premise: no additional
   unstated proposition concerning a parameter within U_3 is required
   for the derivations established in this document.  It does not mean
   that the Internet, the OSI Reference Model, an implementation, or
   cybersecurity generally is a closed or completely enumerated system.

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   +====================+==========================+===========+
   | Parameter category | Formal object / scope    | Governing |
   |                    |                          | axiom(s)  |
   +====================+==========================+===========+
   | Governing          | Native IPv4/IPv6 logical | Axiom 0   |
   | independence       | separation within U_3    |           |
   +--------------------+--------------------------+-----------+
   | Enable/disable     | (p_4,p_6) in {0,1}^2     | Axioms    |
   | state              |                          | 1-7, 11   |
   +--------------------+--------------------------+-----------+
   | Traffic-flow       | Protocol flow after      | Axioms    |
   | consequence        | state transition         | 8-11      |
   +--------------------+--------------------------+-----------+
   | Continuity of      | Surviving stack's own    | Axioms    |
   | remaining protocol | Layer 3 mechanics        | 5-7       |
   +--------------------+--------------------------+-----------+
   | Addressing and     | Protocol-tagged domains  | Axiom 12  |
   | routing lookup     | A_4 and A_6              |           |
   +--------------------+--------------------------+-----------+
   | Control/resolution | Protocol-associated      | Axiom 13  |
   | functions          | control/resolution state |           |
   +--------------------+--------------------------+-----------+
   | Header parsing     | Version-specific header  | Axiom 14  |
   |                    | semantics                |           |
   +--------------------+--------------------------+-----------+
   | Vulnerability      | Protocol-specific        | Axiom 15  |
   | execution          | necessary execution path |           |
   +--------------------+--------------------------+-----------+

         Table 1: Coverage of U_3 by the Axiomatic Premise

2.4.  Native-Stack and Scope Boundary

   The axioms describe native IPv4 and IPv6 protocol mechanics within
   the selected host or network boundary.  They do not assert that real
   implementations share no code, memory, CPU, configuration,
   application behavior, or failure modes.  Shared-resource and cross-
   layer effects are outside U_3 unless they are expressly made part of
   a protocol-specific execution condition.

   Likewise, Axioms 5-7 concern continuity of the remaining protocol's
   own Layer 3 mechanics; they do not claim preservation of end-to-end
   reachability to destinations that require the retired protocol.  A
   translator, tunnel endpoint, compatibility mechanism, or other
   component that performs active IPv4 Layer 3 processing inside the
   selected boundary means the premise P_4 = 0 is not satisfied for that
   boundary.

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3.  Statement of the Single-Stack 100/50 Principle

   In Dual-Stack Mode of Operations, using both IPv4 and IPv6, the
   moment the IPv4 stack is retired at Layer 3:

   *  100% Elimination - 100% elimination of executable
      IPv4-attributable attack vectors within the defined Layer 3 scope
      because their necessary IPv4 processing condition is absent.

   *  Minimum 50% Reduction - a minimum 50% reduction in the count of
      concurrently exposed network-layer attack surfaces: IPv4 + IPv6
      becomes IPv6 only.

   The two percentages have independent denominators.  The 100% clause
   measures the defined set of IPv4-attributable attack vectors and
   whether they remain executable.  The minimum 50% clause measures the
   count S of concurrently exposed Layer 3 protocol-stack surfaces.
   Neither percentage is derived from attack-volume statistics, and
   neither percentage asserts that IPv6 is inherently more secure than
   IPv4.

4.  Axiomatic Foundation

   The axioms form one continuous stipulated premise for Theorems I and
   II.  Axioms 1-11 enumerate operational state and traffic-flow
   consequences.  Axioms 12-15 state the structural parameters used by
   the proofs.  Each axiom is bounded by Section 1 and U_3.  The word
   'TRUE' in the confirmations below means true within those
   stipulations; it is not a claim about every implementation, cross-
   layer dependency, shared resource, or transition mechanism.

4.1.  Axiom 0 - Protocol Independence at Layer 3

   Within U_3, native IPv4 and IPv6 are logically distinct Layer 3
   protocol instances.  Each has its own address domain, header
   semantics, forwarding/control behavior, and protocol-specific
   processing path.  The native specification and operation of one IP
   version do not require an active instance of the other.  This axiom
   does not deny coexistence mechanisms, translation/tunneling, shared
   implementation resources, or application-level coupling outside U_3.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.  RFC
   791 and RFC 8200 specify different IP versions, address lengths, and
   header-processing rules; RFC 4213 describes dual IP layer operation
   as complete support for both protocol versions [RFC0791], [RFC8200],
   [RFC4213].

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4.2.  Axiom 1 - Enabling Either Protocol Is Non-Interfering

   Enabling either native IPv4 or native IPv6 does not alter the
   protocol-specific Layer 3 mechanics of the other IP version within
   U_3.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   Enabling one stack does not change the other version's address-domain
   definition or header semantics.  System-level preference or
   application-selection effects outside U_3 are not part of this axiom.

4.3.  Axiom 2 - Enabling Both Protocols Is Non-Interfering

   When both native IPv4 and IPv6 are enabled, each retains its own
   protocol-specific Layer 3 mechanics within U_3.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.  RFC
   4213 describes dual IP layer operation as complete implementations of
   both IP versions operating on the same node [RFC4213].

4.4.  Axiom 3 - Enabling IPv4 Does Not Affect IPv6

   Enabling native IPv4 does not alter the protocol-specific IPv6 Layer
   3 mechanics defined in U_3.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   IPv4 activation does not redefine IPv6 addressing, IPv6 header
   semantics, or the IPv6 protocol-specific processing path.

4.5.  Axiom 4 - Enabling IPv6 Does Not Affect IPv4

   Enabling native IPv6 does not alter the protocol-specific IPv4 Layer
   3 mechanics defined in U_3.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   IPv6 activation does not redefine IPv4 addressing, IPv4 header
   semantics, or the IPv4 protocol-specific processing path.

4.6.  Axiom 5 - Disabling Either Protocol Preserves the Other

   Disabling either IPv4 or IPv6 does not remove or alter the remaining
   protocol stack's own Layer 3 mechanics within U_3.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   Removing Stack A leaves Stack B's protocol-specific processing path
   intact.  This does not claim continued reachability to destinations
   that require Stack A.

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4.7.  Axiom 6 - Disabling IPv4 Preserves IPv6

   Retiring IPv4 preserves the IPv6 stack's own Layer 3 mechanics within
   U_3.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   IPv6 addressing, header processing, ICMPv6, and IPv6 forwarding
   remain defined and operable independently of an active IPv4 stack.
   Reachability to IPv4-only destinations is outside the claim.

4.8.  Axiom 7 - Disabling IPv6 Preserves IPv4

   Retiring IPv6 preserves the IPv4 stack's own Layer 3 mechanics within
   U_3.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   IPv4 addressing, header processing, ICMPv4, and IPv4 forwarding
   remain defined and operable independently of an active IPv6 stack.
   Reachability to IPv6-only destinations is outside the claim.

4.9.  Axiom 8 - Disabling a Protocol Terminates Its Traffic

   Within the selected boundary, disabling either IP version terminates
   packet processing and Layer 3 traffic on the protocol that has been
   disabled or removed.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.  The
   active Layer 3 parsing and processing path for that protocol is
   absent within the selected boundary.

4.10.  Axiom 9 - Disabling IPv4 Terminates All IPv4 Traffic

   Within the selected boundary, retiring IPv4 terminates IPv4 Layer 3
   packet processing and IPv4 traffic through that retired path.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   Zero IPv4 PDUs are processed by an active IPv4 Layer 3 instance
   within the boundary because no such instance remains.

4.11.  Axiom 10 - Disabling IPv6 Terminates All IPv6 Traffic

   Within the selected boundary, retiring IPv6 terminates IPv6 Layer 3
   packet processing and IPv6 traffic through that retired path.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   Zero IPv6 PDUs are processed by an active IPv6 Layer 3 instance
   within the boundary because no such instance remains.

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4.12.  Axiom 11 - Disabling Both Protocols Terminates All IP Networking

   Within the selected boundary, retiring both IPv4 and IPv6 terminates
   all native IP Layer 3 processing for both protocol versions; no IPv4-
   or IPv6-based IP delivery path remains there.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   Native IP Layer 3 processing for both versions is absent, while
   lower-layer connectivity may still physically exist.

4.13.  Axiom 12 - Disjoint Address-Space Isolation

   An IPv4 addressing/routing lookup is evaluated over the IPv4 address
   domain, while an IPv6 addressing/routing lookup is evaluated over the
   IPv6 address domain.  With the protocol tag included in the formal
   objects, the two domains are disjoint and a lookup in one domain is
   not a lookup in the other.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.
   Define A_4 = {(4,x): x in {0,1}^32} and A_6 = {(6,y): y in
   {0,1}^128}. The protocol tag makes A_4 intersect A_6 = {} by
   definition.  A_4 and A_6 are address domains referenced by U_3; they
   are not asserted to be subsets of the parameter universe itself.

4.14.  Axiom 13 - Disjoint Control-Protocol State Machines

   Protocol-associated control and resolution functions for IPv4 and
   IPv6 are logically distinct within U_3.  For Ethernet-based address
   resolution, ARP serves IPv4 address-to-link-layer mapping, whereas
   IPv6 uses ICMPv6 Neighbor Discovery; a protocol-specific state
   transition in one does not, by definition, constitute a state
   transition in the other.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.  ARP
   and IPv6 Neighbor Discovery are separately specified mechanisms
   [RFC0826], [RFC4861].  ARP is included here only as a protocol-
   associated resolution function supporting IPv4 Layer 3 forwarding;
   its formal OSI layer classification is not a proof premise.

4.15.  Axiom 14 - Disjoint Header-Parsing Execution Paths

   Under the standards-defined semantics, an IPv4 header is not a valid
   IPv6 header and an IPv6 header is not a valid IPv4 header.  The
   version-specific parsing semantics are logically disjoint within U_3,
   even if a particular implementation shares code or hardware resources
   between the two parsing paths.

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   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.  RFC
   791 and RFC 8200 define distinct version-specific header formats and
   processing semantics [RFC0791], [RFC8200].

4.16.  Axiom 15 - Absence of Transitive Vulnerability Inheritance

   A vulnerability is protocol-specific within U_3 only when its
   necessary execution condition lies in a version-specific protocol-
   processing path.  An IPv4-specific malformed-packet or header-
   processing exploit cannot execute through the IPv6-specific path
   merely because IPv6 remains enabled.  A vulnerability in shared code,
   shared memory, a common driver, or an upper/lower layer is not
   classified as protocol-specific by this axiom unless its execution
   still requires the retired IPv4 Layer 3 path.

   Formal confirmation: TRUE within the stated Layer 3/U_3 premise.  By
   definition, the stipulated vulnerability condition and its necessary
   execution path are confined to the protocol-specific routine
   represented in U_3; shared-implementation vulnerabilities that do not
   satisfy that necessity test are outside the axiom.

4.17.  Operational-State Completeness

   For the two-protocol binary state vector (p_4,p_6) in {0,1}^2, the
   complete joint state set is {(0,0),(1,0),(0,1),(1,1)}. Axioms 1-4
   govern enabling and coexistence; Axioms 5-7 govern preservation of
   the remaining protocol's own Layer 3 mechanics after disabling; and
   Axioms 8-11 govern traffic termination for the disabled protocol or
   protocols.  These axioms enumerate every state and every traffic
   consequence admitted by the binary-state parameters in U_3.

4.18.  Structural-Parameter Completeness

   Axioms 12-15 enumerate the structural parameter categories used by
   the proofs: address/routing domain, protocol-associated control and
   resolution functions, header-parsing semantics, and protocol-specific
   vulnerability execution.  Together with Axiom 0, and as mapped in
   Section 1.3, they provide the complete structural premise required by
   Theorems I and II within U_3.  No additional domain-specific premise
   external to U_3 is invoked as a proof premise; ordinary rules of
   logic, set notation, and arithmetic remain the mathematical framework
   in which the derivations are expressed.

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5.  Layer 3 Vertical-Stack Mechanics

   When IPv4 is retired, the active IPv4 Layer 3 protocol instance is
   absent within the network or host boundary to which the Principle is
   applied.  Layer 2 may still receive and identify a frame carrying an
   IPv4 payload, but no active IPv4 Layer 3 state machine exists within
   that boundary to accept and process the IPv4 PDU.  The deterministic
   consequence relevant to this document is failure of IPv4 Layer 3
   processing and, consequently, failure of delivery through an IPv4
   path.  This section assumes the retirement boundary defined in
   Section 2.1 and excludes mechanisms that reintroduce active IPv4
   processing inside that boundary.

   +======+================+===========================================+
   | Step | Layer          | Deterministic consequence within          |
   |      | interaction    | the premise                               |
   +======+================+===========================================+
   | 1    | Physical and   | Signals may be received and framed        |
   |      | data-link      | at Layers 1-2.                            |
   |      | ingress        |                                           |
   +------+----------------+-------------------------------------------+
   | 2    | Protocol       | The payload is identified as IPv4,        |
   |      | identification | such as by EtherType 0x0800 on            |
   |      |                | Ethernet.                                 |
   +------+----------------+-------------------------------------------+
   | 3    | Layer 3        | No active IPv4 Layer 3 protocol           |
   |      | handoff        | instance exists to accept and             |
   |      |                | process the IPv4 PDU.                     |
   +------+----------------+-------------------------------------------+
   | 4    | Processing     | The IPv4 PDU is rejected or               |
   |      | termination    | discarded before IPv4 Layer 3             |
   |      |                | processing and cannot be delivered        |
   |      |                | upward through an IPv4 path.              |
   +------+----------------+-------------------------------------------+

              Table 2: IPv4 Retirement at the Layer 3 Boundary

   *  Zero IPv4 parsing by an active IPv4 stack.  No active IPv4 Layer 3
      parser executes the IPv4 header or its IPv4-specific fields.

   *  Zero IPv4 processing.  No active IPv4 Layer 3 state machine
      performs IPv4 forwarding, ICMPv4 handling, fragmentation/
      reassembly, or other IPv4 protocol mechanics.

   *  Zero IPv4-path upper-layer delivery.  The payload cannot reach
      Layer 4 or higher through the retired IPv4 Layer 3 path.  IPv6
      delivery remains governed separately by Axiom 6.

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6.  Theorem I: The 100% Clause

6.1.  Basis

   Theorem I is grounded in the definition of IPv4-Attributable Attack,
   Axiom 0, Axioms 8-9, and Axioms 14-15.  It is a necessary-condition
   proof: every member of the defined attack class requires the active
   IPv4 Layer 3 processing path that retirement removes.

6.2.  Formalization

   Let P_4 = 1 mean that the applicable IPv4 Layer 3 protocol instance
   is active and reachable, and let P_4 = 0 mean that it is retired.
   Let C_4 be the set of IPv4-attributable attack vectors under
   Section 2.1.  For every a in C_4:

   Exec(a) => P_4 = 1.                                      (1)

                                  Figure 1

   IPv4 retirement gives:

   P_4 = 0.                                                    (2)

                                  Figure 2

   Therefore, by contraposition of the defining necessity relation:

   For all a in C_4: not Exec(a).                            (3)

                                  Figure 3

   Accordingly, the post-retirement executable set is:

   E_4,post = {a in C_4 : Exec(a)} = empty set.                (4)

                                  Figure 4

   Let E_4,pre subseteq C_4 denote any nonempty pre-retirement set of
   executable IPv4-attributable attack vectors.  Then:

   Elimination Rate = (|E_4,pre| - |E_4,post|) / |E_4,pre|
                    = 1 = 100%.                                (5)

                                  Figure 5

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6.3.  Theorem I

   |  Theorem I - 100% Elimination.  Within the defined retirement
   |  boundary, retiring the IPv4 Layer 3 protocol stack renders every
   |  attack vector in C_4 non-executable because the necessary IPv4
   |  Layer 3 execution condition is absent.  If the pre-retirement
   |  executable set E_4,pre is nonempty, its elimination rate is 100%.
   |  Q.E.D.

7.  Theorem II: The Minimum 50% Clause

7.1.  Basis

   Theorem II is grounded in the Network-Layer Attack Surface
   definition, Axiom 0, Axiom 6, and Axioms 12-15.  It counts
   concurrently exposed Layer 3 protocol-stack surfaces as defined in
   Section 2.1.  The derivation is structural and does not weight the
   stacks by traffic volume, exploit count, or incident frequency.

7.2.  Direct Enumeration

   Let S denote the number of concurrently active and reachable Network-
   Layer Attack Surfaces under the document's definition.

   S(dual-stack)   = |{IPv4, IPv6}| = 2.                     (6)
   S(IPv4 retired) = |{IPv6}|       = 1.                     (7)
   Structural reduction = (2 - 1) / 2 = 0.5 = 50%.           (8)

                                  Figure 6

   The two-to-one count establishes an exact 50% reduction in S.  The
   Principle states this exact result as a minimum structural floor
   because S deliberately counts only complete protocol-stack surfaces.
   IPv4 retirement may also remove coexistence, transition, or other
   IPv4-specific sub-surfaces, but no additional reduction is required
   for Theorem II and no additional percentage is quantified here.

7.3.  Theorem II

   |  Theorem II - Minimum 50% Reduction.  Retiring IPv4 from a dual-
   |  stack Layer 3 environment reduces S, the count of concurrently
   |  exposed Network-Layer Attack Surfaces, from two to one.  The
   |  reduction in S is exactly 50%; the Principle states that exact
   |  stack-count result as its minimum structural floor.  Q.E.D.

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8.  Comparative Summary

   +=============+==========================+=====================+
   | Dimension   | Theorem I - 100%         | Theorem II -        |
   |             |                          | Minimum 50%         |
   +=============+==========================+=====================+
   | Quantity    | Executable               | Concurrently        |
   | measured    | IPv4-attributable attack | exposed network-    |
   |             | vectors (C_4)            | layer protocol-     |
   |             |                          | stack surfaces (S)  |
   +-------------+--------------------------+---------------------+
   | Controlling | Definition plus Axioms   | Definition plus     |
   | basis       | 0, 8-9, and 14-15        | Axioms 0, 6, and    |
   |             |                          | 12-15               |
   +-------------+--------------------------+---------------------+
   | Derivation  | Removal of a necessary   | Direct enumeration: |
   |             | execution precondition   | 2 -> 1              |
   +-------------+--------------------------+---------------------+
   | Empirical   | No                       | No                  |
   | data        |                          |                     |
   | required?   |                          |                     |
   +-------------+--------------------------+---------------------+
   | Formal      | Post-retirement          | S: 2 -> 1 = exact   |
   | result      | executable set is empty; | 50%; stated as      |
   |             | 100% elimination rate    | minimum structural  |
   |             | when E_4,pre is nonempty | floor               |
   +-------------+--------------------------+---------------------+
   | Separate    | Attempt frequency,       | Change in attack    |
   | empirical   | attacker substitution,   | traffic, incidents, |
   | question    | or attacks not requiring | financial loss, or  |
   |             | IPv4                     | measured            |
   |             |                          | organizational risk |
   +-------------+--------------------------+---------------------+

         Table 3: Independent Denominators and Formal Results

9.  Scope and Boundary Conditions

   Theorems I and II are definitional and structural.  Their admissible
   propositions are confined to U_3 and the functional Layer 3 meanings
   fixed in Section 2.  The document does not use empirical attack
   volume, incident totals, or attacker reallocation behavior as proof
   premises.  Those observations may be studied separately, but they
   neither establish nor negate the two formal results.

   *  Theorem I does not claim elimination of attacks that do not
      require the retired IPv4 Layer 3 processing path.

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   *  Theorem II does not claim a specific percentage change in attack
      traffic, incident count, exploit attempts, financial loss, or
      total organizational risk.

   *  The Principle does not claim that IPv6 is inherently more secure
      than IPv4; the surviving IPv6 stack still requires independent
      security engineering.

   *  The term Network-Layer Attack Surface is used only as expressly
      defined in this document: one active and reachable IP-version-
      specific Layer 3 protocol-stack surface.

   *  Shared-code, shared-memory, driver, application-layer, and other
      cross-layer vulnerabilities are outside the protocol-specific
      claim unless their execution requires the retired IPv4 path.

   *  A translator, tunnel endpoint, compatibility mechanism, or other
      component that performs active IPv4 Layer 3 processing inside the
      selected boundary means IPv4 is not retired there under the
      document's definition.

   *  Axioms 5-7 do not promise continued access to IPv4-only or
      IPv6-only destinations after the corresponding protocol is
      retired; they concern continuity of the remaining stack's own
      Layer 3 mechanics.

   *  The truth status and completeness of Axiom 0 and Axioms 1-15 are
      relative to the stipulated premise and U_3; they do not assert
      completeness of an implementation or of cybersecurity generally.

10.  Standards Basis

   The formal premise is anchored to the OSI Basic Reference Model and
   the protocol specifications for IPv4, IPv6, dual IP layer operation,
   IPv4 address resolution, and IPv6 Neighbor Discovery.  RFC 4213
   expressly describes dual IP layer operation as complete support for
   both IPv4 and IPv6 and notes that either stack may be disabled for
   operational reasons [RFC4213].  RFC 7381 and RFC 9099 independently
   observe that dual-stack operation requires security treatment for
   both protocol versions and creates additional exposure/management
   complexity [RFC9099], [RFC7381].  Those standards provide
   corroborating architectural context; the mathematical results in
   Theorems I and II still follow from the document's definitions,
   axioms, and enumeration rather than from those external statements.

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11.  Security Considerations

   This document specifies no new packet format, protocol mechanism,
   configuration requirement, or implementable behavior and therefore
   introduces no new protocol attack surface of its own.

   The Single-Stack 100/50 Principle does not assert that IPv6 is
   inherently more secure than IPv4.  The surviving IPv6 stack remains
   subject to IPv6-specific security considerations and requires
   independent security engineering.  Operational security
   considerations for IPv6 networks are discussed in [RFC9099].

   The formal results apply only when the retirement boundary is
   actually satisfied.  If translation, tunneling, compatibility
   processing, or another mechanism retains or reintroduces active IPv4
   Layer 3 processing inside the selected boundary, the premise P_4 = 0
   is not satisfied there.  Likewise, shared-code or cross-layer
   vulnerabilities that do not require the retired IPv4 path are outside
   Theorem I.

12.  IANA Considerations

   This document has no IANA actions.

13.  Conclusion

   The Single-Stack 100/50 Principle establishes two definitionally
   independent results of IPv4 retirement within a defined dual-stack
   Layer 3 boundary.  First, retirement removes the necessary IPv4 Layer
   3 execution condition for every IPv4-attributable attack vector in
   C_4, rendering the defined class non-executable; when the pre-
   retirement executable set is nonempty, the elimination rate is 100%.
   Second, the count S of concurrently exposed network-layer protocol-
   stack surfaces falls from two to one; direct enumeration yields an
   exact 50% reduction, stated by the Principle as its minimum
   structural floor.

   Both results are derived exclusively from the defined Layer 3/U_3
   premise, Axiom 0, Axioms 1-15, and the associated definitions.  The
   axioms collectively provide the complete set of stipulated domain-
   specific premises used by these derivations relative to U_3; they do
   not assert completeness of the Internet, an implementation, or
   cybersecurity generally.  Theorems I and II require no empirical
   attack-volume dataset and remain logically independent of any
   separate measurement of traffic, incidents, attacker behavior, or
   comparative protocol security.  The Principle therefore formalizes
   the structural consequence of removing one active IP stack without
   claiming that the surviving protocol is inherently secure.

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14.  Changes from -00

   This section is to be removed before publishing as an RFC.

   This revision expands and tightens the initial formulation without
   changing the two core results.

   *  Defines a bounded Layer 3 parameter universe U_3 and states proof-
      completeness only relative to that universe and the stipulated
      premise.

   *  Adds an axiom-to-parameter coverage mapping and clarifies that the
      IPv4 and IPv6 address domains A_4 and A_6 are referenced by U_3
      but are not subsets of the parameter universe.

   *  Adds a native-stack and retirement-boundary definition covering
      translators, tunnels, compatibility mechanisms, shared resources,
      and cross-layer effects.

   *  Expands Axiom 0 and Axioms 1-15 to state their domain precisely
      and adds operational-state and structural-parameter completeness
      sections.

   *  Adds explicit formal notation for Theorem I and distinguishes the
      exact 50% stack-count reduction in S from the Principle's minimum
      structural floor.

   *  Adds vertical-stack mechanics, a comparative summary, expanded
      scope boundaries, standards basis, and stronger security
      considerations.

15.  Normative References

   [ISO7498-1]
              International Organization for Standardization,
              "Information technology - Open Systems Interconnection -
              Basic Reference Model: The Basic Model", ISO/
              IEC 7498-1:1994, 1994,
              <https://www.iso.org/standard/20269.html>.

   [RFC0791]  Postel, J., "Internet Protocol", STD 5, RFC 791,
              DOI 10.17487/RFC791, September 1981,
              <https://www.rfc-editor.org/info/rfc791>.

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   [RFC0826]  Plummer, D., "An Ethernet Address Resolution Protocol: Or
              Converting Network Protocol Addresses to 48.bit Ethernet
              Address for Transmission on Ethernet Hardware", STD 37,
              RFC 826, DOI 10.17487/RFC826, November 1982,
              <https://www.rfc-editor.org/info/rfc826>.

   [RFC4213]  Nordmark, E. and R. Gilligan, "Basic Transition Mechanisms
              for IPv6 Hosts and Routers", RFC 4213,
              DOI 10.17487/RFC4213, October 2005,
              <https://www.rfc-editor.org/info/rfc4213>.

   [RFC4861]  Narten, T., Nordmark, E., Simpson, W., and H. Soliman,
              "Neighbor Discovery for IP version 6 (IPv6)", RFC 4861,
              DOI 10.17487/RFC4861, September 2007,
              <https://www.rfc-editor.org/info/rfc4861>.

   [RFC8200]  Deering, S. and R. Hinden, "Internet Protocol, Version 6
              (IPv6) Specification", STD 86, RFC 8200,
              DOI 10.17487/RFC8200, July 2017,
              <https://www.rfc-editor.org/info/rfc8200>.

16.  Informative References

   [RFC7381]  Chittimaneni, K., Chown, T., Howard, L., Kuarsingh, V.,
              Pouffary, Y., and E. Vyncke, "Enterprise IPv6 Deployment
              Guidelines", RFC 7381, DOI 10.17487/RFC7381, October 2014,
              <https://www.rfc-editor.org/info/rfc7381>.

   [RFC9099]  Vyncke, E., Chittimaneni, K., Kaeo, M., and E. Rey,
              "Operational Security Considerations for IPv6 Networks",
              RFC 9099, DOI 10.17487/RFC9099, August 2021,
              <https://www.rfc-editor.org/info/rfc9099>.

Author's Address

   Charles C. Sun
   Alliance for Universal Computing
   Washington, DC
   United States of America
   Email: charles.sun@aucglobal.com

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