Global network and telecoms infrastructure

The internet routing layer visualised as ordered light

Elara-Cortex Technical Report · TR-2026-06 · 20 July 2026

Elara7G: a control-plane compression standard for inter-domain routing, measured on the CAIDA 2024 internet topology.

K. Lekola. Elara-Cortex Mathematical Infrastructure for Complex Systems · New Jersey and Johannesburg · route.elara-cortex.com

Abstract. The inter-domain routing layer of the internet still follows a discipline designed for a network of a few thousand participants: when a router learns of a change, it propagates a full picture to its neighbours. On the modern internet, with hundreds of thousands of networks and a routing table of billions of paths, that full-refresh discipline transmits the whole picture for tiny local changes. Elara7G is a control-plane compression standard we have designed that removes this repetition without altering routing semantics: on a change it ships only the minimal, losslessly recoverable difference, in the smallest representation that lets the receiver rebuild the exact picture, so the receiver's routing decisions are bit-for-bit identical to those it would have made without Elara7G. We evaluate on the real CAIDA January-2024 AS-relationships topology, 76,351 networks and 499,651 peerings, published with its SHA-256 for exact reproduction. A naive all-pairs reachability enumeration of that network (5,829,475,201 = 76,351² entries, 11.66 GB; a theoretical worst case, not what routers store) is represented in 2.14 MB (a ≈5,450× reduction, quoted as an illustrative upper bound) and any inter-network path is computed in single-digit milliseconds; at the prefix level, on a separate real BGP snapshot, the measured compression is ~24,000×, and the per-event representation measured 63 bytes. Elara7G sits above the radio layer and is independent of it: it operates over 4G, 5G, 6G, fibre, satellite and submarine transport rather than replacing any of them. The internal mathematics is proprietary; every reported figure is verifiable from the public CAIDA source and public BGP services without it. We state the standard's guarantees as formal theorems, report the measurements against their exact bases, and give the reproduction and independent- verification protocol.

1 · The problem: full-refresh at internet scale

Border Gateway Protocol (BGP), the system by which every network announces reachability to every other, was specified when the global internet held a few thousand networks (RFC 4271). At that scale, propagating a full view on each change was affordable. Today the global routing system spans hundreds of thousands of networks; for the CAIDA January-2024 topology the reachability table holds 5,829,475,201 entries. The full-refresh discipline persists: a small local change can still trigger the transmission of a large table. The redundancy between the pre-change and post-change views is where Elara7G operates.

Elara7G compresses the control plane, the routing-maintenance information exchanged between routers. It does not alter the data plane: the user payload itself, and per-hop propagation delay, are identical on both stacks. It does not change which route is chosen, what is encrypted, or how lawful-intercept obligations are met. It is mathematically equivalent to a smaller representation of the same information.

2 · The standard: minimal recoverable difference

Elara7G specifies that, on a routing change, a participant transmits the minimal difference between the prior and current view, encoded so that the receiver can reconstruct the current view exactly, and accompanied by a cryptographic digest that gates acceptance. Two properties are guaranteed by construction and stated formally in §5: exact reconstruction (the receiver's rebuilt view is byte-identical to the sender's) and decision equivalence (routing decisions computed on the rebuilt view are identical to those on the uncompressed view). The standard is a transport for the same information, layered above radio and independent of it (§6). On a change the standard transmits a minimal, losslessly recoverable difference, gated by a cryptographic digest; the compressor that produces that difference is proprietary and is not disclosed here (§9).

3 · Measurement on the real 2024 internet

All figures below are computed on the CAIDA UCSD AS-Relationships dataset for 1 January 2024, the widely used AS-topology reference in network-measurement research. The dataset and its fingerprint are published so any reader reproduces the exact input.

Table 1. Dataset provenance (independently verifiable).
Property	Value
Source	CAIDA UCSD, AS-Relationships, serial-1, 2024-01-01
Networks (autonomous systems)	76,351
Peerings (adjacencies)	499,651
SHA-256 of the source file	f58bf0e3fae1deeea4a6de940753d451b4e9927efabd633c910fadfd35e85da6
Inference method	Luckie, Huffaker, Dhamdhere, Giotsas & claffy, ACM IMC 2013

Figure 1. Illustrative upper bound: size of the naive all-pairs reachability enumeration of the CAIDA 2024 topology (11.66 GB) versus the Elara7G representation (2.14 MB), log scale (≈5,450× on this enumeration). At the prefix level a separate real-BGP measurement (Oregon-1) gives ≈24,000×. Data: Table 2.

Table 2. Measured representation and compression. Each figure states its exact basis.
Quantity	Result	Basis
Naive all-pairs reachability enumeration (N², ~2 B/entry; theoretical worst case, not a deployed table)	11.66 GB (76,351² = 5,829,475,201 entries)	CAIDA 2024 topology, enumerated
Elara7G representation of the same enumeration	2.14 MB (≈5,450×)	computed and routed in-browser
Any inter-network path	single-digit milliseconds	in-browser on a consumer laptop
Prefix-level compression on real BGP	~24,000×	Stanford Oregon-1 BGP snapshot
Per routing-event representation	63 bytes	measured, N = 5,000 event simulation (seed 42)
Per-event convergence (modelled, §4)	~50 ms	delta-only, vs full-reconvergence baseline

The all-pairs enumeration in Table 2 is quoted as an illustrative upper bound on the redundancy; a deployed routing table stores far less, so the operative real-world results are the prefix-level compression on real BGP (~24,000×) and the per-event control-plane comparison in Table 3. The compression arises entirely from removing the redundancy between successive full views; no routing information is discarded. The 2.14 MB representation and the ~24,000× prefix-level figure are on real published topology and real BGP respectively; the 63-byte per-event figure is from a controlled 5,000-network event simulation whose seed and script are published (§8).

4 · Control-plane effect, from public engineering constants

The operational consequence of a smaller per-event representation is modelled below from publicly-sourced constants (cited per row), not asserted. The model isolates the control plane; the data plane is identical on both stacks and is excluded from the difference.

Table 3. Per-event control-plane comparison. Constants are from public vendor and measurement sources.
Quantity	Today (BGP)	Elara7G	Source of the constant
Per-event representation	200 B (single UPDATE) up to a full-table refresh	63 B	RFC 4271 §4.3; RouteViews; measured
Per-event processing time	2 ms	0.1 ms	Cisco IOS XR convergence whitepaper; measured
Full reconvergence after a flap	~10 s	~50 ms	Cisco IOS XR; Juniper convergence studies

Data-plane bytes, per-hop propagation (RIPE Atlas 2024 ≈ 15 ms/hop) and longest-prefix-match latency (Cisco CRS-X / Juniper PTX datasheets ≈ 100 ns/hop) are identical on both stacks and are reported as such in the live demonstration; only the routing-maintenance layer differs.

5 · Formal guarantees

The two safety properties are stated below. For the inter-domain-routing encoding they are established by construction; the operative runtime guarantee is the SHA-256 acceptance gate (Theorem 1). The machine-checked proof and the large-scale counterexample search of §5.1 were run on the analogous route-geometry instance and are offered as corroboration of the shared principle, not as a machine check of the BGP encoding itself. The proprietary compressor is not required to state or check these properties: they concern the recovered view, which is observable.

Theorem 1 (Exact reconstruction). For any prior view V and current view V′, let Δ be the Elara7G difference from V to V′ and let R(V, Δ) be the receiver's reconstruction. Then R(V, Δ) = V′ exactly, and acceptance is gated by a SHA-256 digest d(V′): the receiver commits the reconstruction only if d(R(V, Δ)) = d(V′). Hence a corrupted or truncated Δ cannot be silently committed.

Corollary 2 (Decision equivalence, from Theorem 1). Let D(·) be the routing-decision function. Because R(V, Δ) = V′ (Theorem 1), D(R(V, Δ)) = D(V′) for every input: the routes chosen on the reconstructed view are identical to those chosen on the uncompressed view. Elara7G therefore changes the size of the control-plane representation and nothing about the routing outcome.

5.1 · Corroboration on the route-geometry instance

The same minimal-difference principle applied to vehicle route geometry (a second deployment of the same Elara7G principle) has been verified independently: an SMT proof of the length/reconstruction invariant (Z3, unsatisfiable on the negation) and a large-scale (100,000-case) counterexample search with zero byte-identical reconstruction failures and zero surviving counterexamples under a parametric sweep. These corroborate Theorem 1 and its Corollary on a fully public instance.

Table 4. Independent verification of the reconstruction guarantee (route-geometry instance).
Check	Scale	Result
Byte-identical reconstruction	100,000 cases	0 mismatches
Parametric counterexample search	100,000 / claim	closed (0 surviving counterexamples)
SMT proof of the length/reconstruction invariant	Z3, negation	UNSAT (proven)
Re-route work model (measured, ergodic Markov chain)	2-state	96.7% of events are O(K) skips; mean work 3.3% of always-recompute

6 · The central engine, and cross-domain generality

Elara7G is one application of a single core: the Elara-Cortex efficiency engine, whose mathematics seeks the lowest-entropy representation of a changing structure, the smallest description that still recovers the information exactly. In routing that low-entropy target is the minimal difference between successive views; in data compression it is the smallest lossless encoding; in each domain the objective is the same. The same core powers Elara-Cortex lossless data compression and the routing optimiser; Elara7G is that engine applied to the inter-domain routing layer. The engine's internal mathematics is proprietary (§9); the same minimal-difference representation yields measured gains in more than one domain (below), which indicates the technique is not specific to routing:

Table 5. The same minimal-difference principle, measured across independent domains.
Domain	What the principle yields	Report
Inter-domain routing (this report)	11.66 GB → 2.14 MB; ~24,000× on real BGP; decisions bit-identical	TR-2026-06
Lossless data compression	93% on a 162 MB production log; never larger than gzip or Brotli on any tested input; SHA-256 round-trip	TR-2026-02 §6
Vehicle route re-optimisation	incremental update at 36.8–244.6× less work for a byte-identical route	TR-2026-02 §3
Adversarial game-tree search	a won game against a strong reference engine at fixed depth (§7)	§7

7 · A note on cross-domain generality

As an out-of-domain check that the minimal-difference representation is not specific to routing, the same representational idea was used as the leaf evaluation of a chess search and evolved against a strong public reference engine. This is reported as a single out-of-domain data point, with its exact boundary stated below. In a recorded run the Elara evaluation won in 79 plies (a forced mate) at an average of 17,296 nodes per second and an average search depth of 3.58 plies.

Table 6. The compute asymmetry of the won game. Figures as recorded in the run receipt.
Quantity	Elara evaluation	Stockfish 18 (this match)
Evaluator	an Elara evaluation function	full NNUE, not weakened (Skill Level 20, UCI_LimitStrength false)
Search depth	3.58 plies avg (iterative deepening, 4 s budget)	2 plies (fixed)
Node throughput	~17,300 nodes/s	conventional engine throughput (orders of magnitude higher)
Outcome	win (forced mate, 79 plies)	loss

The result is reported with its exact boundary, from the run's own honest disclosure: Stockfish 18 was not skill-weakened; it ran its full neural evaluator at Skill Level 20, and was constrained only in search depth (2 plies), a configuration estimated at roughly 1900–2200 ELO (per the run's own disclosure). This is therefore a win against a strong-evaluator, shallow-search configuration of the reference engine, not a claim of superiority over deep, full-strength Stockfish. It is included as an out-of-domain check on the generality of the representation, not as a contribution to computer chess.

8 · Reproduction and independent verification

Every figure on this page can be re-derived from public data. No trust in Elara-Cortex is required to confirm the topology, the adjacencies or the routes.

The topology. Download the CAIDA source (publicdata.caida.org/datasets/as-relationships/serial-1/20240101.as-rel.txt.bz2) and confirm its SHA-256 against Table 1.
Any adjacency or route. Cross-check against the CAIDA source directly, or against public BGP services: bgp.tools, bgpview.io, RIPEstat and PeeringDB.
The compression ratio. Reproduce the per-event figure with the published simulation (5,000-network topology, fixed seed 42, 50 routing cycles); reproduce the prefix-level figure against the Stanford Oregon-1 BGP snapshot. Unlike the CAIDA figure (§3, SHA-256 published), the exact Oregon-1 snapshot date and file digest are not yet pinned on this page; this is named as a gap to close before the prefix-level figure carries the same reproduction guarantee as the CAIDA result.
An independent verdict. The live demonstration emits a self-contained, timestamped verification bundle (the literal CAIDA lines for every adjacency in every route, plus their combined SHA-256) that a third-party language model or auditor can check without downloading anything.

9 · Intellectual property and disclosure model

The Elara7G compressor and its underlying mathematics are the intellectual property of Elara-Cortex; patent applications are in progress. This report discloses what the standard guarantees and the measurements that support it, enough to verify every claim, and does not disclose how the compressor works. This is the deliberate posture of the series: verification without disclosure. The interface can be standardised and audited while the method remains protected; recovering the compressor's internals from the standard's outputs is not required for the interface to be audited. Source escrow is available to licensees requiring continuity assurance.

10 · Standardisation and deployment

Elara7G runs as a software component alongside an existing routing stack; it requires no new hardware, no new radio standard, and no change to the data plane. It can be deployed today within a bilateral peering or a single operator's backbone under its own wire format, with a standardised version slotting in later under the same format. Standards engagement with the IETF on a draft specification for the routing-layer carrier is in progress; such processes typically run 18–30 months, and customers need not wait for them.

11 · Economic implications (estimates, not measured results)

The cost Elara7G removes is control-plane, not data-plane: the router CPU spent processing routing updates, the memory held for routing state, and the churn-processing load during reconvergence. The data plane is unchanged (§1), so we deliberately do not attach a wire-bytes-times-price headline figure: control-plane traffic is a small fraction of a carrier's transit volume, and a transit-bytes estimate would misstate the driver. The saving instead scales with control-plane event rate and update volume, with faster convergence (§4) and with lower router CPU and memory pressure, and is computed per operator against its own peer count and event-rate logs. Any figure derived this way is an estimate calibrated to that operator's measured control-plane load, not a measured result of this report.

12 · Limitations

Elara7G compresses the control plane only; data-plane volume and per-hop propagation are unchanged, and this report claims no reduction in them.
The per-event and per-flow operational figures in §4 are modelled from public engineering constants (cited per row), not measured end-to-end on a production carrier network; the topology and prefix- level compression figures (§3) are measured on real public data.
The economic figures (§11) are estimates from public pricing, not measured savings.
The game-search result (§7) is a won game against a fixed-depth (2) configuration of the reference engine, not a claim against full-strength play.
Standardisation (§10) is in progress, not complete.

References

CAIDA (2024). The CAIDA UCSD AS-Relationships Dataset, 2024-01-01. https://www.caida.org/catalog/datasets/as-relationships/
Luckie, M., Huffaker, B., Dhamdhere, A., Giotsas, V., & claffy, k. (2013). AS relationships, customer cones, and validation. In Proc. ACM Internet Measurement Conference (IMC), 243–256.
Rekhter, Y., Li, T., & Hares, S. (2006). A Border Gateway Protocol 4 (BGP-4). RFC 4271, IETF.
Gao, L., & Rexford, J. (2001). Stable internet routing without global coordination. IEEE/ACM Transactions on Networking, 9(6), 681–692.
University of Oregon (2024). Route Views Project. http://www.routeviews.org

Data, receipts & series

Dataset: CAIDA UCSD AS-Relationships 2024-01-01 (publicdata.caida.org), SHA-256 f58bf0e3…35e85da6 · Method: Luckie, Huffaker, Dhamdhere, Giotsas & claffy, ACM IMC 2013 · BGP cross-checks: bgp.tools · bgpview.io · RIPEstat · PeeringDB · Baselines/constants: RFC 4271 · RouteViews · Cisco IOS XR & Juniper convergence studies · RIPE Atlas 2024 · TeleGeography 2024 · Corroborating proofs: Z3 length/reconstruction invariant · 100,000-case reconstruction battery · parametric counterexample search
Series: TR-2026-01 · TR-2026-02 · TR-2026-03 · TR-2026-04 · TR-2026-05 · EL-2026-01
© 2026 Elara-Cortex Mathematical Infrastructure for Complex Systems · New Jersey · Johannesburg · The Elara7G compressor and its underlying mathematics are proprietary (patents in progress); all data and materials needed to verify the reported figures are public; every measured result is measured, never simulated except where a simulation is named as such.