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What is Astrée?

Astrée is a static program analyzer for C software, developed to prove the absence of run-time errors (RTEs) before a program is ever executed. It was created at the École Normale Supérieure and is associated with CNRS and INRIA; its name is short for Analyseur statique de logiciels temps-réel embarqués (static analyzer for real-time embedded software). Rather than testing inputs and observing failures, it examines the source code and attempts to establish, for all possible executions, that operations such as arithmetic overflow, division by zero, out-of-bounds array access and invalid pointer use cannot occur.

Its design targets a specific class of software: structured C programs with complex memory usage, but without dynamic memory allocation or recursion. That restriction is deliberate. It matches many synchronous, time-triggered control programs found in aerospace, aeronautics, nuclear energy, medical instrumentation and earth transportation — the kind of embedded code where a run-time fault can be far more serious than a desktop crash.

What it is used for

Astrée is aimed at safety-critical embedded software, especially automatically generated or carefully structured control code. The best-known result is from November 2003, when it automatically proved the absence of run-time errors in the primary flight-control software of the Airbus A340 fly-by-wire system — 132,000 lines of C analyzed in about 1 hour 20 minutes on a 2.8 GHz 32-bit PC using 300 MB of memory. From January 2004 it was extended to electric flight-control code under development and test for the A380 series.

That example shows the practical value: a proof of RTE-freedom can support certification and review of software that is difficult or impossible to exhaustively test.

Who should consider it

  • Embedded software engineers who need evidence about all executions, not just sampled test cases.
  • Safety and certification teams working on control software where run-time faults are unacceptable.
  • Researchers interested in abstract interpretation, the theoretical foundation behind the analyzer.

Trade-offs to weigh

The precision that makes Astrée useful comes with constraints. Programs using dynamic memory allocation or recursion fall outside its intended scope. Analysis can also require substantial memory and time on large codebases, though the A340 result shows it can remain practical at industrial scale. Finally, Astrée is a specialized tool: it proves run-time properties of C programs, not general functional correctness, and it should be understood alongside testing and review rather than as a replacement for them.

A useful next step is to check whether your codebase matches the supported profile — structured C, no dynamic allocation, no recursion — and to look at the project's own material on which run-time properties it proves and how it is licensed for industrial use.

How does Astrée prove the absence of run-time errors in C programs?

Astrée proves the absence of run-time errors (RTEs) by performing abstract interpretation–based static analysis of C source code: it computes an over-approximation of all possible executions and checks whether any execution can reach an error state. If the analysis proves that no execution reaches such states, the absence of those RTEs is established without running the program.

What it proves

Astrée targets run-time errors in structured C programs, including those with complex memory usage. The site lists the class of programs it handles as excluding dynamic memory allocation and recursion, which covers many synchronous, time-triggered embedded control programs. Typical properties include invalid arithmetic (such as division by zero), out-of-bounds array accesses, and other undefined or erroneous operations that would cause a run-time failure.

How the analysis works

The analyzer uses abstract interpretation: instead of enumerating concrete program states, it propagates abstract descriptions of sets of states through the control-flow graph. Each abstract domain captures a different property (for example, intervals, relational constraints, or memory-shape information), and the results are combined to refine the approximation. The analysis iterates to a fixed point, so loops and recursive control flow are handled by widening and narrowing rather than by unrolling. Because the abstraction is sound, any reported absence of an error holds for every possible input and execution path—not just for tested inputs.

Why it is sound and precise enough

Soundness comes from the abstract semantics being a superset of the concrete semantics: if the abstract analysis finds no error state, none exists concretely. Precision comes from the choice and combination of abstract domains, which the project tailored to the numerical and memory patterns of embedded control software. This is what allowed Astrée to prove the absence of RTEs in the primary flight control software of the Airbus A340 fly-by-wire system—132,000 lines of C analyzed in about 1 hour 20 minutes on a 2.8 GHz 32-bit PC with 300 MB of memory, and in about 50 minutes on a 64-bit AMD Athlon 64 with 580 MB. The site also notes the analysis was extended from January 2004 to electric flight control code under development and test for the A380 series.

Practical implications

  • No test vectors required: the proof covers all inputs and paths, which matters for safety-critical embedded software where exhaustive testing is impossible.
  • Assumptions matter: the guarantee depends on the analyzed program matching Astrée's supported subset (structured C, no dynamic allocation, no recursion) and on the environment model supplied to the analyzer.
  • False alarms are possible: soundness does not guarantee that every warning is a real error; imprecision in the abstraction can produce alarms that require manual inspection or domain tuning.

A useful next step is to check whether your code fits the supported subset and to read the site's section on which run-time properties are proved, so you can map your own safety requirements to the analyzer's guarantees. For background on the research group and related tools, see École Normale Supérieure and INRIA.

Can Astrée analyze my embedded C code if it uses dynamic memory allocation or recursion?

No. Astrée is designed for structured C programs that do not use dynamic memory allocation or recursion. The analyzer's stated scope is embedded, synchronous control/command software, so code built around malloc/free or recursive functions falls outside the class of programs it is meant to prove free of run-time errors.

What it does cover

  • Structured C with complex memory usage, such as arrays, pointers and aliasing, as long as the memory layout is statically bounded.
  • Safety-critical, time-triggered, real-time embedded code, including automatically generated C.
  • Proof of the absence of run-time errors (RTE), for example out-of-bounds accesses, division by zero, invalid pointer dereferences and arithmetic overflow.

Why the restriction matters

Astrée works by abstract interpretation: it computes an over-approximation of every reachable program state and checks that no error state is included. Dynamic allocation and recursion can create unbounded or input-dependent state spaces, which breaks the finiteness assumptions that make such a proof tractable. Rather than silently reporting false alarms or unsound results, the tool defines them out of its input language.

If your code uses them

You have three practical routes:

Situation Practical option
Recursion can be rewritten iteratively with an explicit stack Refactor, then analyze with Astrée
Allocation is confined to a fixed pool with known bounds Replace with static or bounded buffers, then analyze
The program genuinely needs unbounded allocation or recursion Use a different analyzer or a bounded model checker; Astrée is not the right fit

A useful first step is to run a simple check for malloc, calloc, realloc, free and self-calling functions in your translation units. If those appear only in initialization or non-flight code, you may be able to isolate the safety-critical core into a separate, allocation-free compilation unit and analyze just that part. The Astrée project publishes its objectives and proved properties at The Astrée Static Analyzer, which is the most reliable place to confirm the exact input restrictions before committing to a toolchain.

What results has Astrée achieved on Airbus flight control software?

Astrée's headline result is a fully automatic proof of the absence of run-time errors in the primary flight control software of the Airbus A340 fly-by-wire system, achieved in November 2003. According to the project's own account, the program comprised 132,000 lines of C and was analyzed in 1 hour 20 minutes on a 2.8 GHz 32-bit PC using 300 MB of memory, or in about 50 minutes on a 64-bit AMD Athlon 64 using 580 MB. The analysis was complete without manual intervention, which is the unusual part: the point was that the tool, not a human proof engineer, discharged the verification.

The work did not stop at the A340. From January 2004 onward, Astrée was extended to analyze the electric flight control code then under development and test for the A380 series. The A340 result is therefore best read as the demonstration that made the later industrial use credible, rather than as an isolated benchmark.

What was actually proved

The property in question is the absence of run-time errors — the class of faults that on a desktop machine produce a crash message but in embedded control software can have graver consequences. Astrée targets structured C programs with complex memory usage but without dynamic memory allocation or recursion, which covers a large share of synchronous, time-triggered control code in aerospace, rail, nuclear, and medical instrumentation.

How to read these numbers

Two cautions are worth keeping in mind when citing this result. First, the figures describe one specific program and one specific tool configuration, so they are evidence of feasibility on that class of code, not a general performance guarantee for other software. Second, the analysis is sound for the stated semantics of the analyzed program; it proves the absence of certain errors, not the presence of correct functional behavior.

If you are weighing a similar verification effort, the practical decision criterion is whether your code fits the analyzable subset — no dynamic allocation, no recursion, structured control flow. Code that violates those assumptions needs rewriting or a different technique before an analyzer of this kind can say anything definitive. For background on the underlying abstract-interpretation methods, the project page at The Astrée Static Analyzer is the primary reference.

Which industries use Astrée for safety-critical embedded software verification?

Astrée is used mainly in industries where embedded C software must be proven free of run-time errors before deployment: earth transportation, nuclear energy, medical instrumentation, aeronautics, and aerospace. The site highlights synchronous control/command software in particular, such as electric flight control and spacecraft manoeuvre systems.

Where it has been applied

  • Aeronautics: The primary flight control software of the Airbus A340 fly-by-wire system was analysed automatically, and Astrée was later extended to electric flight control code under development and test for the A380.
  • Aerospace: Space vessel manoeuvre software is cited as a target application.
  • Nuclear energy, medical instrumentation, and earth transportation: These are listed among the embedded domains the analyzer is designed to cover.

What makes a program a fit

Astrée targets structured C programs with complex memory usage but without dynamic memory allocation or recursion — a profile common in time-triggered, safety-critical embedded control software, including automatically generated code.

If you are assessing whether Astrée suits a project, check three things first: the code is C, it avoids dynamic allocation and recursion, and the property you need to prove is absence of run-time errors. For background on the analyzer's design and proof techniques, see The Astrée Static Analyzer.

How can I obtain an exploitation license for Astrée?

Astrée is not distributed as a self-serve download; the project page describes an "Exploitation license of Astrée" as a separate topic, indicating that commercial or operational use is handled through a licensing arrangement rather than a public package. The practical route is to contact the Astrée team directly using the contact address published on The Astrée Static Analyzer and explain your intended use.

What to prepare before you make contact

A licensing discussion moves faster if you can describe your situation concretely:

  • The program under analysis — Astrée targets structured C programs, including complex memory usage, but not dynamic memory allocation or recursion. Confirm your code fits that profile.
  • Your goal — proving absence of run-time errors in safety-critical embedded software is the analyzer's stated objective, so say whether you need a one-off verification or an ongoing part of a development process.
  • Deployment context — whether the analysis runs on your own machines or in a service arrangement, and who will operate it.
  • Organizational status — academic, industrial, or public-sector use can affect the terms offered.

How to judge the options you are given

If you are comparing Astrée against other static analyzers, the decision usually turns on the property you need proved, the language subset your code uses, and whether the tool must run unattended on large codebases. Astrée's documented strength is fully automatic proof of run-time error freedom on synchronous, time-triggered embedded C, so weigh any alternative against whether it can deliver that same guarantee without manual annotation effort. Ask for a trial analysis on a representative slice of your own code; that is more informative than a feature list.

Related questions

More questions →
How to Get an Exploitation License for Astrée

Astrée is not distributed as a free download. The official site lists a dedicated "Exploitation license of Astrée" section, which means commercial or operational use is handled through a licensing arrangement rather than a public package. To pursue a license, the practical starting point is the project contact page at https://www.astree.ens.fr/, since the tool is developed and maintained under CNRS, École Normale Supérieure (ENS), and INRIA. The site does not publish pricing, license tiers, or a self-service request form, so any specific terms must come from the team directly.

What the license covers

Astrée is a static analyzer that proves the absence of run-time errors (RTE) in C programs. Its intended use is on structured C code with complex memory usage but without dynamic memory allocation or recursion — the profile of synchronous, time-triggered, real-time, safety-critical embedded software. A license is therefore relevant if you need to apply the analyzer to production or industrial code, not just to read about the method.

The project's own history shows the scale of use a license is meant to support:

  • In November 2003, Astrée automatically proved the absence of any RTE in the primary flight control software of the Airbus A340 fly-by-wire system — 132,000 lines of C analyzed in 1 h 20 on a 2.8 GHz 32-bit PC with 300 Mb of memory.
  • From January 2004, it was extended to analyze the electric flight control code under development and test for the A380 series.

These results are cited on the site as unprecedented for static analysis of this class of software, which is the context in which an exploitation license would be sought.

Who to contact

The site names the following institutions behind the tool:

Role Entity
Research center Centre National de la Recherche Scientifique (CNRS)
Host institution École Normale Supérieure (ENS)
Since Sep. 2007 INRIA (Paris—Rocquencourt)

Project leadership listed on the page: Patrick Cousot (project leader), Radhia Cousot, Jérôme Feret, Antoine Miné, Xavier Rival. Former participants include Bruno Blanchet, David Monniaux, and Laurent Mauborgne.

The contact link given is https://www.astree.ens.fr/. Because the page provides no direct licensing email or form, use that entry point to reach the team and ask about exploitation terms.

What to prepare before you ask

Since the site does not state license conditions, be ready to describe your use case so the team can route your request. Useful details to include:

  • The type of program you want to analyze (for example, synchronous control/command software in transportation, nuclear energy, medical instrumentation, aeronautics, or aerospace).
  • Whether the code is written or automatically generated in C.
  • Whether it avoids dynamic memory allocation and recursion, since Astrée targets structured C programs with those constraints.
  • Your deployment context (industrial, research, or evaluation).

Practical notes

  • There is no indication on the page that Astrée is free or open to unlicensed use; the existence of a separate exploitation-license section points the other way.
  • No pricing signals, payment platforms, or license links appear in the available page material, so cost and terms cannot be inferred — they must be confirmed with the team.
  • The contact URL is the only concrete channel the page supplies. Start there rather than looking for a download or checkout page.
What Is the Theoretical Background of Astrée?

Astrée's theoretical foundation is abstract interpretation, the program-analysis framework introduced by Patrick Cousot and Radhia Cousot. Astrée applies this framework to automatically prove run-time properties of C programs — most notably the absence of run-time errors (RTE) — without executing them. The approach is sound by construction: it computes an over-approximation of all possible program behaviors, so a proof covers every execution path rather than a sample of them.

Abstract interpretation in one paragraph

Abstract interpretation replaces the concrete semantics of a program (all possible states, all possible traces) with an abstract semantics defined over a simpler domain. Each concrete operation has a corresponding abstract operation, and the analysis iterates to a fixed point. If the abstract result says "no error state is reachable," that conclusion holds for the concrete program too, because the abstraction is a superset of the real behaviors. The price of soundness is imprecision: an over-approximation can report a possible error that never actually occurs (a false alarm), which is why the choice of abstract domain matters so much in practice.

Why Astrée needed more than one domain

A single abstract domain cannot track every property precisely. Astrée is built as a reduced product of several abstract domains, each specialized for a class of properties, and it selects and combines them per program point. This design is what let it scale to large embedded control code while keeping false alarms low enough to be usable.

Properties Astrée is designed to prove

  • Absence of invalid arithmetic operations (for example, division by zero, overflow on integers and floating-point values)
  • Absence of invalid memory accesses (out-of-bounds array indexing, invalid pointer dereferences)
  • Absence of invalid control flow and other run-time errors in the analyzed C program

The analyzer targets structured C programs with complex memory usage but without dynamic memory allocation and without recursion — a restriction that matches many embedded and synchronous control/command programs.

From theory to industrial proof

The theoretical work was validated on real safety-critical software. In November 2003, Astrée proved completely automatically the absence of any RTE in the primary flight control software of the Airbus A340 fly-by-wire system — 132,000 lines of C analyzed in 1 h 20 on a 2.8 GHz 32-bit PC using 300 MB of memory (and 50 minutes on a 64-bit AMD Athlon 64 using 580 MB). From January 2004, it was extended to analyze the electric flight control code then in development and test for the A380 series. These results are the practical argument for the theory: soundness plus sufficient precision, at a cost that fits an industrial workflow.

How to evaluate the approach for your own use

Question What to check
Does your code fit the model? Structured C, no dynamic allocation, no recursion
Do you need a sound proof or just bug finding? Abstract interpretation gives soundness; bug-finding tools generally do not
Can you tolerate false alarms? Precision depends on the abstract domains; expect some manual review
Is the tooling available to you? Astrée is developed at ENS/CNRS/INRIA; licensing terms are separate from the theory

If your goal is to understand why Astrée's results can be trusted, the answer is the soundness of abstract interpretation combined with domain precision tuned for embedded control code. If your goal is to apply it, the practical constraints above — the C subset it accepts and the licensing path — matter as much as the theory.

Which Program Run-Time Properties Can Astrée Prove?

Astrée is a static program analyzer that aims to prove the absence of Run Time Errors (RTE) in programs written in the C programming language. It targets structured C programs with complex memory usage, but it does not handle dynamic memory allocation or recursion. This makes it applicable to many embedded programs—particularly synchronous control/command software such as electric flight control or space vessel maneuvers—where run-time errors can have graver consequences than on personal computers.

What Astrée proves

The core property Astrée establishes is the absence of run-time errors (RTE). On a personal computer, such errors typically produce error messages and terminate the application, and sometimes crash the system. In embedded applications, the consequences can be more serious, which is why a proof of their absence matters.

What kinds of programs it accepts

Astrée analyzes structured C programs with complex memory usages. The documented boundary conditions are:

  • Supported: structured C programs, including complex memory usage
  • Not supported: dynamic memory allocation
  • Not supported: recursion

This scope covers many embedded programs found in earth transportation, nuclear energy, medical instrumentation, aeronautic, and aerospace applications—in particular synchronous control/command software.

Evidence from industrial use

The project's documented results show the scale of programs Astrée has handled:

  • In November 2003, Astrée completely automatically proved the absence of any RTE in the primary flight control software of the Airbus A340 fly-by-wire system—a program of 132,000 lines of C, analyzed in 1 h 20 on a 2.8 GHz 32-bit PC using 300 Mb of memory (and 50 minutes on a 64-bit AMD Athlon 64 using 580 Mb of memory).
  • From January 2004 on, Astrée was extended to analyze the electric flight control codes then in development and test for the A380 series.

How to decide whether it fits your code

Use these conditions as a checklist:

Question If yes If no
Is your code written in C? Within scope Outside Astrée's stated target
Is it a structured program? Within scope Outside scope
Does it use dynamic memory allocation? Outside scope Within scope
Does it use recursion? Outside scope Within scope
Is it synchronous control/command embedded software? Typical target domain Evaluate against the scope above

If your program relies on dynamic memory allocation or recursion, Astrée's documented scope does not cover it. If your goal is to prove the absence of run-time errors in a structured, embedded C program, that is exactly the property Astrée is designed to establish.

What industrial applications has Astrée been used for?

Astrée's best-documented industrial use is in avionics: in November 2003 it automatically proved the absence of run-time errors (RTEs) in the primary flight control software of the Airbus A340 fly-by-wire system, and from January 2004 it was extended to the electric flight control code then in development and test for the A380 series. These results apply to synchronous, time-triggered, real-time, safety-critical embedded software written or automatically generated in C — the class of programs Astrée was built to handle.

The A340 result in detail

The A340 analysis is the reference point for what Astrée can do at industrial scale:

  • Program size: 132,000 lines of C.
  • Result: complete automatic proof of the absence of any RTE — no manual intervention or annotation of the proof was required.
  • Cost: about 1 h 20 on a 2.8 GHz 32-bit PC using 300 MB of memory, or about 50 minutes on a 64-bit AMD Athlon 64 using 580 MB.

Two things are worth separating here. The first is the soundness claim: Astrée proves the absence of RTEs, it does not merely test for them. The second is the automation claim: the analysis ran without a human guiding it, which is what makes the result meaningful for a program of that size.

From A340 to A380

From January 2004, Astrée was extended to analyze the electric flight control codes then in development and test for the A380 series. The extension matters because the A380 work pushed the analyzer beyond the single proven case: it had to handle code that was still changing, not just a frozen flight-control program.

Which domains this covers

Astrée targets structured C programs with complex memory usage but without dynamic memory allocation and recursion. That restriction is not incidental — it is what makes the analysis tractable, and it happens to match a large share of embedded code. The domains the project lists are:

  • Earth transportation
  • Nuclear energy
  • Medical instrumentation
  • Aeronautics and aerospace
  • In particular, synchronous control/command software such as electric flight control and space vessel maneuvers

If your program allocates memory dynamically or uses recursion, it falls outside the analyzed class, regardless of domain.

What to check before assuming Astrée fits your case

Condition Why it matters
Language is C Astrée analyzes C programs
No dynamic memory allocation Explicitly outside the analyzed class
No recursion Explicitly outside the analyzed class
Structured control flow The analyzer targets structured programs
Synchronous / time-triggered / real-time The industrial results are all in this category

Practical takeaway

If you are working on safety-critical embedded C in avionics, space, nuclear, medical, or ground transport, and your code avoids dynamic allocation and recursion, Astrée's track record — a 132,000-line flight control program proven RTE-free in roughly an hour — is direct evidence that the approach scales to real production code. If your code depends on dynamic allocation or recursion, the documented results do not transfer, and you should treat the tool as out of scope rather than as an untested option.

For licensing and the theoretical background behind these results, see the corresponding sections of the Astrée site.

What is the Astrée Static Analyzer?

Astrée is a static program analyzer designed to prove the absence of run-time errors (RTE) in programs written in the C programming language. It is developed by the Centre National de la Recherche Scientifique (CNRS), the École Normale Supérieure (ENS), and INRIA (since September 2007), with Patrick Cousot as project leader. The name stands for Analyseur statique de logiciels temps-réel embarqués (real-time embedded software static analyzer). It is most relevant if you work with synchronous, time-triggered, safety-critical embedded software written or automatically generated in C.

What Astrée does

Astrée analyzes structured C programs that may have complex memory usage, but it targets programs without dynamic memory allocation and recursion. Its core objective is to prove that no run-time errors can occur — not merely to find some bugs, but to establish the absence of RTE across the analyzed program.

This focus makes it suited to embedded domains such as:

  • Earth transportation
  • Nuclear energy
  • Medical instrumentation
  • Aeronautic and aerospace applications
  • Synchronous control/command systems, including electric flight control and space vessel maneuvers

Proven industrial results

Astrée's main applications appeared two years after the project started. Since then it has produced notable results on static analysis of synchronous, time-triggered, real-time, safety-critical embedded software:

Milestone Detail
Nov. 2003 Proved completely automatically the absence of any RTE in the primary flight control software of the Airbus A340 fly-by-wire system
Program size 132,000 lines of C
Analysis time 1 h 20 on a 2.8 GHz 32-bit PC using 300 Mb of memory; 50 min on a 64-bit AMD Athlon 64 using 580 Mb
From Jan. 2004 Extended to analyze the electric flight control codes then in development and test for the A380 series

Development and background

The development of Astrée started from scratch in November 2001 at the Laboratoire d'Informatique of the École Normale Supérieure (LIENS). It was initially supported by the ASTRÉE project, CNRS, and ENS, and since September 2007 by INRIA (Paris—Rocquencourt).

Participants listed include Patrick Cousot (project leader), Radhia Cousot, Jérôme Feret, Antoine Miné, and Xavier Rival. Former participants include Bruno Blanchet (Nov. 2001 — Nov. 2003), David Monniaux (Nov. 2001 — Aug. 2007), and Laurent Mauborgne (Nov. 2001 — Aug. 2010).

When Astrée is a fit

Astrée is aimed at proving run-time properties of C programs under specific constraints. It is a strong match when your code is:

  • Written in C
  • Structured, with no dynamic memory allocation and no recursion
  • Embedded, real-time, and safety-critical
  • Synchronous or time-triggered in nature

If your program relies on dynamic memory allocation or recursion, Astrée's documented scope does not cover it. For licensing and exploitation details, the site provides a dedicated "Exploitation license of Astrée" section, and further technical depth is available under "Theoretical Background of Astrée" and "Which Program Run-Time Properties are Proved by Astrée?".

Website Overview

An established domain and managed infrastructure suggest continuity of operations and may support dependable delivery, although neither guarantees service quality. Several search or sharing settings need attention. Together they may make snippets, preview images or preferred URLs less consistent across platforms.

Domain and Registration

Registered in 1994, this domain has about 31 years of history. That suggests continuity, although ownership and purpose may have changed. Registration contact information is publicly available through RDAP. The domain uses the common .fr extension, which is not an independent safety signal.

DNS and Email

Nameservers are provided by lri.fr, indicating managed DNS hosting. MX records point to the renater.fr email service. SPF and DMARC are configured. DKIM status is unknown. TXT records include verification markers for Google, Apple, Microsoft. Such markers may also remain after a service stops being used. The lowest observed DNS TTL is 300 seconds.

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The certificate includes the organization field École Normale Supérieure. The public key uses EC with 256 bits. The server supplied a complete certificate chain. The certificate is valid for about 365 days in total, with 19 days remaining. The certificate SAN covers 29 names.

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The checked browser-security headers were not detected, leaving fewer explicit browser-side safeguards. No X-Powered-By header was found, reducing one common source of backend fingerprinting information. No obvious internal addresses or debug information were found in the headers. The Server header identifies Apache without an exact version. No explicit CDN or WAF marker was found in the response headers.

Technology Stack Analysis

The public page identifies Apache without precise versions, leaving fewer clues for version-specific scanning.

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No homepage meta description was detected, leaving snippet selection more dependent on page text. No viewport meta tag was detected, which may affect mobile layout behavior. No homepage canonical URL was detected. If duplicate URLs exist, consolidation may be less explicit. No Open Graph metadata was detected, so social previews may depend on platform inference. The title has 26 characters, within a common display range.

Hosting and Email

DNSlri.fr
Hostingens.fr
Emailrenater.fr
Approximate IP geolocation (inferred; a CDN or proxy may differ from the origin server) France flagParis, Paris Department, France Inferred 129.199.99.14

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RegistrarGIP RENATER
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Certificate subjectwww.di.ens.fr
IssuerHellenic Academic and Research Institutions CA
Valid until2026-11-03T13:14 · Remaining when checked: 19 days
Verification detailsCertificate trust: Passed · Hostname match: Passed

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