Sphere packing in dimension 8: Lean formalisation completed, final steps by Gauss
Status
Formally verified
Recorded on · github.com
What this status means
Source reading : Source read word for word (level 3 of 3)
A named third party has checked a machine proof. Lean supplied by the claimant alone is not enough.
The gist
In 2026-02, the Lean project team (Hariharan, Viazovska and others) and Math, Inc. (Gauss) completed the formal Lean verification of sphere packing in dimension 8. Status: formally verified; the proof was already known.
Cite this entry
The status has changed 2 times since Oct 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-gauss-sphere-packing-dim8-r1
@misc{discoveria-gauss-sphere-packing-dim8-r1,
author = {{DiscoverIA}},
title = {Sphere packing in dimension 8: Lean formalisation completed, final steps by Gauss},
howpublished = {DiscoverIA registry, entry gauss-sphere-packing-dim8},
note = {Status « Formally verified », snapshot 1, recorded on October 11, 2026. formalisation of a known result},
year = {2026},
url = {https://discoveria.ai/en/fiche/gauss-sphere-packing-dim8/#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
Cite snapshot 2, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-gauss-sphere-packing-dim8-r2
@misc{discoveria-gauss-sphere-packing-dim8-r2,
author = {{DiscoverIA}},
title = {Sphere packing in dimension 8: Lean formalisation completed, final steps by Gauss},
howpublished = {DiscoverIA registry, entry gauss-sphere-packing-dim8},
note = {Status « Not evaluated », snapshot 2, recorded on October 12, 2026. formalisation of a known result},
year = {2026},
url = {https://discoveria.ai/en/fiche/gauss-sphere-packing-dim8/#releve-2},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
Cite snapshot 3, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-gauss-sphere-packing-dim8-r3
@misc{discoveria-gauss-sphere-packing-dim8-r3,
author = {{DiscoverIA}},
title = {Sphere packing in dimension 8: Lean formalisation completed, final steps by Gauss},
howpublished = {DiscoverIA registry, entry gauss-sphere-packing-dim8},
note = {Status « Formally verified », snapshot 3, recorded on October 12, 2026. formalisation of a known result},
year = {2026},
url = {https://discoveria.ai/en/fiche/gauss-sphere-packing-dim8/#releve-3},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
Text written by an AI (DiscoverIA pipeline), on Reviewed by: nobody yetReport an error
What has not been reviewed?
The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Key facts
- Claimed by
- équipe du projet Lean (Hariharan, Viazovska et al.) ; Math, Inc. (Gauss)
announced on Feb 2026 - Nature
- formalisation of a known result
- Field
- Mathematics (geometry / formalisation)
- Checked by
- the project's human authors; re-run by a third party (public CI, run 38101133826, 2026-10-11)
- Sources (domains)
- 2 : 1 read word for word, 1 links only
- This entry
- AI draft, not reviewed
To understand
Analogy
It is like checking the plan of an already-built building against software that recomputes every measurement: the building existed, and the check confirms that no measurement is wrong.
What it changes
Sphere packing means arranging identical spheres as tightly as possible. This formalisation discovers nothing: it is a machine check of an existing proof (Viazovska 2016). An external replay of the Lean proof succeeded on 11 October 2026 on a public CI, a service that reruns the computation automatically.
What remains unclear
Only one external replay exists: by a contributor, an individual replayer whose pull request was merged by the same person, and who was assisted by an AI. The fidelity of the formalised statement has not been judged. The project's human team are co-claimants, not third parties.
2 sources.
For experts
Sources(domains)
- primairearxiv.orglink only, reading not recorded
- source-statutgithub.compage read word for word · consulted on Oct 12, 2026
Method
Status “formally verified” recorded on 12 October 2026 from github.com (page read, quotation checked word for word). History: 3 dated observations, oldest first. Checked by a named third party: a contributor (compte GitHub), CI publique du dépôt a contributor/D4-D24-Hales--D3--Viazovska. Fidelity of the formal statement: non-jugee, assessed on 12 October 2026.
Limits
Nature: formalisation, that is a machine check of an already known result, not a discovery. Whether the formal statement matches the intended statement has not yet been assessed.
It is like checking the plan of an already-built building against software that recomputes every measurement: the building existed, and the check confirms that no measurement is wrong.
Does the Lean statement say what is announced?
Not judgedrecorded on Proposed scale, to be validated
Not judged yet: the formal statement has not been compared with what is announced.
Status history
The numbers link the band (order of observations) and the thread (most recent first). Band segments have equal widths, not a time scale.
- 03
Not evaluatedbecomesFormally verifiedCurrent status
back to formally verified: the proof is a public CI run by a third party (deterministic Lean kernel, leanchecker 828/828 modules; byte-for-byte copy of…
Read the full reason
back to formally verified: the proof is a public CI run by a third party (deterministic Lean kernel, leanchecker 828/828 modules; byte-for-byte copy of math-inc/Sphere-Packing-Lean@1e98fb4), that is one external re-run; faithfulness of the statement not judged; caveats: a single re-runner (PR merged by its author), AI-assisted re-run
Source: github.comread word for word
- 02
Formally verifiedbecomesNot evaluated
reclassified from formally verified to not evaluated under the independence rule: the only named checker is a co-claimant of the formalisation, so not a third party; no third…
Read the full reason
reclassified from formally verified to not evaluated under the independence rule: the only named checker is a co-claimant of the formalisation, so not a third party; no third party named in the sources read; reclassification based on a single reading, to be confirmed
Source: arxiv.orgread through an AI summary
- 01
First observation:Formally verified
existing proof (Viazovska 2016); a formalisation, not a new result
Source: arxiv.orgread through an AI summary
An observation is added; none is ever erased.
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