Pith Number

pith:E4H4P5WT

pith:2026:E4H4P5WTDDDG3IV6QJSHMJTHHW

not attested not anchored not stored refs pending

Conjecture I for unirational algebraic groups over imperfect fields

Alexandre Lourdeaux, Anis Zidani

Unirational algebraic groups have trivial first Galois cohomology over fields of Kato cohomological dimension at most 1.

arxiv:2604.05148 v2 · 2026-04-06 · math.AG

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\usepackage{pith}
\pithnumber{E4H4P5WTDDDG3IV6QJSHMJTHHW}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we prove that the first Galois cohomology set of any unirational algebraic group is always trivial if the cohomological dimension of the field is less or equal to 1 in Kato's sense.

C2weakest assumption

The recent advancements in the structure of algebraic groups over imperfect fields are sufficient to establish the triviality result for unirational groups under the stated cohomological dimension condition.

C3one line summary

Unirational algebraic groups over fields with Kato cohomological dimension ≤1 have trivial first Galois cohomology.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-09T01:05:16.870308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

270fc7f6d318c66da2be82647626673db05c7c1aa6ee4eb6ccfe18d5494deb7f

Aliases

arxiv: 2604.05148 · arxiv_version: 2604.05148v2 · doi: 10.48550/arxiv.2604.05148 · pith_short_12: E4H4P5WTDDDG · pith_short_16: E4H4P5WTDDDG3IV6 · pith_short_8: E4H4P5WT

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E4H4P5WTDDDG3IV6QJSHMJTHHW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 270fc7f6d318c66da2be82647626673db05c7c1aa6ee4eb6ccfe18d5494deb7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b03b72e5bd81df5050d8079f97480effdec31857b3bd239f38dcadaf0cbee31a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-06T20:22:01Z",
    "title_canon_sha256": "bdb33d4c0f18453faf2aa5e8824bb0e907ef9b34636ee7882050385a14f7aca1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.05148",
    "kind": "arxiv",
    "version": 2
  }
}