Pith Number

pith:7CK4ZO3G

pith:2026:7CK4ZO3GRILQT2HNKZC6D7TJLI

not attested not anchored not stored refs pending

Explicit Brauer-Manin obstructions on plane quartics

Brendan Creutz, Nils Bruin

A method makes Brauer-Manin obstructions explicit on plane quartics without computing full S-unit groups of étale algebras.

arxiv:2601.16975 v2 · 2026-01-23 · math.NT

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\usepackage{pith}
\pithnumber{7CK4ZO3GRILQT2HNKZC6D7TJLI}

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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

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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

Our approach significantly improves on the applicability over previous 2-cover descent methods by not requiring the computation of the full S-unit group of the étale algebras involved.

C2weakest assumption

The Brauer-Manin obstruction is assumed to be the dominant or only obstruction that needs to be made explicit, and the adaptation to divisors of degree 1 or 2 is presumed to work without introducing new computational bottlenecks or unaccounted local obstructions.

C3one line summary

A computational method uses explicit Brauer-Manin obstructions to obstruct rational points on plane quartics without requiring full S-unit group calculations.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:16.597088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f895ccbb668a1709e8ed5645e1fe695a0956b5033cc658a2e139c4cd1d4d661e

Aliases

arxiv: 2601.16975 · arxiv_version: 2601.16975v2 · doi: 10.48550/arxiv.2601.16975 · pith_short_12: 7CK4ZO3GRILQ · pith_short_16: 7CK4ZO3GRILQT2HN · pith_short_8: 7CK4ZO3G

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/7CK4ZO3GRILQT2HNKZC6D7TJLI \
  | 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: f895ccbb668a1709e8ed5645e1fe695a0956b5033cc658a2e139c4cd1d4d661e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e5d136767db5fd63f11247357e1c72832925c461eaed93fbdd0c97495adf5a5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-01-23T18:53:19Z",
    "title_canon_sha256": "08c57f6c63df42473d4fa7819c2bab012418e9d08a3fe73d82c133b970516b7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.16975",
    "kind": "arxiv",
    "version": 2
  }
}