Pith Number

pith:TFYNSEUU

pith:2018:TFYNSEUUDCQTBR2EZBDIDYNJVJ

not attested not anchored not stored refs pending

Brauer-Manin obstruction for Markoff surfaces

Dasheng Wei, Fei Xu, J.-L. Colliot-Th\'el\`ene

arxiv:1808.01584 v4 · 2018-08-05 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TFYNSEUUDCQTBR2EZBDIDYNJVJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-17T23:41:01.197676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9970d9129418a130c744c84681e1a9aa4bd991a38b2a0a9c91ba3c12678e2053

Aliases

arxiv: 1808.01584 · arxiv_version: 1808.01584v4 · doi: 10.48550/arxiv.1808.01584 · pith_short_12: TFYNSEUUDCQT · pith_short_16: TFYNSEUUDCQTBR2E · pith_short_8: TFYNSEUU

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/TFYNSEUUDCQTBR2EZBDIDYNJVJ \
  | 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: 9970d9129418a130c744c84681e1a9aa4bd991a38b2a0a9c91ba3c12678e2053

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6646f2d83156cadc62704200cb9295d5c380c8ebbccdc796fe945610c87d6ff4",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-08-05T09:06:13Z",
    "title_canon_sha256": "028090e4609d45bcaabf7b070719f46a413326e0a4f93f371c5bd87c75b311fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.01584",
    "kind": "arxiv",
    "version": 4
  }
}