Pith Number

pith:GRKRI4MR

pith:2012:GRKRI4MRQE6UEMWXNGQT755PGM

not attested not anchored not stored refs pending

Singular curves and the etale Brauer-Manin obstruction for surfaces

Alexei Skorobogatov, Yonatan Harpaz

arxiv:1212.6019 v2 · 2012-12-25 · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GRKRI4MRQE6UEMWXNGQT755PGM}

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	2026-05-18T03:06:32.813285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3455147191813d4232d769a13ff7af331259fa7aa4adf3980ac265e2ef3d8f89

Aliases

arxiv: 1212.6019 · arxiv_version: 1212.6019v2 · doi: 10.48550/arxiv.1212.6019 · pith_short_12: GRKRI4MRQE6U · pith_short_16: GRKRI4MRQE6UEMWX · pith_short_8: GRKRI4MR

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/GRKRI4MRQE6UEMWXNGQT755PGM \
  | 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: 3455147191813d4232d769a13ff7af331259fa7aa4adf3980ac265e2ef3d8f89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c41302a26fa11d6edc8b96e03c6ac6dfc448fc78ebb47b723f7c8a872d722513",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-12-25T11:03:03Z",
    "title_canon_sha256": "3c5525dfc11df1e9cfa2816b99969f8df8b38b12c05fe9326cf923cfc7a580e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6019",
    "kind": "arxiv",
    "version": 2
  }
}