Pith Number

pith:4VGYQ3UN

pith:2007:4VGYQ3UNLO6JEAO2DJ4XIX5BMA

not attested not anchored not stored refs pending

Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms

Fei Xu, Jean-Louis Colliot-Th\'el\`ene

arxiv:0712.1957 v1 · 2007-12-12 · 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{4VGYQ3UNLO6JEAO2DJ4XIX5BMA}

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	2026-05-18T03:02:45.074948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e54d886e8d5bbc9201da1a79745fa1600cded709e61130cd8a6ffac701dc380a

Aliases

arxiv: 0712.1957 · arxiv_version: 0712.1957v1 · doi: 10.48550/arxiv.0712.1957 · pith_short_12: 4VGYQ3UNLO6J · pith_short_16: 4VGYQ3UNLO6JEAO2 · pith_short_8: 4VGYQ3UN

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/4VGYQ3UNLO6JEAO2DJ4XIX5BMA \
  | 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: e54d886e8d5bbc9201da1a79745fa1600cded709e61130cd8a6ffac701dc380a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5b42457ad49abacd3ce101c5ae96e6d3b7d399dc2fac4dbacafcb5ae50540de",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-12-12T16:00:18Z",
    "title_canon_sha256": "ca7f75e88ab553770ecfbf2c0f5466304e2e813dc0efb5ea886c4a69954c9ab2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.1957",
    "kind": "arxiv",
    "version": 1
  }
}