Pith Number

pith:UYF6G743

pith:2015:UYF6G743QQWUKN7SLM2WNOIQ7R

not attested not anchored not stored refs pending

Strong approximation with Brauer-Manin obstruction for groupic varieties

Fei Xu, Yang Cao

arxiv:1507.04340 v4 · 2015-07-15 · 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{UYF6G743QQWUKN7SLM2WNOIQ7R}

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	2026-05-18T00:17:46.598934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a60be37f9b842d4537f25b3566b910fc7f772cf9d035ec683061dcaa12256835

Aliases

arxiv: 1507.04340 · arxiv_version: 1507.04340v4 · doi: 10.48550/arxiv.1507.04340 · pith_short_12: UYF6G743QQWU · pith_short_16: UYF6G743QQWUKN7S · pith_short_8: UYF6G743

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/UYF6G743QQWUKN7SLM2WNOIQ7R \
  | 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: a60be37f9b842d4537f25b3566b910fc7f772cf9d035ec683061dcaa12256835

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06ecdb2f144b1ee5655a23289d3199ef39af9c441e2c824c447ecb664f67a69c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-07-15T19:54:49Z",
    "title_canon_sha256": "be724f650fc2db95b74fd4f1f2f5d2885f0dc7a2fcdb7bf2a2e01afae8242b37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.04340",
    "kind": "arxiv",
    "version": 4
  }
}