Pith Number

pith:F7PXGPCP

pith:1999:F7PXGPCPQHSOEY5BKA4RH7KY6U

not attested not anchored not stored refs pending

A positive solution to the Busemann-Petty problem in R^4

Gaoyong Zhang

arxiv:math/9903205 v1 · 1999-03-01 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F7PXGPCPQHSOEY5BKA4RH7KY6U}

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	2026-05-18T01:05:33.150357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fdf733c4f81e4e263a1503913fd58f5359d96f88e6af9e5b6011c210379f238

Aliases

arxiv: math/9903205 · arxiv_version: math/9903205v1 · doi: 10.48550/arxiv.math/9903205 · pith_short_12: F7PXGPCPQHSO · pith_short_16: F7PXGPCPQHSOEY5B · pith_short_8: F7PXGPCP

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/F7PXGPCPQHSOEY5BKA4RH7KY6U \
  | 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: 2fdf733c4f81e4e263a1503913fd58f5359d96f88e6af9e5b6011c210379f238

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba3a9c2d9db4de6af3e268e069ce4863912ca77b263a732b10a71c10f441f0d4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "1999-03-01T00:00:00Z",
    "title_canon_sha256": "676591565e095ef86f5e0cd393649582e69800eed7f5d6e19ef12902fdf4f13e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9903205",
    "kind": "arxiv",
    "version": 1
  }
}