Pith Number

pith:XFUMFODY

pith:2005:XFUMFODYHK4NYWAABSWWH4PCDM

not attested not anchored not stored refs pending

A sharp result on m-covers

Hao Pan, Zhi-Wei Sun

arxiv:math/0504413 v2 · 2005-04-20 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XFUMFODYHK4NYWAABSWWH4PCDM}

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	2026-07-04T14:50:12.826707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b968c2b8783ab8dc58000cad63f1e21b204de013d0815713cec3ea1b7f7c0c43

Aliases

arxiv: math/0504413 · arxiv_version: math/0504413v2 · doi: 10.48550/arxiv.math/0504413 · pith_short_12: XFUMFODYHK4N · pith_short_16: XFUMFODYHK4NYWAA · pith_short_8: XFUMFODY

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/XFUMFODYHK4NYWAABSWWH4PCDM \
  | 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: b968c2b8783ab8dc58000cad63f1e21b204de013d0815713cec3ea1b7f7c0c43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6175da51b6df3a792e1b3b2fc720f0a6dd3fc3c01b08fb4178eaf31aaf6cefbc",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-04-20T14:11:53Z",
    "title_canon_sha256": "bf14aa32265090242fb9e55d93869bfac1e972655b6bb4272b58893890fa23f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504413",
    "kind": "arxiv",
    "version": 2
  }
}