Pith Number

pith:Q52RU2A2

pith:2004:Q52RU2A2QT2AS6KJZB3OSXAW2B

not attested not anchored not stored refs pending

A characterization of covering equivalence

Hao Pan, Zhi-Wei Sun

arxiv:math/0409521 v2 · 2004-09-27 · 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{Q52RU2A2QT2AS6KJZB3OSXAW2B}

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	2026-07-04T15:05:03.391858Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87751a681a84f4097949c876e95c16d07cf99da3538c158d78ff76ae180c0e6c

Aliases

arxiv: math/0409521 · arxiv_version: math/0409521v2 · doi: 10.48550/arxiv.math/0409521 · pith_short_12: Q52RU2A2QT2A · pith_short_16: Q52RU2A2QT2AS6KJ · pith_short_8: Q52RU2A2

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/Q52RU2A2QT2AS6KJZB3OSXAW2B \
  | 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: 87751a681a84f4097949c876e95c16d07cf99da3538c158d78ff76ae180c0e6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f5a5ab643c119f57bdadbfe700b3d82ff492eff468444ea3892cdea5b4b6066",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-09-27T15:02:53Z",
    "title_canon_sha256": "3c904b28f05400915defdab6f0ca521d15750810916f3d74506ff90f8c9a94b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409521",
    "kind": "arxiv",
    "version": 2
  }
}