Pith Number

pith:EFBCVAJP

pith:2005:EFBCVAJP4K3QVJF5H5JXRCWHHQ

not attested not anchored not stored refs pending

Menger's covering property and groupwise density

Boaz Tsaban, Lyubomyr Zdomskyy

arxiv:math/0510680 v3 · 2005-10-31 · math.GN · math.CO · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EFBCVAJP4K3QVJF5H5JXRCWHHQ}

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	2026-05-18T04:37:23.136571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21422a812fe2b70aa4bd3f53788ac73c0db3fa08a36ea95b636db9b281b5fe56

Aliases

arxiv: math/0510680 · arxiv_version: math/0510680v3 · doi: 10.48550/arxiv.math/0510680 · pith_short_12: EFBCVAJP4K3Q · pith_short_16: EFBCVAJP4K3QVJF5 · pith_short_8: EFBCVAJP

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/EFBCVAJP4K3QVJF5H5JXRCWHHQ \
  | 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: 21422a812fe2b70aa4bd3f53788ac73c0db3fa08a36ea95b636db9b281b5fe56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b105ecc4a65eaca58377a73b5a8b08a93dcee2d4ce6d148895f2116141a4cf2",
    "cross_cats_sorted": [
      "math.CO",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2005-10-31T15:55:55Z",
    "title_canon_sha256": "be8069e8ebc68fa07f023c8df999a0d2f65b25341e2b9b178f01effa67c0b4d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0510680",
    "kind": "arxiv",
    "version": 3
  }
}