Pith Number

pith:WAN4PF2J

pith:2004:WAN4PF2JLNSE4DYQMG27LNT45L

not attested not anchored not stored refs pending

The combinatorics of tau-covers

Boaz Tsaban, Heike Mildenberger, Saharon Shelah

arxiv:math/0409068 v4 · 2004-09-05 · 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{WAN4PF2JLNSE4DYQMG27LNT45L}

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	2026-05-18T04:37:23.165679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b01bc797495b644e0f1061b5f5b67ceacb1117e3da16220ac16f8bf73f1b933a

Aliases

arxiv: math/0409068 · arxiv_version: math/0409068v4 · doi: 10.48550/arxiv.math/0409068 · pith_short_12: WAN4PF2JLNSE · pith_short_16: WAN4PF2JLNSE4DYQ · pith_short_8: WAN4PF2J

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/WAN4PF2JLNSE4DYQMG27LNT45L \
  | 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: b01bc797495b644e0f1061b5f5b67ceacb1117e3da16220ac16f8bf73f1b933a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0515de630de9c67bbd756956030d31c9b4476ae6c984686a5e2e9ff55020a783",
    "cross_cats_sorted": [
      "math.CO",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2004-09-05T14:59:05Z",
    "title_canon_sha256": "42fb3899e87d9f8273ffdd2e8897b786f5727ccf74bd1fada8491b74f6c5aade"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409068",
    "kind": "arxiv",
    "version": 4
  }
}