Pith Number

pith:YWZT6YI2

pith:2003:YWZT6YI27CWXGDKKVF4BTF5HCB

not attested not anchored not stored refs pending

On the Herzog-Sch\"onheim conjecture for uniform covers of groups

Zhi-Wei Sun

arxiv:math/0306099 v2 · 2003-06-05 · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YWZT6YI27CWXGDKKVF4BTF5HCB}

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	2026-07-04T14:37:22.955828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5b33f611af8ad730d4aa9781997a7106be0b3d18d433ac5218008228323c45c

Aliases

arxiv: math/0306099 · arxiv_version: math/0306099v2 · doi: 10.48550/arxiv.math/0306099 · pith_short_12: YWZT6YI27CWX · pith_short_16: YWZT6YI27CWXGDKK · pith_short_8: YWZT6YI2

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/YWZT6YI27CWXGDKKVF4BTF5HCB \
  | 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: c5b33f611af8ad730d4aa9781997a7106be0b3d18d433ac5218008228323c45c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b933561657e9ad14a66a39d9e5e75691dc6298e110b4049e4b370fe0e1d0eeda",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2003-06-05T16:38:18Z",
    "title_canon_sha256": "d31db4ab5bd9b5ee840aa0f3927e04afc4df66718372a0aad085442b3ef889f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0306099",
    "kind": "arxiv",
    "version": 2
  }
}