Pith Number

pith:VQEMYVFG

pith:2012:VQEMYVFGDPFDFWCWKZZGUYKGMQ

not attested not anchored not stored refs pending

Various Theorems on Tournaments

Gaku Liu

arxiv:1207.0237 v1 · 2012-07-01 · 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{VQEMYVFGDPFDFWCWKZZGUYKGMQ}

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	2026-05-18T03:51:59.821951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac08cc54a61bca32d85656726a6146643deacb45077d40c720b536a6aa35dbfc

Aliases

arxiv: 1207.0237 · arxiv_version: 1207.0237v1 · doi: 10.48550/arxiv.1207.0237 · pith_short_12: VQEMYVFGDPFD · pith_short_16: VQEMYVFGDPFDFWCW · pith_short_8: VQEMYVFG

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/VQEMYVFGDPFDFWCWKZZGUYKGMQ \
  | 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: ac08cc54a61bca32d85656726a6146643deacb45077d40c720b536a6aa35dbfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf92ad90aacf32c4369293d70e918f56bed30abdc0496879c24a5f36ea3f480f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-01T19:11:42Z",
    "title_canon_sha256": "bfd9b1e5dce6e8c7ef0e165ccfae83fa77f655bcae86e44cc0ed4fd9c7237273"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0237",
    "kind": "arxiv",
    "version": 1
  }
}