Pith Number

pith:GQ3SXI3I

pith:2016:GQ3SXI3I72OLDURZX2ETHVBEFH

not attested not anchored not stored refs pending

The extremal function for cycles of length $\ell$ mod $k$

Benny Sudakov, Jacques Verstraete

arxiv:1606.08532 v1 · 2016-06-28 · 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{GQ3SXI3I72OLDURZX2ETHVBEFH}

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	2026-05-18T01:11:47.506252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34372ba368fe9cb1d239be8933d42429ff6f026943b0f717f09be97c2653da90

Aliases

arxiv: 1606.08532 · arxiv_version: 1606.08532v1 · doi: 10.48550/arxiv.1606.08532 · pith_short_12: GQ3SXI3I72OL · pith_short_16: GQ3SXI3I72OLDURZ · pith_short_8: GQ3SXI3I

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/GQ3SXI3I72OLDURZX2ETHVBEFH \
  | 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: 34372ba368fe9cb1d239be8933d42429ff6f026943b0f717f09be97c2653da90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef77dc3fadba89fb2809bf1bae755a67364e11a868c3796b05118f85efef8822",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-28T01:47:50Z",
    "title_canon_sha256": "82656eece7a88d0a0c4f3e52f1a875f77e89bc287b010d8308523ddecc417712"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08532",
    "kind": "arxiv",
    "version": 1
  }
}