Pith Number

pith:6JZZVOZO

pith:2025:6JZZVOZOKD7QCFLZSRPIMMA6HZ

not attested not anchored not stored refs pending

Cycle lengths in the percolated hypercube

Joshua Erde, Lyuben Lichev, Michael Anastos, Michael Krivelevich, Mihyun Kang, Sahar Diskin

arxiv:2506.16858 v1 · 2025-06-20 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6JZZVOZOKD7QCFLZSRPIMMA6HZ}

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	2026-07-05T11:24:44.116097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2739abb2e50ff011579945e86301e3e4f21a50d5dc17e5334c7fdd3704356d3

Aliases

arxiv: 2506.16858 · arxiv_version: 2506.16858v1 · doi: 10.48550/arxiv.2506.16858 · pith_short_12: 6JZZVOZOKD7Q · pith_short_16: 6JZZVOZOKD7QCFLZ · pith_short_8: 6JZZVOZO

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/6JZZVOZOKD7QCFLZSRPIMMA6HZ \
  | 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: f2739abb2e50ff011579945e86301e3e4f21a50d5dc17e5334c7fdd3704356d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b2913c5cbbcdf31a61477f13c432cd0bfa3f3ad9c4a7dae776d4f8a0edffd28",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-20T09:15:22Z",
    "title_canon_sha256": "db143d8c03b3a69561569718b7dc172ca7d95dff1c0e54fedc3b9b6864d49c58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.16858",
    "kind": "arxiv",
    "version": 1
  }
}