Pith Number

pith:OPHDQTIY

pith:2021:OPHDQTIYUPHIXLKXRQG3KSRRN3

not attested not anchored not stored refs pending

Degrees in link graphs of regular graphs

Itai Benjamini, John Haslegrave

arxiv:2106.15464 v2 · 2021-06-29 · 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{OPHDQTIYUPHIXLKXRQG3KSRRN3}

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	2026-07-05T04:30:37.680960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73ce384d18a3ce8bad578c0db54a316ef8b40196395b30c47a2f337e6c14311d

Aliases

arxiv: 2106.15464 · arxiv_version: 2106.15464v2 · doi: 10.48550/arxiv.2106.15464 · pith_short_12: OPHDQTIYUPHI · pith_short_16: OPHDQTIYUPHIXLKX · pith_short_8: OPHDQTIY

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/OPHDQTIYUPHIXLKXRQG3KSRRN3 \
  | 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: 73ce384d18a3ce8bad578c0db54a316ef8b40196395b30c47a2f337e6c14311d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f69337b34af35374152a9521fc6b9fdc102d62cc601924e5fa77795e20904fa",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-06-29T14:49:59Z",
    "title_canon_sha256": "673f3fe144e190fa185353b9f7be9fdf90e86f7798df746f11af4bd928891bb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.15464",
    "kind": "arxiv",
    "version": 2
  }
}