Pith Number

pith:PQ2N2GUT

pith:2014:PQ2N2GUT2HK5WYVIEH4O5OWD3O

not attested not anchored not stored refs pending

Sharp threshold for embedding combs and other spanning trees in random graphs

Richard Montgomery

arxiv:1405.6560 v1 · 2014-05-26 · 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{PQ2N2GUT2HK5WYVIEH4O5OWD3O}

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	2026-05-18T02:51:07.124478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c34dd1a93d1d5db62a821f8eebac3dba8edabb07ec5ca981b3bd7f895828bdc

Aliases

arxiv: 1405.6560 · arxiv_version: 1405.6560v1 · doi: 10.48550/arxiv.1405.6560 · pith_short_12: PQ2N2GUT2HK5 · pith_short_16: PQ2N2GUT2HK5WYVI · pith_short_8: PQ2N2GUT

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/PQ2N2GUT2HK5WYVIEH4O5OWD3O \
  | 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: 7c34dd1a93d1d5db62a821f8eebac3dba8edabb07ec5ca981b3bd7f895828bdc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fec165c4f6f7396d1cd12860e2844cbbeed148f58f73d0b61f4345e96f093a15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-05-26T13:02:03Z",
    "title_canon_sha256": "2912c915f91bcdd84e9456006fa266fc33ab36c54a9126b08a1a8df36ceba4f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.6560",
    "kind": "arxiv",
    "version": 1
  }
}