Pith Number

pith:HHITTGSW

pith:2014:HHITTGSW72X76JOWDXXJBEXB2K

not attested not anchored not stored refs pending

Long paths in random Apollonian networks

Alan Frieze, Colin Cooper

arxiv:1403.1472 v1 · 2014-02-07 · math.PR · 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{HHITTGSW72X76JOWDXXJBEXB2K}

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	2026-05-18T02:56:58.963735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39d1399a56feafff25d61dee9092e1d2a963c8f279f105f0fb827b551ae25555

Aliases

arxiv: 1403.1472 · arxiv_version: 1403.1472v1 · doi: 10.48550/arxiv.1403.1472 · pith_short_12: HHITTGSW72X7 · pith_short_16: HHITTGSW72X76JOW · pith_short_8: HHITTGSW

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/HHITTGSW72X76JOWDXXJBEXB2K \
  | 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: 39d1399a56feafff25d61dee9092e1d2a963c8f279f105f0fb827b551ae25555

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1c4136e381bd02a083a689492d79778b9d05920f641a4044a7bf2843b169c33",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-02-07T02:22:25Z",
    "title_canon_sha256": "a3b6c7bcd6be877366fbeee93d8628eb65278e0f974a3e4c6c2bd4bd921cfb18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.1472",
    "kind": "arxiv",
    "version": 1
  }
}