Pith Number

pith:S64L652P

pith:2018:S64L652PG3SJ43IAKDCZ5MSXFE

not attested not anchored not stored refs pending

Locality of the critical probability for transitive graphs of exponential growth

Tom Hutchcroft

arxiv:1808.08940 v2 · 2018-08-27 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S64L652PG3SJ43IAKDCZ5MSXFE}

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	2026-05-17T23:39:32.247052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97b8bf774f36e49e6d0050c59eb257292bac7e9eabadef54478047117a23a83f

Aliases

arxiv: 1808.08940 · arxiv_version: 1808.08940v2 · doi: 10.48550/arxiv.1808.08940 · pith_short_12: S64L652PG3SJ · pith_short_16: S64L652PG3SJ43IA · pith_short_8: S64L652P

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/S64L652PG3SJ43IAKDCZ5MSXFE \
  | 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: 97b8bf774f36e49e6d0050c59eb257292bac7e9eabadef54478047117a23a83f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b59ce131283b3ddff2fa7604d1e4010100e7c208ec1aa56056c1032a29a19c7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-08-27T17:39:40Z",
    "title_canon_sha256": "7fef52222b9ee66f7757f72dfa857c6daf23d9efb387488da5a0b44eaa5d42ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.08940",
    "kind": "arxiv",
    "version": 2
  }
}