Pith Number

pith:BKSTWI3W

pith:2019:BKSTWI3WWUBQH6WC37KBU5JGT6

not attested not anchored not stored refs pending

A discontinuous phase transition in the threshold-$\theta \geq 2$ contact process on random graphs

Danny Nam

arxiv:1907.05005 v1 · 2019-07-11 · 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{BKSTWI3WWUBQH6WC37KBU5JGT6}

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	2026-05-17T23:40:54.198534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0aa53b2376b50303fac2dfd41a75269fab09ef8317a94f399b5c22e8c44d288f

Aliases

arxiv: 1907.05005 · arxiv_version: 1907.05005v1 · doi: 10.48550/arxiv.1907.05005 · pith_short_12: BKSTWI3WWUBQ · pith_short_16: BKSTWI3WWUBQH6WC · pith_short_8: BKSTWI3W

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/BKSTWI3WWUBQH6WC37KBU5JGT6 \
  | 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: 0aa53b2376b50303fac2dfd41a75269fab09ef8317a94f399b5c22e8c44d288f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0f71fc5ddcfa41ec2875e5993952bda128ce1acdf1eb8f3bd97c35ce5b06efc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-07-11T05:41:10Z",
    "title_canon_sha256": "1619208026d0befce9c7d2aa82c37bd7c621fde4cdb0e207eb1bb2adde4890ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.05005",
    "kind": "arxiv",
    "version": 1
  }
}