Pith Number

pith:S32RSGD3

pith:2015:S32RSGD3S2JJOPRQIXD6W42SR7

not attested not anchored not stored refs pending

Limits of subcritical random graphs and random graphs with excluded minors

Agelos Georgakopoulos, Stephan Wagner

arxiv:1512.03572 v2 · 2015-12-11 · math.CO · 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{S32RSGD3S2JJOPRQIXD6W42SR7}

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	2026-05-18T00:56:46.558637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96f519187b9692973e3045c7eb73528fd92678ae47a8b1e020f1bd77d5e6e7e1

Aliases

arxiv: 1512.03572 · arxiv_version: 1512.03572v2 · doi: 10.48550/arxiv.1512.03572 · pith_short_12: S32RSGD3S2JJ · pith_short_16: S32RSGD3S2JJOPRQ · pith_short_8: S32RSGD3

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/S32RSGD3S2JJOPRQIXD6W42SR7 \
  | 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: 96f519187b9692973e3045c7eb73528fd92678ae47a8b1e020f1bd77d5e6e7e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84138885b4a654a21bd0ebce763ef6d8e4d55d9deb80fdaa2abdb05c17b2edad",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-11T10:03:47Z",
    "title_canon_sha256": "e6c19275c1f657a4d5a651573879173b19690e4476e4ace64df659f50f3fb611"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03572",
    "kind": "arxiv",
    "version": 2
  }
}