Pith Number

pith:WRP5WGGA

pith:2024:WRP5WGGA2MSJ3GH45JUOS7N7GB

not attested not anchored not stored refs pending

On the $H$-space of a random graph

Jeff Kahn, Quentin Dubroff

arxiv:2410.06421 v1 · 2024-10-08 · 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{WRP5WGGA2MSJ3GH45JUOS7N7GB}

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.

Cited by

1 paper in Pith

When does a tree activate the random graph?

Receipt and verification

First computed	2026-07-05T09:18:01.322699Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b45fdb18c0d3249d98fcea68e97dbf304e21d336ffdda25e9c76bee9a80faa47

Aliases

arxiv: 2410.06421 · arxiv_version: 2410.06421v1 · doi: 10.48550/arxiv.2410.06421 · pith_short_12: WRP5WGGA2MSJ · pith_short_16: WRP5WGGA2MSJ3GH4 · pith_short_8: WRP5WGGA

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/WRP5WGGA2MSJ3GH45JUOS7N7GB \
  | 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: b45fdb18c0d3249d98fcea68e97dbf304e21d336ffdda25e9c76bee9a80faa47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d08c82e2d3485ce56be01438a6a0ab87c6bef69fc6341c2b4839b0b49720d095",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-10-08T23:20:40Z",
    "title_canon_sha256": "271d22336565ff6adbfc803be43d8eb0239a8cc6dbb643c35ef46133727d7f5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.06421",
    "kind": "arxiv",
    "version": 1
  }
}