Pith Number

pith:X6T7SL7I

pith:2021:X6T7SL7IMUNXVUYECPKJS5QQRW

not attested not anchored not stored refs pending

On the Rank, Kernel, and Core of Sparse Random Graphs

Alexander Moreira, Margalit Glasgow, Patrick DeMichele

arxiv:2105.11718 v2 · 2021-05-25 · 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{X6T7SL7IMUNXVUYECPKJS5QQRW}

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	2026-07-05T03:50:35.334120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfa7f92fe8651b7ad30413d49976108db741f879bc534f149cfec8aded656302

Aliases

arxiv: 2105.11718 · arxiv_version: 2105.11718v2 · doi: 10.48550/arxiv.2105.11718 · pith_short_12: X6T7SL7IMUNX · pith_short_16: X6T7SL7IMUNXVUYE · pith_short_8: X6T7SL7I

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/X6T7SL7IMUNXVUYECPKJS5QQRW \
  | 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: bfa7f92fe8651b7ad30413d49976108db741f879bc534f149cfec8aded656302

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79db32f2b5e5dfb0a58992cc765b5f5c9558ee8e8efa125dce5bf63d3a0a3044",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-05-25T07:41:58Z",
    "title_canon_sha256": "70c87330a315b6e03dabe65b72dc2a85152b304cdb47d9caafbe36025f921d07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.11718",
    "kind": "arxiv",
    "version": 2
  }
}