Pith Number

pith:GQIFF7BP

pith:2021:GQIFF7BPXK4XSKA7XU4HQKGAQK

not attested not anchored not stored refs pending

The full rank condition for sparse random matrices

Amin Coja-Oghlan, Joon Lee, Maurice Rolvien, Max Hahn-Klimroth, Noela M\"uller, Pu Gao

arxiv:2112.14090 v2 · 2021-12-28 · math.CO · cs.DM · 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{GQIFF7BPXK4XSKA7XU4HQKGAQK}

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	2026-07-05T03:54:26.623398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

341052fc2fbab979281fbd387828c082ba31d3d0d957c5bd26a17cf53f79ef42

Aliases

arxiv: 2112.14090 · arxiv_version: 2112.14090v2 · doi: 10.48550/arxiv.2112.14090 · pith_short_12: GQIFF7BPXK4X · pith_short_16: GQIFF7BPXK4XSKA7 · pith_short_8: GQIFF7BP

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/GQIFF7BPXK4XSKA7XU4HQKGAQK \
  | 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: 341052fc2fbab979281fbd387828c082ba31d3d0d957c5bd26a17cf53f79ef42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc9ae16ca5449d4c3122883d1e0b50a7b3ac19e21130c61dc83664ce33eca171",
    "cross_cats_sorted": [
      "cs.DM",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-12-28T11:02:37Z",
    "title_canon_sha256": "f341fc6e9bcdcd14811a7bbf6ebff807cdc69b28146d80d3a9fcb6a804c65296"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.14090",
    "kind": "arxiv",
    "version": 2
  }
}