Pith Number

pith:OHC52E5I

pith:2026:OHC52E5I4U73SPBAAJL47SIKX2

not attested not anchored not stored refs pending

Universality for cokernels of partially random integral matrices

Isaac Rajagopal

arxiv:2607.06952 v1 · 2026-07-08 · math.PR · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OHC52E5I4U73SPBAAJL47SIKX2}

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	2026-07-09T00:19:40.990002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71c5dd13a8e53fb93c200257cfc90abe85128aea10887488829159ef2c07c7c1

Aliases

arxiv: 2607.06952 · arxiv_version: 2607.06952v1 · doi: 10.48550/arxiv.2607.06952 · pith_short_12: OHC52E5I4U73 · pith_short_16: OHC52E5I4U73SPBA · pith_short_8: OHC52E5I

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/OHC52E5I4U73SPBAAJL47SIKX2 \
  | 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: 71c5dd13a8e53fb93c200257cfc90abe85128aea10887488829159ef2c07c7c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0aadba9d0ae14823f56a15bd562c468764580de7864fcc5df1dc8ce5c20a35f",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-08T03:26:29Z",
    "title_canon_sha256": "54f60c7f17751ce923118baf7be4a4859782d5ed58828a0738f02833eb31a2dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06952",
    "kind": "arxiv",
    "version": 1
  }
}