Pith Number

pith:VEBUKDAX

pith:2026:VEBUKDAXBFAPY2AGZIBNQQMXIP

not attested not anchored not stored refs pending

Exponential Rank Bounds for Random Matrices

Achintya Raya Polavarapu

arxiv:2606.25204 v1 · 2026-06-23 · 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{VEBUKDAXBFAPY2AGZIBNQQMXIP}

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	2026-06-25T00:18:20.764376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a903450c170940fc6806ca02d8419743d36c766cbbfaf420e74c7f98d0e32157

Aliases

arxiv: 2606.25204 · arxiv_version: 2606.25204v1 · doi: 10.48550/arxiv.2606.25204 · pith_short_12: VEBUKDAXBFAP · pith_short_16: VEBUKDAXBFAPY2AG · pith_short_8: VEBUKDAX

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/VEBUKDAXBFAPY2AGZIBNQQMXIP \
  | 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: a903450c170940fc6806ca02d8419743d36c766cbbfaf420e74c7f98d0e32157

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edd70b768333fe82ddb4c28adeb2773aa22bd2dee52c3e59d35b817b860481f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-23T21:53:58Z",
    "title_canon_sha256": "4207e05c4d3c9bad8eee2a4b212ceec5393ba4afa2bc7bb0137293e25b15ad4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25204",
    "kind": "arxiv",
    "version": 1
  }
}