Pith Number

pith:ZU5ES5GX

pith:2025:ZU5ES5GXF2K53H62VPFP3PGLSW

not attested not anchored not stored refs pending

Edge statistics for singular values of products of rectangular complex Ginibre matrices

Yandong Gu

arxiv:2507.07431 v1 · 2025-07-10 · 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{ZU5ES5GXF2K53H62VPFP3PGLSW}

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	2026-07-05T11:34:57.742860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd3a4974d72e95dd9fdaabcafdbccb95a1da990815b5ba41ae695b1e058d2a7b

Aliases

arxiv: 2507.07431 · arxiv_version: 2507.07431v1 · doi: 10.48550/arxiv.2507.07431 · pith_short_12: ZU5ES5GXF2K5 · pith_short_16: ZU5ES5GXF2K53H62 · pith_short_8: ZU5ES5GX

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/ZU5ES5GXF2K53H62VPFP3PGLSW \
  | 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: cd3a4974d72e95dd9fdaabcafdbccb95a1da990815b5ba41ae695b1e058d2a7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f00929262a68f60278d57d44360b706637418f60ac3d208ba3dd4ae647c1a65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-10T05:05:33Z",
    "title_canon_sha256": "c904f03e45005c1b02e4d829d84ce6b37d865784c05c62fe61b0dfdaf3d0713a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.07431",
    "kind": "arxiv",
    "version": 1
  }
}