Pith Number

pith:ZQVIDCXF

pith:2025:ZQVIDCXFAUT74Z6V4TX4IIQMNU

not attested not anchored not stored refs pending

Local Statistics of Singular Values for Products of Truncated Unitary Matrices

Dang-Zheng Liu, Yandong Gu

arxiv:2506.14193 v1 · 2025-06-17 · 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{ZQVIDCXFAUT74Z6V4TX4IIQMNU}

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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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-05T11:22:50.573212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc2a818ae50527fe67d5e4efc4220c6d214760f2ed71976d704244330bdc14b4

Aliases

arxiv: 2506.14193 · arxiv_version: 2506.14193v1 · doi: 10.48550/arxiv.2506.14193 · pith_short_12: ZQVIDCXFAUT7 · pith_short_16: ZQVIDCXFAUT74Z6V · pith_short_8: ZQVIDCXF

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/ZQVIDCXFAUT74Z6V4TX4IIQMNU \
  | 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: cc2a818ae50527fe67d5e4efc4220c6d214760f2ed71976d704244330bdc14b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce35eba90435abd88dd1b8facccc90d7c5d5a91ab59dd9c00bea4a27fe17e0ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-06-17T05:17:32Z",
    "title_canon_sha256": "41c2a64e94cc1eb27ab25f2dec46bc987001e508ad1eda903ec3f603ed9fe9f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.14193",
    "kind": "arxiv",
    "version": 1
  }
}