Pith Number

pith:5O5YIIQS

pith:2026:5O5YIIQSRO4HDDXUCFCUGA4GU2

not attested not anchored not stored refs pending

Spectral Concentration and Recovery in Sparse High-Dimensional Random Geometric Graphs

Manuel Fernandez V, Yizhe Zhu

arxiv:2607.14304 v1 · 2026-07-15 · stat.ML · cs.LG · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5O5YIIQSRO4HDDXUCFCUGA4GU2}

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	2026-07-17T00:21:04.318673Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebbb8422128bb8718ef41145430386a6b89655032ee50672cb484bf2059a0921

Aliases

arxiv: 2607.14304 · arxiv_version: 2607.14304v1 · doi: 10.48550/arxiv.2607.14304 · pith_short_12: 5O5YIIQSRO4H · pith_short_16: 5O5YIIQSRO4HDDXU · pith_short_8: 5O5YIIQS

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/5O5YIIQSRO4HDDXUCFCUGA4GU2 \
  | 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: ebbb8422128bb8718ef41145430386a6b89655032ee50672cb484bf2059a0921

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23535b88e3597b8a1207f1671318fafaaad01c0654476987c5554a700bcca654",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-07-15T19:09:14Z",
    "title_canon_sha256": "ef95ec9b4231daa18bd5ea4524c36254360b5078afe7781275a8831c82315fad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14304",
    "kind": "arxiv",
    "version": 1
  }
}