Pith Number

pith:PH3WK2PM

pith:2013:PH3WK2PM2F5BSVE4ER6OD6UMQI

not attested not anchored not stored refs pending

Minima and maxima of elliptical arrays and spherical processes

Enkelejd Hashorva

arxiv:1307.5965 v1 · 2013-07-23 · 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{PH3WK2PM2F5BSVE4ER6OD6UMQI}

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	2026-05-18T03:17:45.683360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79f76569ecd17a19549c247ce1fa8c8234fafc85472a3076d02f51d86ce1feea

Aliases

arxiv: 1307.5965 · arxiv_version: 1307.5965v1 · doi: 10.48550/arxiv.1307.5965 · pith_short_12: PH3WK2PM2F5B · pith_short_16: PH3WK2PM2F5BSVE4 · pith_short_8: PH3WK2PM

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/PH3WK2PM2F5BSVE4ER6OD6UMQI \
  | 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: 79f76569ecd17a19549c247ce1fa8c8234fafc85472a3076d02f51d86ce1feea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c2248aab32eb8ea4e56947864881c4c8971b79c44ca0c57141ae8e15bd41b47",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-07-23T07:34:11Z",
    "title_canon_sha256": "9d3057cfc48f7333f5905503b4960b0b514136e107167e44f6f735bdaad501bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5965",
    "kind": "arxiv",
    "version": 1
  }
}