Pith Number

pith:4DKNIZSD

pith:2015:4DKNIZSDDOBDVD7OLMAF3RH4WE

not attested not anchored not stored refs pending

The Complex Roots of Random Sums

Robert J. Vanderbei

arxiv:1508.05162 v2 · 2015-08-21 · 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{4DKNIZSDDOBDVD7OLMAF3RH4WE}

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	2026-05-18T01:09:57.913464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0d4d466431b823a8fee5b005dc4fcb12df56063dc932621b3bba0e1cb6ae3e7

Aliases

arxiv: 1508.05162 · arxiv_version: 1508.05162v2 · doi: 10.48550/arxiv.1508.05162 · pith_short_12: 4DKNIZSDDOBD · pith_short_16: 4DKNIZSDDOBDVD7O · pith_short_8: 4DKNIZSD

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/4DKNIZSDDOBDVD7OLMAF3RH4WE \
  | 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: e0d4d466431b823a8fee5b005dc4fcb12df56063dc932621b3bba0e1cb6ae3e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac72daeffb0b318eecfa2ddd3abfd6b4aefe74cdd30d536cf9ca66e6739036cb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-08-21T01:36:46Z",
    "title_canon_sha256": "50d41daa47c910efbbd419c9d33e604f4965f34bde5494b4a93cce504728cf37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05162",
    "kind": "arxiv",
    "version": 2
  }
}