Pith Number

pith:2U5IDC3O

pith:2016:2U5IDC3OHNWBYYXTSWR7FIONKW

not attested not anchored not stored refs pending

Weak Convergence (IA). Sequences of Random Vectors

Gane Samb Lo, Modou Ngom, Tchilabalo Atozou Kpanzou

arxiv:1610.05415 v4 · 2016-10-18 · 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{2U5IDC3OHNWBYYXTSWR7FIONKW}

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	2026-05-18T00:08:36.732017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d53a818b6e3b6c1c62f395a3f2a1cd55b5920b2c17acd2b2d258a0404b18ceb9

Aliases

arxiv: 1610.05415 · arxiv_version: 1610.05415v4 · doi: 10.48550/arxiv.1610.05415 · pith_short_12: 2U5IDC3OHNWB · pith_short_16: 2U5IDC3OHNWBYYXT · pith_short_8: 2U5IDC3O

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/2U5IDC3OHNWBYYXTSWR7FIONKW \
  | 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: d53a818b6e3b6c1c62f395a3f2a1cd55b5920b2c17acd2b2d258a0404b18ceb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9128dfc1677cc3e9e0032b0b5833b2c5250d26214e2a92439360b50abe17519",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-18T03:20:37Z",
    "title_canon_sha256": "578e9a9e36ebd9abd8cd99e3f9b4ff9e7829b76b4f132389502791417d2ef9fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05415",
    "kind": "arxiv",
    "version": 4
  }
}