Pith Number

pith:WNGV5DB5

pith:2013:WNGV5DB5KIKE6TMLYKTENLG5AW

not attested not anchored not stored refs pending

Weak convergence of probability measures: a topological vector space point of view

Liang Hong

arxiv:1310.1607 v2 · 2013-10-06 · math.ST · math.FA · 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{WNGV5DB5KIKE6TMLYKTENLG5AW}

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	2026-05-18T03:04:06.250874Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b34d5e8c3d52144f4d8bc2a646acdd059450d848a7fd0f715e3efc25a1d24aa8

Aliases

arxiv: 1310.1607 · arxiv_version: 1310.1607v2 · doi: 10.48550/arxiv.1310.1607 · pith_short_12: WNGV5DB5KIKE · pith_short_16: WNGV5DB5KIKE6TML · pith_short_8: WNGV5DB5

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/WNGV5DB5KIKE6TMLYKTENLG5AW \
  | 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: b34d5e8c3d52144f4d8bc2a646acdd059450d848a7fd0f715e3efc25a1d24aa8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c1efb04b722de5713b150607c5191ffa505466b0dbd4bc0fbb3abb2d94333a2",
    "cross_cats_sorted": [
      "math.FA",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-10-06T17:36:09Z",
    "title_canon_sha256": "fa08b22cd3b76ec96211706f0fd1fc1aab71c367d9254d7d32045199f7b59d0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.1607",
    "kind": "arxiv",
    "version": 2
  }
}