Pith Number

pith:BRF77W26

pith:2012:BRF77W26SSOHQD2S7EMWR7PYME

not attested not anchored not stored refs pending

BV functions in a Gelfand triple for differentiable measure and its applications

Michael R\"ockner, Rongchan Zhu, Xiangchan Zhu

arxiv:1209.2980 v2 · 2012-09-13 · 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{BRF77W26SSOHQD2S7EMWR7PYME}

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	2026-05-18T03:30:02.576161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c4bffdb5e949c780f52f91968fdf86139e05d3a8970d3f157b2360a0cb83ad2

Aliases

arxiv: 1209.2980 · arxiv_version: 1209.2980v2 · doi: 10.48550/arxiv.1209.2980 · pith_short_12: BRF77W26SSOH · pith_short_16: BRF77W26SSOHQD2S · pith_short_8: BRF77W26

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/BRF77W26SSOHQD2S7EMWR7PYME \
  | 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: 0c4bffdb5e949c780f52f91968fdf86139e05d3a8970d3f157b2360a0cb83ad2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf979df30bcfd7a8bdff67d934a807999babe464bda42d7e2d672f960f642f3e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-09-13T18:08:09Z",
    "title_canon_sha256": "46597d692cdd91921b600f14e6dcabcc97785a64a87cc3f9d576aad2d21c88b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2980",
    "kind": "arxiv",
    "version": 2
  }
}