Pith Number

pith:SEQ4XXTN

pith:2019:SEQ4XXTNFKG5YIWT545II27YIF

not attested not anchored not stored refs pending

On barycenters of probability measures

Azat Miftakhov, Sergey Berezin

arxiv:1911.07680 v2 · 2019-11-18 · math.PR · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SEQ4XXTNFKG5YIWT545II27YIF}

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	2026-07-05T01:53:18.370027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9121cbde6d2a8ddc22d3ef3a846bf84143fcfdd1ddf4feee99716562429fb0f6

Aliases

arxiv: 1911.07680 · arxiv_version: 1911.07680v2 · doi: 10.48550/arxiv.1911.07680 · pith_short_12: SEQ4XXTNFKG5 · pith_short_16: SEQ4XXTNFKG5YIWT · pith_short_8: SEQ4XXTN

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/SEQ4XXTNFKG5YIWT545II27YIF \
  | 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: 9121cbde6d2a8ddc22d3ef3a846bf84143fcfdd1ddf4feee99716562429fb0f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a49956e278303ac5546b513610b429a4cde75a5ed383378f05b67b6822fc11d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-11-18T15:04:44Z",
    "title_canon_sha256": "f76048232a8a8b75730d0f669eefd4e744bf43fff69092b433687fba57f37ccf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.07680",
    "kind": "arxiv",
    "version": 2
  }
}