Pith Number

pith:Q32USF4T

pith:2012:Q32USF4TNNQXF3372BHQYIHKMV

not attested not anchored not stored refs pending

Hessian metrics, CD(K,N)-spaces, and optimal transportation of log-concave measures

Alexander V. Kolesnikov

arxiv:1201.2342 v3 · 2012-01-11 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q32USF4TNNQXF3372BHQYIHKMV}

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	2026-05-18T03:19:57.044690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86f54917936b6172ef7fd04f0c20ea657afeced1ca604dbe943d2b7769dd6f13

Aliases

arxiv: 1201.2342 · arxiv_version: 1201.2342v3 · doi: 10.48550/arxiv.1201.2342 · pith_short_12: Q32USF4TNNQX · pith_short_16: Q32USF4TNNQXF337 · pith_short_8: Q32USF4T

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/Q32USF4TNNQXF3372BHQYIHKMV \
  | 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: 86f54917936b6172ef7fd04f0c20ea657afeced1ca604dbe943d2b7769dd6f13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82f20edf51fb0b9a3dd03b84262a90d71f60ac9f6bd8fe2c0c5ecef79f03c759",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-01-11T16:26:42Z",
    "title_canon_sha256": "dcdf9017984c4f8c956cd492ebb1670ddb52e462d60e7fc4a1b4bb35957c07a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2342",
    "kind": "arxiv",
    "version": 3
  }
}