Pith Number

pith:XJ7CTMUH

pith:2010:XJ7CTMUH2QG7ERAJEDCXOWR6VS

not attested not anchored not stored refs pending

Alexandrov meets Lott--Villani--Sturm

Anton Petrunin

arxiv:1003.5948 v3 · 2010-03-30 · math.MG · math.DG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XJ7CTMUH2QG7ERAJEDCXOWR6VS}

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.

Cited by

1 paper in Pith

Alexandrov spaces with non negative curvature and displacement convexity of the entropy tensor

Receipt and verification

First computed	2026-07-05T00:04:25.198360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba7e29b287d40df2440920c5775a3eacbc7220ab1a2606dc9a8c8b226ed002ed

Aliases

arxiv: 1003.5948 · arxiv_version: 1003.5948v3 · doi: 10.48550/arxiv.1003.5948 · pith_short_12: XJ7CTMUH2QG7 · pith_short_16: XJ7CTMUH2QG7ERAJ · pith_short_8: XJ7CTMUH

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/XJ7CTMUH2QG7ERAJEDCXOWR6VS \
  | 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: ba7e29b287d40df2440920c5775a3eacbc7220ab1a2606dc9a8c8b226ed002ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5f5d22084698a4a022917bfb57062f3cde6f939ea31a15f83106f1f81bb2f57",
    "cross_cats_sorted": [
      "math.DG",
      "math.OC"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-03-30T23:44:43Z",
    "title_canon_sha256": "2727f0325b7cf7c1af0e8029e2e7dbb891c4536398a304cc68f186bbb1d6fb64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.5948",
    "kind": "arxiv",
    "version": 3
  }
}