Pith Number

pith:F42V2OUI

pith:2012:F42V2OUIGPZ5LYNAII5L5HWJYK

not attested not anchored not stored refs pending

A formula for Popp's volume in sub-Riemannian geometry

Davide Barilari, Luca Rizzi

arxiv:1211.2325 v2 · 2012-11-10 · 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{F42V2OUIGPZ5LYNAII5L5HWJYK}

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	2026-05-18T03:36:04.080820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f355d3a8833f3d5e1a0423abe9ec9c29a9e991ab7d6113e591e3963ca74024c

Aliases

arxiv: 1211.2325 · arxiv_version: 1211.2325v2 · doi: 10.48550/arxiv.1211.2325 · pith_short_12: F42V2OUIGPZ5 · pith_short_16: F42V2OUIGPZ5LYNA · pith_short_8: F42V2OUI

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/F42V2OUIGPZ5LYNAII5L5HWJYK \
  | 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: 2f355d3a8833f3d5e1a0423abe9ec9c29a9e991ab7d6113e591e3963ca74024c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae6728dcab501922f6d5917f8be70786eef2e2356207fc12b206afcc6c0cb0cd",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-11-10T13:43:23Z",
    "title_canon_sha256": "ebca556316da8549792f61cb57296ffa5b3b7049af5d4e4663bd1445954d8f36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2325",
    "kind": "arxiv",
    "version": 2
  }
}