Pith Number

pith:YLEWXUML

pith:2017:YLEWXUMLOSV4ALQ6QAIFBFJL2Q

not attested not anchored not stored refs pending

A probabilistic proof of the Gauss-Bonnet formula for manifolds with boundary

Levi Lopes de Lima

arxiv:1709.03772 v1 · 2017-09-12 · math.DG · 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{YLEWXUMLOSV4ALQ6QAIFBFJL2Q}

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	2026-05-18T00:35:29.522467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2c96bd18b74abc02e1e801050952bd40002616be2efd5546141d65cc9c19fd0

Aliases

arxiv: 1709.03772 · arxiv_version: 1709.03772v1 · doi: 10.48550/arxiv.1709.03772 · pith_short_12: YLEWXUMLOSV4 · pith_short_16: YLEWXUMLOSV4ALQ6 · pith_short_8: YLEWXUML

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/YLEWXUMLOSV4ALQ6QAIFBFJL2Q \
  | 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: c2c96bd18b74abc02e1e801050952bd40002616be2efd5546141d65cc9c19fd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a177f6c469508e1879e70a5011d5f3aa0587160d8a18f489538a8efb7337fb84",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-09-12T10:10:57Z",
    "title_canon_sha256": "5c408868b31a54b2210b636dd7a692819e1a6a921e43b231a9aec67ed063ac4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.03772",
    "kind": "arxiv",
    "version": 1
  }
}