Pith Number

pith:UOL4Q5DE

pith:2010:UOL4Q5DER4EZSR7HZDWWKJT6RZ

not attested not anchored not stored refs pending

On the flatness of Riemannian cylinders without conjugate points

Patrick Emmerich, Victor Bangert

arxiv:1012.0659 v2 · 2010-12-03 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UOL4Q5DER4EZSR7HZDWWKJT6RZ}

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	2026-05-18T03:08:47.959129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a397c874648f099947e7c8ed65267e8e4d54966badaaa0a22471ff253ccc236a

Aliases

arxiv: 1012.0659 · arxiv_version: 1012.0659v2 · doi: 10.48550/arxiv.1012.0659 · pith_short_12: UOL4Q5DER4EZ · pith_short_16: UOL4Q5DER4EZSR7H · pith_short_8: UOL4Q5DE

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/UOL4Q5DER4EZSR7HZDWWKJT6RZ \
  | 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: a397c874648f099947e7c8ed65267e8e4d54966badaaa0a22471ff253ccc236a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f0d2ad6cecc3bc16c02cfd1a9f429aa6ac75b97890d40504bc38abe99658762",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-12-03T08:37:40Z",
    "title_canon_sha256": "4482a406d7f40c59b9d1660fd455dfef6763806e53b24518b7a656804e1cdf0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0659",
    "kind": "arxiv",
    "version": 2
  }
}