Pith Number

pith:URBKXZTD

pith:2020:URBKXZTDOWDQAC7G5VVG2W4NPF

not attested not anchored not stored refs pending

Closed geodesics on surfaces without conjugate points

Gerhard Knieper, Khadim War, Vaughn Climenhaga

arxiv:2008.02249 v2 · 2020-08-05 · math.DS · 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{URBKXZTDOWDQAC7G5VVG2W4NPF}

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	2026-07-05T02:42:26.305543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a442abe6637587000be6ed6a6d5b8d795f0821077b4ec4a630590a24b963df7d

Aliases

arxiv: 2008.02249 · arxiv_version: 2008.02249v2 · doi: 10.48550/arxiv.2008.02249 · pith_short_12: URBKXZTDOWDQ · pith_short_16: URBKXZTDOWDQAC7G · pith_short_8: URBKXZTD

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/URBKXZTDOWDQAC7G5VVG2W4NPF \
  | 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: a442abe6637587000be6ed6a6d5b8d795f0821077b4ec4a630590a24b963df7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11a6573c805d939ad8c1a3aeed4548d54a78c275abaf0662fe2bc4315818352a",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2020-08-05T17:27:02Z",
    "title_canon_sha256": "332e9330dddec0c241f1283c8d899ca0bdcd95d5a019aa1adc290802fb48493b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2008.02249",
    "kind": "arxiv",
    "version": 2
  }
}