Pith Number

pith:LPGH44JM

pith:2013:LPGH44JM4SS5BBMZNVHMXDD5GL

not attested not anchored not stored refs pending

Geodesic Completeness for Sobolev Metrics on the Space of Immersed Plane Curves

David Mumford, Martins Bruveris, Peter W. Michor

arxiv:1312.4995 v2 · 2013-12-17 · math.AP · 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{LPGH44JM4SS5BBMZNVHMXDD5GL}

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	2026-05-18T02:41:08.769672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bcc7e712ce4a5d085996d4ecb8c7d32e8691c5bf22db4e692718c490d82b12c

Aliases

arxiv: 1312.4995 · arxiv_version: 1312.4995v2 · doi: 10.48550/arxiv.1312.4995 · pith_short_12: LPGH44JM4SS5 · pith_short_16: LPGH44JM4SS5BBMZ · pith_short_8: LPGH44JM

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/LPGH44JM4SS5BBMZNVHMXDD5GL \
  | 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: 5bcc7e712ce4a5d085996d4ecb8c7d32e8691c5bf22db4e692718c490d82b12c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a3fc0af4c79de63ad1201771db94d3ebe1f09381998718d6d9ae5af17e5b027",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-12-17T23:04:15Z",
    "title_canon_sha256": "3c472c2323dc915885e25736a01399716f4fb3309a1323f1df981701dfc661fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4995",
    "kind": "arxiv",
    "version": 2
  }
}