Pith Number

pith:MLO4DSCX

pith:2011:MLO4DSCXWAM63QQHJ4PRTBUQJM

not attested not anchored not stored refs pending

Volume Growth, Number of Ends and the Topology of a Complete Submanifold

Vicente Palmer, Vicent Gimeno

arxiv:1112.4042 v2 · 2011-12-17 · 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{MLO4DSCXWAM63QQHJ4PRTBUQJM}

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	2026-05-18T03:57:36.936213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62ddc1c857b019edc2074f1f1986904b2154c3958943aebd6ebc069d97fde550

Aliases

arxiv: 1112.4042 · arxiv_version: 1112.4042v2 · doi: 10.48550/arxiv.1112.4042 · pith_short_12: MLO4DSCXWAM6 · pith_short_16: MLO4DSCXWAM63QQH · pith_short_8: MLO4DSCX

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/MLO4DSCXWAM63QQHJ4PRTBUQJM \
  | 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: 62ddc1c857b019edc2074f1f1986904b2154c3958943aebd6ebc069d97fde550

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00099bca48c4fbd4fbc002643dbef5b580df65241f61319927fe1c136c2a7f90",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-17T09:17:29Z",
    "title_canon_sha256": "9a23cd0df64ac75272d08b945228a8df7e0b492bdc465992523c7d2da52d2ff5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4042",
    "kind": "arxiv",
    "version": 2
  }
}