Pith Number

pith:MHFFIMK4

pith:2013:MHFFIMK4OG5CJI6DVLO3CCL4FL

not attested not anchored not stored refs pending

Monotonicity of the optimal perimeter in isoperimetric problems on ${\mathbb{Z}}^{k} \times {\mathbb{N}}^{d}$

Emmanuel Tsukerman

arxiv:1303.4139 v2 · 2013-03-18 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHFFIMK4OG5CJI6DVLO3CCL4FL}

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	2026-05-18T03:13:58.057858Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61ca54315c71ba24a3c3aaddb1097c2ad9907f5062ee836621d665f7e253b66f

Aliases

arxiv: 1303.4139 · arxiv_version: 1303.4139v2 · doi: 10.48550/arxiv.1303.4139 · pith_short_12: MHFFIMK4OG5C · pith_short_16: MHFFIMK4OG5CJI6D · pith_short_8: MHFFIMK4

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/MHFFIMK4OG5CJI6DVLO3CCL4FL \
  | 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: 61ca54315c71ba24a3c3aaddb1097c2ad9907f5062ee836621d665f7e253b66f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55d7f61a330a7aaf84201d24335e2ab226acd10a2df949adb2ee3b007ffb9751",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-03-18T02:09:48Z",
    "title_canon_sha256": "5444338bb3b3ce132775b5737b5c4e9f2da664a6914ec06b58ca38dc0f9229b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.4139",
    "kind": "arxiv",
    "version": 2
  }
}