Pith Number

pith:KIB2JQ2B

pith:2012:KIB2JQ2BDB6JYLR74XQ3EB7CGX

not attested not anchored not stored refs pending

The Isoperimetric Problem in Higher Codimension

Frank Morgan, Isabel M. C. Salavessa

arxiv:1203.3304 v2 · 2012-03-15 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KIB2JQ2BDB6JYLR74XQ3EB7CGX}

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	2026-05-18T03:40:51.387674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5203a4c341187c9c2e3fe5e1b207e235c23eab321922bc809d455e37397136fa

Aliases

arxiv: 1203.3304 · arxiv_version: 1203.3304v2 · doi: 10.48550/arxiv.1203.3304 · pith_short_12: KIB2JQ2BDB6J · pith_short_16: KIB2JQ2BDB6JYLR7 · pith_short_8: KIB2JQ2B

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/KIB2JQ2BDB6JYLR74XQ3EB7CGX \
  | 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: 5203a4c341187c9c2e3fe5e1b207e235c23eab321922bc809d455e37397136fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13cc1144ee2c39201262dc63db11392d9e6511e6c8212c8e3db8b5b50fee021d",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-03-15T10:12:26Z",
    "title_canon_sha256": "165b61ebeb7731c3c570c2a8d9316b365571b8e1746b5a6f292af0c01a97821f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3304",
    "kind": "arxiv",
    "version": 2
  }
}