Pith Number

pith:4MNMLFEE

pith:2009:4MNMLFEE2WDEZTEDDC4E3G72N5

not attested not anchored not stored refs pending

How to take shortcuts in Euclidean space: making a given set into a short quasi-convex set

Jonas Azzam, Raanan Schul

arxiv:0912.1356 v2 · 2009-12-07 · math.MG · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MNMLFEE2WDEZTEDDC4E3G72N5}

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	2026-05-18T02:24:45.866798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e31ac59484d5864ccc8318b84d9bfa6f5ff7c7bb60c728fef7a980ac2d076db4

Aliases

arxiv: 0912.1356 · arxiv_version: 0912.1356v2 · doi: 10.48550/arxiv.0912.1356 · pith_short_12: 4MNMLFEE2WDE · pith_short_16: 4MNMLFEE2WDEZTED · pith_short_8: 4MNMLFEE

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/4MNMLFEE2WDEZTEDDC4E3G72N5 \
  | 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: e31ac59484d5864ccc8318b84d9bfa6f5ff7c7bb60c728fef7a980ac2d076db4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "209a45b8a0fe5fe8b4bec3ef7fd281539cf6598efd5ab3252056cf0690d10dd8",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2009-12-07T22:05:36Z",
    "title_canon_sha256": "6f8d97a30ad86446b303c2702f65e60d70066066f98173b23c1ca35b9f898b92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1356",
    "kind": "arxiv",
    "version": 2
  }
}