Pith Number

pith:4E6OIAAE

pith:2014:4E6OIAAE4BVFNDTJZDAFTFLI6P

not attested not anchored not stored refs pending

Discrete length-volume inequalities and lower volume bounds in metric spaces

Kyle Kinneberg

arxiv:1410.5692 v2 · 2014-10-21 · math.MG · 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{4E6OIAAE4BVFNDTJZDAFTFLI6P}

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	2026-05-18T01:20:12.217057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e13ce40004e06a568e69c8c0599568f3ea3ae9324cbdf5ede495bfb058395cf3

Aliases

arxiv: 1410.5692 · arxiv_version: 1410.5692v2 · doi: 10.48550/arxiv.1410.5692 · pith_short_12: 4E6OIAAE4BVF · pith_short_16: 4E6OIAAE4BVFNDTJ · pith_short_8: 4E6OIAAE

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/4E6OIAAE4BVFNDTJZDAFTFLI6P \
  | 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: e13ce40004e06a568e69c8c0599568f3ea3ae9324cbdf5ede495bfb058395cf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a03722d9aaeb99e6bb056af3a8edc22d0022993c7f92e17a9875aed5d2604cb",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2014-10-21T14:51:37Z",
    "title_canon_sha256": "7e2c66dec5be20300a9b6d361a58358526f5d34136c303560d628978b77e1c6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.5692",
    "kind": "arxiv",
    "version": 2
  }
}