Pith Number

pith:LNMQOKB3

pith:2011:LNMQOKB3FLVDD6NDLFJA2V4VYI

not attested not anchored not stored refs pending

On the boundary of the attainable set of the Dirichlet spectrum

Aldo Pratelli, Carlo Nitsch, Lorenzo Brasco

arxiv:1112.4689 v1 · 2011-12-20 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LNMQOKB3FLVDD6NDLFJA2V4VYI}

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	2026-05-18T01:59:04.675743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b5907283b2aea31f9a359520d5795c20412e0be3b58e67ab50db98ef65e866a

Aliases

arxiv: 1112.4689 · arxiv_version: 1112.4689v1 · doi: 10.48550/arxiv.1112.4689 · pith_short_12: LNMQOKB3FLVD · pith_short_16: LNMQOKB3FLVDD6ND · pith_short_8: LNMQOKB3

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/LNMQOKB3FLVDD6NDLFJA2V4VYI \
  | 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: 5b5907283b2aea31f9a359520d5795c20412e0be3b58e67ab50db98ef65e866a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e9fdf32ef70713b30f3818af00ba4172eb64e454e2575d9f61aabf869264511",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-12-20T13:56:48Z",
    "title_canon_sha256": "1ac6eee58178656388a3d8be3bc1269eb3abf686a918d6c52810495b364e9f62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4689",
    "kind": "arxiv",
    "version": 1
  }
}