Pith Number

pith:VR2CS4OS

pith:2016:VR2CS4OSORORJS7ANXLGZ5AQAO

not attested not anchored not stored refs pending

Some constants related to numerical ranges

Michel Crouzeix (IRMAR)

arxiv:1601.06159 v1 · 2016-01-22 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VR2CS4OSORORJS7ANXLGZ5AQAO}

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	2026-05-18T01:22:05.238574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac742971d2745d14cbe06dd66cf41003bc207cd2ef040335e2901c1f3ed2bdc1

Aliases

arxiv: 1601.06159 · arxiv_version: 1601.06159v1 · doi: 10.48550/arxiv.1601.06159 · pith_short_12: VR2CS4OSOROR · pith_short_16: VR2CS4OSORORJS7A · pith_short_8: VR2CS4OS

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/VR2CS4OSORORJS7ANXLGZ5AQAO \
  | 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: ac742971d2745d14cbe06dd66cf41003bc207cd2ef040335e2901c1f3ed2bdc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9320838ec82ee5a9a367667d8c21cf8a23a5beb7656d05cbe3d169a223309b0f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-01-22T09:18:05Z",
    "title_canon_sha256": "b7ab09c216c1e6a7641ab1e3cf6002fb9ec922b156c728db82b4453b8d37e640"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.06159",
    "kind": "arxiv",
    "version": 1
  }
}