Pith Number

pith:GLZKDJD3

pith:2001:GLZKDJD3THOSREMJBI4ZR34PXM

not attested not anchored not stored refs pending

Birkhoff's theorem and multidimensional numerical range

Yuri Safarov

arxiv:math/0110131 v2 · 2001-10-12 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GLZKDJD3THOSREMJBI4ZR34PXM}

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	2026-07-04T14:49:40.907483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32f2a1a47b99dd2891890a3998ef8fbb30aaa957b9c0d6f6652321d6c3e3ebc5

Aliases

arxiv: math/0110131 · arxiv_version: math/0110131v2 · doi: 10.48550/arxiv.math/0110131 · pith_short_12: GLZKDJD3THOS · pith_short_16: GLZKDJD3THOSREMJ · pith_short_8: GLZKDJD3

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/GLZKDJD3THOSREMJBI4ZR34PXM \
  | 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: 32f2a1a47b99dd2891890a3998ef8fbb30aaa957b9c0d6f6652321d6c3e3ebc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ac26ac7a65430a94107495f6a1c8444f4c13f3500784ad076e0a139f8c2d088",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2001-10-12T14:01:03Z",
    "title_canon_sha256": "91ce944146d5cdd775979dfcf97f6433e8ecb754b49ef78d1e696d27a51a70f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0110131",
    "kind": "arxiv",
    "version": 2
  }
}