Pith Number

pith:QNTXXXGK

pith:2001:QNTXXXGK3GDM6KNL3LZM2FCKS5

not attested not anchored not stored refs pending

Convex Multivariable Trace Functions

Elliott H. Lieb, Gert K. Pedersen

arxiv:math/0107062 v3 · 2001-07-08 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QNTXXXGK3GDM6KNL3LZM2FCKS5}

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	2026-05-18T01:38:29.888091Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83677bdccad986cf29abdaf2cd144a977c76e029b7822712261b8f19c992c55e

Aliases

arxiv: math/0107062 · arxiv_version: math/0107062v3 · doi: 10.48550/arxiv.math/0107062 · pith_short_12: QNTXXXGK3GDM · pith_short_16: QNTXXXGK3GDM6KNL · pith_short_8: QNTXXXGK

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/QNTXXXGK3GDM6KNL3LZM2FCKS5 \
  | 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: 83677bdccad986cf29abdaf2cd144a977c76e029b7822712261b8f19c992c55e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f31288e4f2dc0d8379af974730474214850b4f7f2aaeb1b5fcfc0bae10d73a51",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2001-07-08T18:28:01Z",
    "title_canon_sha256": "3837009d687e8335399e8e4b5c205ce3a3a1fbea862ed76ff2a6534b4a218c3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0107062",
    "kind": "arxiv",
    "version": 3
  }
}