Pith Number

pith:SB4OPR2P

pith:2021:SB4OPR2PQIMNOWOYMZW64WJILL

not attested not anchored not stored refs pending

The Constant Trace Property in Noncommutative Optimization

Abhishek Bhardwaj, Ngoc Hoang Anh Mai, Victor Magron

arxiv:2102.02162 v1 · 2021-02-03 · 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{SB4OPR2PQIMNOWOYMZW64WJILL}

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	2026-07-05T02:12:37.496381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9078e7c74f8218d759d8666dee59285aebfe4cf614a815b3944d9e1197e875df

Aliases

arxiv: 2102.02162 · arxiv_version: 2102.02162v1 · doi: 10.48550/arxiv.2102.02162 · pith_short_12: SB4OPR2PQIMN · pith_short_16: SB4OPR2PQIMNOWOY · pith_short_8: SB4OPR2P

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/SB4OPR2PQIMNOWOYMZW64WJILL \
  | 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: 9078e7c74f8218d759d8666dee59285aebfe4cf614a815b3944d9e1197e875df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "993fdfcfc1b412295ae5622b6fb04c67b1824e0efaeea4f4788a6f32735279e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-02-03T17:40:54Z",
    "title_canon_sha256": "4d2e4ed2da4a2bfdd7c76d7b427b1e913687a1bb13b9bb15e95fadce57dc3ddd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.02162",
    "kind": "arxiv",
    "version": 1
  }
}