Pith Number

pith:JMQKCZGZ

pith:2017:JMQKCZGZY2ZLBC2DGN2UCXLGIK

not attested not anchored not stored refs pending

Optimality of broken extremals

Andrei A. Agrachev, Carolina Biolo

arxiv:1709.07775 v1 · 2017-09-21 · 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{JMQKCZGZY2ZLBC2DGN2UCXLGIK}

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	2026-05-18T00:34:32.373730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b20a164d9c6b2b08b433375415d66428a01c7d12d5abe55cadd71fc85019817

Aliases

arxiv: 1709.07775 · arxiv_version: 1709.07775v1 · doi: 10.48550/arxiv.1709.07775 · pith_short_12: JMQKCZGZY2ZL · pith_short_16: JMQKCZGZY2ZLBC2D · pith_short_8: JMQKCZGZ

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/JMQKCZGZY2ZLBC2DGN2UCXLGIK \
  | 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: 4b20a164d9c6b2b08b433375415d66428a01c7d12d5abe55cadd71fc85019817

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8763bd9ca0bf76f365d45d9549c4572c37147b73c22f7165ed16159ffe0c7d80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2017-09-21T16:48:08Z",
    "title_canon_sha256": "90cc4d6a153f82aa437f640e9131f34ce5af169c02a301e39a8bdf6cac68224c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.07775",
    "kind": "arxiv",
    "version": 1
  }
}