Pith Number

pith:JCSBBRZF

pith:2020:JCSBBRZF2B7YK6PIYWU7OSH6UE

not attested not anchored not stored refs pending

Minimizing rational functions: a hierarchy of approximations via pushforward measures

Jean Bernard Lasserre, Olivier Zahm, Swann Marx, Victor Magron

arxiv:2012.05793 v1 · 2020-12-10 · 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{JCSBBRZF2B7YK6PIYWU7OSH6UE}

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	2026-07-05T01:58:37.010726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48a410c725d07f8579e8c5a9f748fea10ba38951ed81cd1f8bb0fa3bb6b6a5b2

Aliases

arxiv: 2012.05793 · arxiv_version: 2012.05793v1 · doi: 10.48550/arxiv.2012.05793 · pith_short_12: JCSBBRZF2B7Y · pith_short_16: JCSBBRZF2B7YK6PI · pith_short_8: JCSBBRZF

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/JCSBBRZF2B7YK6PIYWU7OSH6UE \
  | 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: 48a410c725d07f8579e8c5a9f748fea10ba38951ed81cd1f8bb0fa3bb6b6a5b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ad2129b28f02d2c1e2c37acfd9837f593994af5907495153b919629f6cb81cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2020-12-10T16:28:56Z",
    "title_canon_sha256": "71f9a52cee14a19045a65e86cb15935ec3bb56be15a9d2bb6299a86da6cd9a15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.05793",
    "kind": "arxiv",
    "version": 1
  }
}