Pith Number

pith:ZHNA4RRE

pith:2009:ZHNA4RREN27PC26X5JLLOBKVXX

not attested not anchored not stored refs pending

Duality between invariant spaces for max-plus linear discrete event systems

Jean-Jacques Loiseau, Michael Di Loreto, Ricardo D. Katz, Stephane Gaubert

arxiv:0901.2915 v1 · 2009-01-19 · 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{ZHNA4RREN27PC26X5JLLOBKVXX}

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	2026-05-18T04:33:04.444263Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9da0e46246ebef16bd7ea56b70555bdd2352e5aab575b1abac4f0930a19ef9b

Aliases

arxiv: 0901.2915 · arxiv_version: 0901.2915v1 · doi: 10.48550/arxiv.0901.2915 · pith_short_12: ZHNA4RREN27P · pith_short_16: ZHNA4RREN27PC26X · pith_short_8: ZHNA4RRE

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/ZHNA4RREN27PC26X5JLLOBKVXX \
  | 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: c9da0e46246ebef16bd7ea56b70555bdd2352e5aab575b1abac4f0930a19ef9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12e6596547d3f21993811bd6f60a32eb77932dbcdf95a14b343c84a8c30ba6ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2009-01-19T19:00:25Z",
    "title_canon_sha256": "dcecc4ce97c72179390cf66e84798f5ea5e893bd798065a5e4849b2d345ef873"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.2915",
    "kind": "arxiv",
    "version": 1
  }
}