Pith Number

pith:FJMP4DB5

pith:2011:FJMP4DB5W5O5ROARRV57CQYT4R

not attested not anchored not stored refs pending

Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

Amir Ali Ahmadi, Mardavij Roozbehani, Pablo A. Parrilo, Rapha\"el Jungers

arxiv:1111.3427 v2 · 2011-11-15 · math.OC · cs.SY

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FJMP4DB5W5O5ROARRV57CQYT4R}

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	2026-05-18T02:44:32.653235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a58fe0c3db75dd8b8118d7bf14313e45cb35b92baeebc8ecbb7d86198f4c18a

Aliases

arxiv: 1111.3427 · arxiv_version: 1111.3427v2 · doi: 10.48550/arxiv.1111.3427 · pith_short_12: FJMP4DB5W5O5 · pith_short_16: FJMP4DB5W5O5ROAR · pith_short_8: FJMP4DB5

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/FJMP4DB5W5O5ROARRV57CQYT4R \
  | 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: 2a58fe0c3db75dd8b8118d7bf14313e45cb35b92baeebc8ecbb7d86198f4c18a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05ca2454f3985ce2ab75fffc450d437582684b52baddc89faa9dd18935cff1bb",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-11-15T04:23:50Z",
    "title_canon_sha256": "74e3d63b399a5c49a9aa886ed5c885fccce806451c603dc6115f843a104cbafc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3427",
    "kind": "arxiv",
    "version": 2
  }
}