Pith Number

pith:XCOP3RKL

pith:2012:XCOP3RKLNKCKSFO3FWZA2K4U24

not attested not anchored not stored refs pending

Explicit Lyapunov functions and estimates of the essential spectral radius for Jackson networks

Danielle Tibi, Irina Ignatiouk-Robert

arxiv:1206.3066 v1 · 2012-06-14 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XCOP3RKLNKCKSFO3FWZA2K4U24}

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	2026-05-18T03:53:32.825607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b89cfdc54b6a84a915db2db20d2b94d71d4f2ece1b44e3cd6bcf9768562a55e9

Aliases

arxiv: 1206.3066 · arxiv_version: 1206.3066v1 · doi: 10.48550/arxiv.1206.3066 · pith_short_12: XCOP3RKLNKCK · pith_short_16: XCOP3RKLNKCKSFO3 · pith_short_8: XCOP3RKL

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/XCOP3RKLNKCKSFO3FWZA2K4U24 \
  | 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: b89cfdc54b6a84a915db2db20d2b94d71d4f2ece1b44e3cd6bcf9768562a55e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37827af982b65948d1c570d610ac16b148131416ea760aa7333b5ebe85b9d821",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-14T10:27:45Z",
    "title_canon_sha256": "3276a81b4399bf4506ed3e9074398c8f8f483960326e734f263b9da87be96a4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3066",
    "kind": "arxiv",
    "version": 1
  }
}