Pith Number

pith:EX7PGBAV

pith:2011:EX7PGBAVTDWCRCMU4GSHW2MLEO

not attested not anchored not stored refs pending

Computable bounds on the spectral gap for unreliable Jackson networks

Pawel Lorek, Ryszard Szekli

arxiv:1101.0332 v3 · 2011-01-01 · 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{EX7PGBAVTDWCRCMU4GSHW2MLEO}

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	2026-05-18T02:23:05.842624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

25fef3041598ec288994e1a47b698b238bd8aef367986ef274d5381512c4fe06

Aliases

arxiv: 1101.0332 · arxiv_version: 1101.0332v3 · doi: 10.48550/arxiv.1101.0332 · pith_short_12: EX7PGBAVTDWC · pith_short_16: EX7PGBAVTDWCRCMU · pith_short_8: EX7PGBAV

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/EX7PGBAVTDWCRCMU4GSHW2MLEO \
  | 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: 25fef3041598ec288994e1a47b698b238bd8aef367986ef274d5381512c4fe06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "900e110ba754eb1e825fb0653566e2a86fdaaab80e13c371c56bb07d2fdbd9de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-01T12:00:30Z",
    "title_canon_sha256": "affa4df132f5eaa6b63644797991f844ae51ba4fccdf3b0ed5a8a071af5cd63c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0332",
    "kind": "arxiv",
    "version": 3
  }
}