Pith Number

pith:DDNYM6N5

pith:2013:DDNYM6N5T5W5GZUBLQF2B5TDMT

not attested not anchored not stored refs pending

Heavy-traffic asymptotic formulas for the multiclass M${}^X$/G/1 queue

Hiroshi Miyawaki, Hiroyuki Masuyama, Yutaka Takahashi

arxiv:1312.6970 v2 · 2013-12-25 · 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{DDNYM6N5T5W5GZUBLQF2B5TDMT}

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	2026-05-18T02:53:26.738267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18db8679bd9f6dd366815c0ba0f66364c885944d2dc819782df48f44cff11adf

Aliases

arxiv: 1312.6970 · arxiv_version: 1312.6970v2 · doi: 10.48550/arxiv.1312.6970 · pith_short_12: DDNYM6N5T5W5 · pith_short_16: DDNYM6N5T5W5GZUB · pith_short_8: DDNYM6N5

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/DDNYM6N5T5W5GZUBLQF2B5TDMT \
  | 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: 18db8679bd9f6dd366815c0ba0f66364c885944d2dc819782df48f44cff11adf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8398c76c13457766339d2d0f72e4fcfab620ae868b055735a42f49b973012272",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-25T13:18:43Z",
    "title_canon_sha256": "4360b8737ca71213d627edbe071fe667d734d683ab753808f7858ec78d010986"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6970",
    "kind": "arxiv",
    "version": 2
  }
}