Pith Number

pith:GWADKUS2

pith:2016:GWADKUS2DOFRFEQWIK3CPKYIWM

not attested not anchored not stored refs pending

A Mean-Field Matrix-Analytic Method for Bike Sharing Systems under Markovian Environment

Quan-Lin Li, Rui-Na Fan

arxiv:1610.01302 v2 · 2016-10-05 · math.PR · cs.PF · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GWADKUS2DOFRFEQWIK3CPKYIWM}

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	2026-05-18T00:23:46.074191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

358035525a1b8b12921642b627ab08b3342975d0f502ad0e72b32be2fdfae3d5

Aliases

arxiv: 1610.01302 · arxiv_version: 1610.01302v2 · doi: 10.48550/arxiv.1610.01302 · pith_short_12: GWADKUS2DOFR · pith_short_16: GWADKUS2DOFRFEQW · pith_short_8: GWADKUS2

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/GWADKUS2DOFRFEQWIK3CPKYIWM \
  | 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: 358035525a1b8b12921642b627ab08b3342975d0f502ad0e72b32be2fdfae3d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c30c619c598ea094b28c53144469ea810ef51d9d1616ce32b0cadaf018d32c13",
    "cross_cats_sorted": [
      "cs.PF",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-05T08:03:38Z",
    "title_canon_sha256": "e92d51fc3d5d0f08052cfb8277dc690099968eae52733b3392e80f47168bc4e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01302",
    "kind": "arxiv",
    "version": 2
  }
}