Pith Number

pith:MQU5VYVS

pith:2015:MQU5VYVSPBUZURKWMQGPG7E2NJ

not attested not anchored not stored refs pending

A Multi-stage Stochastic Programming Approach for Network Capacity Expansion with Multiple Sources of Capacity

Kai Huang, Majid Taghavi

arxiv:1511.01922 v2 · 2015-11-05 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MQU5VYVSPBUZURKWMQGPG7E2NJ}

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	2026-05-18T00:51:03.348959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6429dae2b278699a4556640cf37c9a6a79cb04b45c13861209228e9d0660a2bf

Aliases

arxiv: 1511.01922 · arxiv_version: 1511.01922v2 · doi: 10.48550/arxiv.1511.01922 · pith_short_12: MQU5VYVSPBUZ · pith_short_16: MQU5VYVSPBUZURKW · pith_short_8: MQU5VYVS

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/MQU5VYVSPBUZURKWMQGPG7E2NJ \
  | 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: 6429dae2b278699a4556640cf37c9a6a79cb04b45c13861209228e9d0660a2bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d3a50eaeff83f26e23cf4f51064faad6476a77dc523beb9dc0a19bd0a6d6b4a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-11-05T21:36:49Z",
    "title_canon_sha256": "a969382edfc79dc9b1fe4d13ca11e90720ee2daa307c4707444305336f37d8cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01922",
    "kind": "arxiv",
    "version": 2
  }
}