Pith Number

pith:DXAHBFS3

pith:2013:DXAHBFS3MKL7I7TZ4DFB2C2YDN

not attested not anchored not stored refs pending

Benders, Nested Benders and Stochastic Programming: An Intuitive Introduction

James Murphy

arxiv:1312.3158 v1 · 2013-12-11 · math.OC · cs.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{DXAHBFS3MKL7I7TZ4DFB2C2YDN}

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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.

Cited by

1 paper in Pith

Combined Stochastic and Robust Optimization for Electric Autonomous Mobility-on-Demand with Nested Benders Decomposition

Receipt and verification

First computed	2026-05-18T03:05:00.340332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1dc070965b6297f47e79e0ca1d0b581b6f4a423171158570f11e8aa6ffc02d36

Aliases

arxiv: 1312.3158 · arxiv_version: 1312.3158v1 · doi: 10.48550/arxiv.1312.3158 · pith_short_12: DXAHBFS3MKL7 · pith_short_16: DXAHBFS3MKL7I7TZ · pith_short_8: DXAHBFS3

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/DXAHBFS3MKL7I7TZ4DFB2C2YDN \
  | 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: 1dc070965b6297f47e79e0ca1d0b581b6f4a423171158570f11e8aa6ffc02d36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78e1c44b0ba72ccbf409f7598ccf583a6452c9cb3067ec60d7219a4a38da18ca",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-12-11T13:38:43Z",
    "title_canon_sha256": "4dc73ffdb057769d6a6554921fb72facd4b0d09afbf843ff3898b8193e36ac5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3158",
    "kind": "arxiv",
    "version": 1
  }
}