Pith Number

pith:XPI3M6I2

pith:2025:XPI3M6I26APJH6UONHOLDNCMKI

not attested not anchored not stored refs pending

Multi-period line planning for varying railway passenger demand with asymmetric lines

Menno de Bruyn, Niels van Oort, Renate J. H. van der Knaap, Rob M. P. Goverde

arxiv:2509.02052 v1 · 2025-09-02 · 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{XPI3M6I26APJH6UONHOLDNCMKI}

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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

Line Planning at Scale: Models, Methods, and Insights

Receipt and verification

First computed	2026-07-05T12:03:13.711172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbd1b6791af01e93fa8e69dcb1b44c522cf45f04fee55f3d4a324b0f1fb96830

Aliases

arxiv: 2509.02052 · arxiv_version: 2509.02052v1 · doi: 10.48550/arxiv.2509.02052 · pith_short_12: XPI3M6I26APJ · pith_short_16: XPI3M6I26APJH6UO · pith_short_8: XPI3M6I2

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/XPI3M6I26APJH6UONHOLDNCMKI \
  | 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: bbd1b6791af01e93fa8e69dcb1b44c522cf45f04fee55f3d4a324b0f1fb96830

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89a0b78a19bfa8e400d52f392c7b2f955124db6c6a0eeb068fb97b32f8d31ff1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-09-02T07:46:00Z",
    "title_canon_sha256": "679d1636bde466eea8fd70b6d8b9c51bd0f7f5202d4a0a318825cdf8bb560ffc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.02052",
    "kind": "arxiv",
    "version": 1
  }
}