Pith Number

pith:MPHV7LUU

pith:2026:MPHV7LUU272S4J2G5Y7B5L7CRA

not attested not anchored not stored refs pending

A duality approach to the dense graph limit for biological transportation networks

Jan Haskovec, Nuno J. Alves

arxiv:2606.04129 v1 · 2026-06-02 · 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{MPHV7LUU272S4J2G5Y7B5L7CRA}

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	2026-06-04T00:06:51.379894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63cf5fae94d7f52e2746ee3e1eafe2881ea1ae94940cdfd2471c9b58620680e8

Aliases

arxiv: 2606.04129 · arxiv_version: 2606.04129v1 · doi: 10.48550/arxiv.2606.04129 · pith_short_12: MPHV7LUU272S · pith_short_16: MPHV7LUU272S4J2G · pith_short_8: MPHV7LUU

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/MPHV7LUU272S4J2G5Y7B5L7CRA \
  | 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: 63cf5fae94d7f52e2746ee3e1eafe2881ea1ae94940cdfd2471c9b58620680e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fa68d10c46d65bb31b7ff7ef5548f04e6883159c7ac57ec4c66947a37eadb29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-02T18:39:14Z",
    "title_canon_sha256": "dc5fc4e467cdcf8cc8bb1eb261b5cd56205215a35afdddda89e0479fa2e3975d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.04129",
    "kind": "arxiv",
    "version": 1
  }
}