Pith Number

pith:4NYG6PFZ

pith:2026:4NYG6PFZYSNIMFLLHFUU3ZH2CW

not attested not anchored not stored refs pending

On the structure of optimal free Dirichlet regions in mass transportation problems

Lucas D. O'Brien

arxiv:2606.30826 v1 · 2026-06-29 · 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{4NYG6PFZYSNIMFLLHFUU3ZH2CW}

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	2026-07-01T00:17:18.561798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3706f3cb9c49a86156b39694de4fa15a2b4eece56c0a48a7a6ef7e5c2ad831e

Aliases

arxiv: 2606.30826 · arxiv_version: 2606.30826v1 · doi: 10.48550/arxiv.2606.30826 · pith_short_12: 4NYG6PFZYSNI · pith_short_16: 4NYG6PFZYSNIMFLL · pith_short_8: 4NYG6PFZ

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/4NYG6PFZYSNIMFLLHFUU3ZH2CW \
  | 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: e3706f3cb9c49a86156b39694de4fa15a2b4eece56c0a48a7a6ef7e5c2ad831e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d45c796dc7a9a5f0358b8ec6d17a24c3895db0e5aa5504d9c66dc18d73d2a2c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-29T18:56:52Z",
    "title_canon_sha256": "dd2da87237978a8372ecb103876951124d4e45ec4fc2861cd014a93074e697be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30826",
    "kind": "arxiv",
    "version": 1
  }
}