Pith Number

pith:A6TLSDUD

pith:2026:A6TLSDUD2NJJR75RZR7HTJV5FD

not attested not anchored not stored refs pending

No-gap second-order conditions for optimization problems involving transport distances

Christian Meyer, Gerd Wachsmuth, Nicolas Borchard

arxiv:2607.28264 v1 · 2026-07-30 · 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{A6TLSDUD2NJJR75RZR7HTJV5FD}

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	2026-07-31T01:36:59.490027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

07a6b90e83d35298ffb1cc7e79a6bd28d43b34076b8bbeec23c686365c4831ee

Aliases

arxiv: 2607.28264 · arxiv_version: 2607.28264v1 · doi: 10.48550/arxiv.2607.28264 · pith_short_12: A6TLSDUD2NJJ · pith_short_16: A6TLSDUD2NJJR75R · pith_short_8: A6TLSDUD

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/A6TLSDUD2NJJR75RZR7HTJV5FD \
  | 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: 07a6b90e83d35298ffb1cc7e79a6bd28d43b34076b8bbeec23c686365c4831ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41ec7c9ef4143bc892bc80eb87cfe2b4724db1ece728e61426c1a44810f3f078",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-07-30T14:21:01Z",
    "title_canon_sha256": "f1273a691c89ab9d82090044b1e8f9104e43e3bfdbd2c296ffff39a250186aa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.28264",
    "kind": "arxiv",
    "version": 1
  }
}