Pith Number

pith:C6NKC334

pith:2026:C6NKC334ROSMJXSGOVAQ7QNTAI

not attested not anchored not stored refs pending

A Unified Variational Framework for Optimal Transport with Lagrangian Costs

Hailiang Liu

arxiv:2607.15471 v1 · 2026-07-16 · 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{C6NKC334ROSMJXSGOVAQ7QNTAI}

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	2026-07-20T00:18:35.740960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

179aa16f7c8ba4c4de4675410fc1b3023e9f0c695bb5ae3e64102c6fbf71e01a

Aliases

arxiv: 2607.15471 · arxiv_version: 2607.15471v1 · doi: 10.48550/arxiv.2607.15471 · pith_short_12: C6NKC334ROSM · pith_short_16: C6NKC334ROSMJXSG · pith_short_8: C6NKC334

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/C6NKC334ROSMJXSGOVAQ7QNTAI \
  | 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: 179aa16f7c8ba4c4de4675410fc1b3023e9f0c695bb5ae3e64102c6fbf71e01a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d9d45be6fc13abff78b6051fdf61cc8bf656dbb31a8ca210bc19cd1ebd3994f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-07-16T21:41:12Z",
    "title_canon_sha256": "fefbef03adc8ff6e8b649e52390461b0e70ca7fa91634188446ab4a08887113e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15471",
    "kind": "arxiv",
    "version": 1
  }
}