Pith Number

pith:MU3LE7B2

pith:2026:MU3LE7B2KEJ247SZWPEIBLVXHI

not attested not anchored not stored refs pending

Wasserstein gradient flows for Coulomb discrepancies

Antonin Chodron de Courcel, Matthew Rosenzweig

arxiv:2607.12579 v1 · 2026-07-14 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MU3LE7B2KEJ247SZWPEIBLVXHI}

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	2026-07-15T01:22:04.927357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6536b27c3a5113ae7e59b3c880aeb73a2ad742a05132c0afe55a21e4175bdd6c

Aliases

arxiv: 2607.12579 · arxiv_version: 2607.12579v1 · doi: 10.48550/arxiv.2607.12579 · pith_short_12: MU3LE7B2KEJ2 · pith_short_16: MU3LE7B2KEJ247SZ · pith_short_8: MU3LE7B2

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/MU3LE7B2KEJ247SZWPEIBLVXHI \
  | 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: 6536b27c3a5113ae7e59b3c880aeb73a2ad742a05132c0afe55a21e4175bdd6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d8db9e073ab3568a22cefb717d31452a1bd29b9f0f38090d64eb3626fd70bc2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-14T09:49:46Z",
    "title_canon_sha256": "243865b09e33e12941d16000d776c2fe2188a0c068e41caf686e8085c910439e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12579",
    "kind": "arxiv",
    "version": 1
  }
}