Pith Number

pith:TMM6PPWK

pith:2015:TMM6PPWKRLS4XUXCZM222IF6FB

not attested not anchored not stored refs pending

Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions

Katy Craig

arxiv:1512.07255 v1 · 2015-12-22 · 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{TMM6PPWKRLS4XUXCZM222IF6FB}

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	2026-05-18T00:45:08.492918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b19e7beca8ae5cbd2e2cb35ad20be287f9d904bba0ac5cf690e8cdccf978fd4

Aliases

arxiv: 1512.07255 · arxiv_version: 1512.07255v1 · doi: 10.48550/arxiv.1512.07255 · pith_short_12: TMM6PPWKRLS4 · pith_short_16: TMM6PPWKRLS4XUXC · pith_short_8: TMM6PPWK

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/TMM6PPWKRLS4XUXCZM222IF6FB \
  | 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: 9b19e7beca8ae5cbd2e2cb35ad20be287f9d904bba0ac5cf690e8cdccf978fd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f419a42ff54aeb0961f301354c8d0ff235704d1ae94ce82fde51c87994f0380",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-22T21:00:16Z",
    "title_canon_sha256": "b539e3e9315f1889da41d3e3c9cb9cf3d9afa9b99a25a3f955bb4cd46a281dc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07255",
    "kind": "arxiv",
    "version": 1
  }
}