Pith Number

pith:USRHL3IW

pith:2026:USRHL3IWPJYIEWHBKGVGLS3YP4

not attested not anchored not stored refs pending

Regularity estimates in transport equations via heat flow and quantitative differentiation

Carl Johan Peter Johansson, Elia Bru\'e, Guido De Philippis, Maria Colombo

arxiv:2607.13751 v1 · 2026-07-15 · 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{USRHL3IWPJYIEWHBKGVGLS3YP4}

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.

Cited by

1 paper in Pith

Osgood meets Ambrosio-DiPerna-Lions

Receipt and verification

First computed	2026-07-16T01:23:04.203795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4a275ed167a708258e151aa65cb787f24229ef1a2c1dba786d9bae9e0890a4c

Aliases

arxiv: 2607.13751 · arxiv_version: 2607.13751v1 · doi: 10.48550/arxiv.2607.13751 · pith_short_12: USRHL3IWPJYI · pith_short_16: USRHL3IWPJYIEWHB · pith_short_8: USRHL3IW

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/USRHL3IWPJYIEWHBKGVGLS3YP4 \
  | 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: a4a275ed167a708258e151aa65cb787f24229ef1a2c1dba786d9bae9e0890a4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f813678680061d0c2dd5e1d21a82ddf224dc3486bc88e7f74ba0fd33f586a7cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-15T12:07:31Z",
    "title_canon_sha256": "34d65b70cb3ea3b0c7bab118a756a50b922132e364ee3bf4791242ac62e86550"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13751",
    "kind": "arxiv",
    "version": 1
  }
}