Pith Number

pith:CX2PNETP

pith:2015:CX2PNETPCJJYXJS7WVXYKFN6PL

not attested not anchored not stored refs pending

Upper bounds for parabolic equations and the Landau equation

Luis Silvestre

arxiv:1511.03248 v3 · 2015-11-10 · 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{CX2PNETPCJJYXJS7WVXYKFN6PL}

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

2 papers in Pith

On the monotonicity of the entropy production in the Landau-Maxwell equation

Propagation of chaos for the Boltzmann equation with very soft potentials

Receipt and verification

First computed	2026-05-18T01:08:26.210341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15f4f6926f12538ba65fb56f8515be7af246bae5968e367f4260200c4d513edf

Aliases

arxiv: 1511.03248 · arxiv_version: 1511.03248v3 · doi: 10.48550/arxiv.1511.03248 · pith_short_12: CX2PNETPCJJY · pith_short_16: CX2PNETPCJJYXJS7 · pith_short_8: CX2PNETP

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/CX2PNETPCJJYXJS7WVXYKFN6PL \
  | 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: 15f4f6926f12538ba65fb56f8515be7af246bae5968e367f4260200c4d513edf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6219d27ebe52082c9a1b72e061e19427ff7ded8b222a1fe127ec8a32c286a997",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-10T20:09:00Z",
    "title_canon_sha256": "1f7e89b0ce53857d1e27f2f0b5bbe9bd6b8754663c75b6c7cba8d71caa1338c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03248",
    "kind": "arxiv",
    "version": 3
  }
}