Pith Number

pith:UCU2UHO4

pith:2011:UCU2UHO4RZ3HSAOR4ZU75W74MA

not attested not anchored not stored refs pending

Improved interpolation inequalities, relative entropy and fast diffusion equations

Giuseppe Toscani, Jean Dolbeault (CEREMADE)

arxiv:1110.5175 v2 · 2011-10-24 · 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{UCU2UHO4RZ3HSAOR4ZU75W74MA}

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	2026-05-18T03:51:23.720712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0a9aa1ddc8e767901d1e669fedbfc601b4fb2d4ccb2bdf4c3e43f15fc6cfd06

Aliases

arxiv: 1110.5175 · arxiv_version: 1110.5175v2 · doi: 10.48550/arxiv.1110.5175 · pith_short_12: UCU2UHO4RZ3H · pith_short_16: UCU2UHO4RZ3HSAOR · pith_short_8: UCU2UHO4

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/UCU2UHO4RZ3HSAOR4ZU75W74MA \
  | 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: a0a9aa1ddc8e767901d1e669fedbfc601b4fb2d4ccb2bdf4c3e43f15fc6cfd06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5fe639e03dac0133a37c68a490806739c39c6d71257a5450dd93b581b049893",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-10-24T09:34:56Z",
    "title_canon_sha256": "6e2ce250e3ee17c46dc6618576ea4f79cb7f0e2bc5cab7ccd6e2fc8707145da6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5175",
    "kind": "arxiv",
    "version": 2
  }
}