Pith Number

pith:ZEEU6GRC

pith:2013:ZEEU6GRCKI3QQQXJQ5OIXYQL3E

not attested not anchored not stored refs pending

Sharp L^p-entropy inequalities on manifolds

Jurandir Ceccon, Marcos Montenegro

arxiv:1307.7115 v2 · 2013-07-26 · 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{ZEEU6GRCKI3QQQXJQ5OIXYQL3E}

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	2026-05-18T03:14:08.204648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9094f1a2252370842e9875c8be20bd93495ac80801842ca140d21fe32509550

Aliases

arxiv: 1307.7115 · arxiv_version: 1307.7115v2 · doi: 10.48550/arxiv.1307.7115 · pith_short_12: ZEEU6GRCKI3Q · pith_short_16: ZEEU6GRCKI3QQQXJ · pith_short_8: ZEEU6GRC

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/ZEEU6GRCKI3QQQXJQ5OIXYQL3E \
  | 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: c9094f1a2252370842e9875c8be20bd93495ac80801842ca140d21fe32509550

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75caa433078ef8ab6d524e611589fb8190e2dc1adc6ef6105eeba6cce3fd9e9a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-07-26T18:08:10Z",
    "title_canon_sha256": "239a82a1c0f279d0d161ea44299004e4af05553bf50f8938763163d3a16c6606"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.7115",
    "kind": "arxiv",
    "version": 2
  }
}