Pith Number

pith:6GC6JQLF

pith:2011:6GC6JQLFZ2EZVV6Y3HFQYALAIJ

not attested not anchored not stored refs pending

Self-improving properties for abstract Poincar\'e type inequalities

Frederic Bernicot (LPP), Jos\'e Maria Martell

arxiv:1107.2260 v2 · 2011-07-12 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6GC6JQLFZ2EZVV6Y3HFQYALAIJ}

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	2026-05-18T01:37:11.788033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f185e4c165ce899ad7d8d9cb0c0160426f39b8f716fce7266ddd925b2f2807af

Aliases

arxiv: 1107.2260 · arxiv_version: 1107.2260v2 · doi: 10.48550/arxiv.1107.2260 · pith_short_12: 6GC6JQLFZ2EZ · pith_short_16: 6GC6JQLFZ2EZVV6Y · pith_short_8: 6GC6JQLF

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/6GC6JQLFZ2EZVV6Y3HFQYALAIJ \
  | 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: f185e4c165ce899ad7d8d9cb0c0160426f39b8f716fce7266ddd925b2f2807af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e611f8bb500ebe3213e9a079d89b69c092631e007ddca22f97a9b630bd0839a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-07-12T12:19:40Z",
    "title_canon_sha256": "4f59d434bb0e9b523c8941e97fbfc25eb65f744e71622246ac6ea90bfb93a53f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2260",
    "kind": "arxiv",
    "version": 2
  }
}