Pith Number

pith:7ZLDINLO

pith:2011:7ZLDINLOIGJW6FRNQ7SAPQK5HJ

not attested not anchored not stored refs pending

Trudinger-Moser inequalities on complete noncompact Riemannian manifolds

Yunyan Yang

arxiv:1112.0724 v1 · 2011-12-04 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ZLDINLOIGJW6FRNQ7SAPQK5HJ}

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	2026-05-18T04:07:05.800536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe5634356e41936f162d87e407c15d3a4f13c16059ea42155bb084983637cf17

Aliases

arxiv: 1112.0724 · arxiv_version: 1112.0724v1 · doi: 10.48550/arxiv.1112.0724 · pith_short_12: 7ZLDINLOIGJW · pith_short_16: 7ZLDINLOIGJW6FRN · pith_short_8: 7ZLDINLO

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/7ZLDINLOIGJW6FRNQ7SAPQK5HJ \
  | 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: fe5634356e41936f162d87e407c15d3a4f13c16059ea42155bb084983637cf17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80ae6296ef98784eacea7ddb87a04c02097bcd7fcd6147629861f3c14b1ff9b3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-04T06:17:05Z",
    "title_canon_sha256": "032c24a727b4b31908469b9757daf986f3b62b4220b676967e03e1db06cbf968"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0724",
    "kind": "arxiv",
    "version": 1
  }
}